What about wave-particle duality? No equity (Analytical Review)
DOI (Low Temperature Physics):
https://doi.org/10.1063/10.0046875Ключові слова:
waves, particles, fields, wave-particle duality, quantum mechanics, quantum electrodynamics, electrons, photons, Cooper pairs, macroscopic quantum tunnelingАнотація
The problem of the so-called wave-particle duality in quantum mechanics is studied from the scientific and historical viewpoints. The evidence is given that quantum electrodynamics unambiguously dictates the field nature of matter at the micro-level rather than the particle-like structure. The “elementary particles” are wave-like disturbances (quanta) of the corresponding fields. The usage of the term “Cooper pairs” in superconductivity is analyzed and its limits are indicated. It is asserted that the Faraday–Einstein field concept is the true basis of all phenomena observed in the physical vacuum and the condensed media so that the alleged duality is simply a tribute to tradition. The comprehensive analysis carried out in the review was needed, although the author’s position is not new and was explicitly or implicitly expressed earlier by a number of leading scientists working in various branches of physics. Nevertheless, the conceptual failure of the obsolete duality is still not accepted in textbooks and popularizations making this situation detrimental to both education and research.
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1. L. N. Cooper, Phys. Rev. 104, 1189 (1956). https://doi.org/10.1103/PhysRev.104.1189
2. J. Bardeen, L. N. Cooper, and J. R. Schrieffer, Phys. Rev. 108, 1175 (1957). https://doi.org/10.1103/PhysRev.108.1175
3. V. L. Ginzburg, Usp. Fiz. Nauk 48, 25 (1952). https://doi.org/10.3367/UFNr.0048.195209b.0025
4. M. R. Schafroth, Phys. Rev. 100, 463 (1955). https://doi.org/10.1103/PhysRev.100.463
5. I. G. Kaplan, O. Navarro, and J. A. Sánchez, Physica C 419, 13 (2005). https://doi.org/10.1016/j.physc.2004.11.025
6. I. G. Kaplan, The Pauli Exclusion Principle. Origin, Verifications and Applications, (John Wiley and Sons, Chichester, 2017).
7. S. Giorgini, L. P. Pitaevskii, and S. Stringari, Rev. Mod. Phys. 80, 1215 (2008). https://doi.org/10.1103/RevModPhys.80.1215
8. Q. Chen, Z. Wang, R. Boyack, S. Yang, and K. Levin, Rev. Mod. Phys. 96, 025002 (2024). https://doi.org/10.1103/RevModPhys.96.025002
9. J. P. Carbotte, Rev. Mod. Phys. 62, 1027 (1990). https://doi.org/10.1103/RevModPhys.62.1027
10. M. de Llano and J. F. Annett, Int. J. Mod. Phys. B 21, 3657 (2007). https://doi.org/10.1142/S0217979207037661
11. A. M. Gabovich and V. I. Kuznetsov, Eur. J. Phys. 34, 371 (2013). https://doi.org/10.1088/0143-0807/34/2/371
12. E. Schrödinger, Phys. Rev. 28, 1049 (1926). https://doi.org/10.1103/PhysRev.28.1049
13. E. Schrödinger, Collected Papers on Wave Mechanics (Blackie and Son Ltd, London, 1928).
14. U. Essmann and H. Träuble, Sci. Amer. 224 (March), 74 (1971). https://doi.org/10.1038/scientificamerican0371-74
15. V. F. Weisskopf, Contemp. Phys. 22, 375 (1981). https://doi.org/10.1080/00107518108231541
16. K. K. Likharev and T. Claeson, Sci. Amer. 266 (June), 80 (1992).
17. D. L. Cox and M. B. Maple, Phys. Today 48 (February), 32 (1995). https://doi.org/10.1063/1.881443
18. J. R. Kirtley, Sci. Amer. 275 (August), 68 (1996). https://doi.org/10.1038/scientificamerican0896-68
19. A. Chubukov and P. J. Hirschfeld, Phys. Today 68 (June), 46 (2015). https://doi.org/10.1063/PT.3.2818
20. A. de Visser, Phys. Today 73 (November), 44 (2020). https://doi.org/10.1063/PT.3.4616
21. J. Clarke, Sci. Amer. 271 (August), 46 (1994). https://doi.org/10.1038/scientificamerican0894-46
22. C. C. W. Taylor, The Atomists: Leucippus and Democritus: Fragments (University of Toronto Press, Toronto, 1999).
23. I. Newton, The Principia: Mathematical Principles of Natural Philosophy (University of California Press, Oakland, California, 1999).
24. S. Chandrasekhar, Newton’s Principia for the Common Reader (Oxford University Press, Oxford, 1995).
25. A. M. Gabovich and V. I. Kuznetsov, Philosophy of Scientific Theories. Essay One: Names and Realities (Naukova Dumka, Kyiv, 2023) (in Ukrainian).
26. E. Mach, Popular Scientific Lectures (The Open Court Publishing, Chicago, 1894).
27. E. Mach, The Science of Mechanics: A Critical and Historical Account of its Development (The Open Court Publishing, Chicago, 1919).
28. G. E. Smith and R. Seth, Brownian Motion and Molecular Reality. A Study in Theory-Mediated Measurement (Oxford University Press, New York, 2020).
29. J. J. Thomson, Phil. Mag. 5, 293 (1897). https://doi.org/10.1080/14786449708621070
30. H. Helmholtz, J. Chem. Soc. Trans. 39, 277 (1881). https://doi.org/10.1039/CT8813900277
31. G. J. Stoney, Phil. Mag. 38, 418 (1894). https://doi.org/10.1080/14786449408620653
32. H. A. Lorentz, The Theory of Electrons and its Applications to the Phenomena of Light and Radiant Heat (Dover Phoenix Editions, New York, 2011).
33. N. Bohr, Phil. Mag. 26, 1 (1913). https://doi.org/10.1080/14786441308634955
34. N. Bohr, Phil. Mag. 26, 476 (1913). https://doi.org/10.1080/14786441308634993
35. H. G. J. Moseley, Phil. Mag. 26, 1024 (1913). https://doi.org/10.1080/14786441308635052
36. C. Davisson and L. H. Germer, Phys. Rev. 30, 705 (1927). https://doi.org/10.1103/PhysRev.30.705
37. G. P. Thomson and A. Reid, Nature 119, 890 (1927). https://doi.org/10.1038/119890a0
38. A. H. Compton, Phys. Rev. 21, 483 (1923). https://doi.org/10.1103/PhysRev.21.483
39. A. Einstein, Ann. der Phys. 322, 132 (1905). https://doi.org/10.1002/andp.19053220607
40. A. Einstein, Collected Papers, Vol. 2. The Swiss Years: Writings, 1900–1909 (Princeton University Press, Princeton, 1989).
41. L. T. Troland, J. Exp. Psychol. 11, 1 (1917). https://doi.org/10.1037/h0071652
42. G. N. Lewis, Nature 118, 874 (1926). https://doi.org/10.1038/118874a0
43. P. A. M. Dirac, Proc. Roy. Soc. A 114, 243 (1927).
44. P. A. M. Dirac, Proc. Roy. Soc. A 117, 610 (1928).
45. P. Jordan and W. Pauli, Z. Phys. 47, 151 (1928). https://doi.org/10.1007/BF02055793
46. W. Heisenberg and W. Pauli, Z. Phys. 56, 1 (1929). https://doi.org/10.1007/BF01340129
47. P. A. M. Dirac, Proc. Roy. Soc. A 126, 360 (1930).
48. P. A. M. Dirac, Math. Proc. Cambr. Philos. Soc. 26, 361 (1930). https://doi.org/10.1017/S0305004100016091
49. W. Heisenberg and W. Pauli, Z. Phys. 59, 168 (1930). https://doi.org/10.1007/BF01341423
50. E. Fermi, Rev. Mod. Phys. 4, 87 (1932). https://doi.org/10.1103/RevModPhys.4.87
51. V. B. Berestetskii, E. M. Lifshits, and L. P. Pitaevskii, Quantum Electrodynamics (Nauka, Moscow, 1989) (in Russian).
52. K. Hentschel, Photons: The History and Mental Models of Light Quanta (Springer, Cham, 2018).
53. L. D. Landau and E. M. Lifshits, Field Theory (Nauka, Moscow, 1988) (in Russian).
54. J. C. Maxwell, A Treatise on Electricity and Magnetism, Vol. 1, Unabridged 3rd ed. (Dover Publications, New York, 1954).
55. J. C. Maxwell, A Treatise on Electricity and Magnetism. Vol. 2, Unabridged 3rd ed. (Dover Publications, New York, 1954).
56. F. Rohrlich, Classical Charged Particles, 3rd ed. (World Scientific, Singapore, 2007).
57. A. Einstein, Ann. der Phys. 322, 639 (1905). https://doi.org/10.1002/andp.19053231314
58. L. B. Okun, Phys. Today 42 (June), 31 (1989). https://doi.org/10.1063/1.881171
59. L. B. Okun, Usp. Fiz. Nauk 158, 511 (1989) [Sov. Phys. Usp. 32, 629 (1989)]. https://doi.org/10.3367/UFNr.0158.198907f.0511
60. L. B. Okun, Energy and Mass in Relativity Theory (World Scientific, Singapore, 2009).
61. A. M. Gabovich and N. A. Gabovich, Eur. J. Phys. 28, 649 (2007). https://doi.org/10.1088/0143-0807/28/4/004
62. R. D. Cowan, The Theory of Atomic Structure and Spectra (University of California, Berkeley, 1981).
63. Yu. A. Berezhnoi, The Quantum World of Nuclear Physics (World Scientific, Singapore, 2005).
64. M. Abraham, Ann. der Phys. 315, 105 (1902). https://doi.org/10.1002/andp.19023150105
65. H. A. Lorentz, Proc. Roy. Acad. Amsterdam 6, 809 (1904).
66. H. A. Lorentz, Phenomena in a System Moving with any Velocity Smaller Than That of Light, edited by H. A. Lorentz (Collected Papers, Vol. V, Springer, Dordrecht, 1937), p. 172.
67. P. A. M. Dirac, Proc. Roy. Soc. A 167, 148 (1938).
68. J. Larmor, Phil. Mag. 44, 503 (1897). https://doi.org/10.1080/14786449708621095
69. L. D. Landau and E. M. Lifshits, The Classical Theory of Fields, Revised 2nd ed. (Pergamon Press, Oxford, 1962).
70. M. Planck, Ann. der Phys. 331, 1 (1908). https://doi.org/10.1002/andp.19083310602
71. L. B. Okun, Leptons and Quarks (North-Holland, Amsterdam, 1985).
72. J. Iliopoulos, The Origin of Mass: Elementary Particles and Fundamental Symmetries (Oxford University Press, Oxford, 2017).
73. J. Iliopoulos and T. N. Tomaras, Elementary Particle Physics: The Standard Theory (Oxford University Press, Oxford, 2021).
74. P. Innocenzi, What is an Electron? An Accessible Guide to its History, Theory, and Physical Properties (Springer, Cham, 2025).
75. N. Bohr, Science 111, 51 (1950). https://doi.org/10.1126/science.111.2873.51
76. A. Plotnitsky, Niels Bohr and Complementarity. An Introduction (Springer, New York, 2013).
77. A. Plotnitsky, The Principles of Quantum Theory, From Planck’s Quanta to the Higgs Boson: The Nature of Quantum Reality and the Spirit of Copenhagen (Springer, Cham, 2016).
78. D. Howard, Phil. Sci. 71, 669 (2004). https://doi.org/10.1086/425941
79. A. J. Leggett, J. Phys. Condens. Matter 14, R415 (2002). https://doi.org/10.1088/0953-8984/14/15/201
80. S. Weinberg, Third Thoughts (Harvard University Press, Harvard, 2018).
81. L. de Broglie, Phil. Mag. 47, 446 (1924). https://doi.org/10.1080/14786442408634378
82. L. de Broglie, Ann. Phys. 10, 22 (1925). https://doi.org/10.1051/anphys/192510030022
83. L. de Broglie, Research on the Theory of Quanta (Minkowski Institute Press, Montreal, 2021).
84. M. Born, The Mechanics of the Atom (G. Bell and Sons, London, 1927).
85. T. Young, Phil. Trans. R. Soc. Lond. 92, 12 (1802).
86. T. Young, Phil. Trans. R. Soc. Lond. 94, 1 (1804).
87. O. Donati, G. P. Missiroli, and G. Pozzi, Amer. J. Phys. 41, 639 (1973).
88. M. Arndt, O. Nairz, J. Vos-Andreae, C. Keller, G. van der Zouw, and A. Zeilinger, Nature 401, 680 (1999). https://doi.org/10.1038/44348
89. P. Guichard, A. Dochain, R. Marion, P. de Crombrugghe de Picquendaele, N. Lejeune, B. Hackens, P.-A. Hervieux, and X. Urbain, Phys. Rev. Lett. 135, 263403 (2025). https://doi.org/10.1103/wdx6-mrvm
90. L.-C. Tu, J. Luo, and G. T. Gillies, Rep. Prog. Phys. 68, 77 (2005). https://doi.org/10.1088/0034-4885/68/1/R02
91. O. Bisi, Visible and Invisible: The Wonders of Light Phenomena (Springer, Cham, 2015).
92. W. Heisenberg, Z. Phys. 33, 879 (1925). https://doi.org/10.1007/BF01328377
93. M. Born, P. Jordan, Z. Phys. 34, 858 (1925). https://doi.org/10.1007/BF01328531
94. M. Born, W. Heisenberg, and P. Jordan, Z. Phys. 35, 557 (1926). https://doi.org/10.1007/BF01379806
95. I. J. R. Aitchison, Contemp. Phys. 26, 333 (1985). https://doi.org/10.1080/00107518508219107
96. S. Weinberg, The Quantum Theory of Fields, Vol. 1, Foundations (Cambridge University Press, Cambridge, 1995).
97. S. Weinberg, The Quantum Theory of Fields, Vol. 2, Modern Applications (Cambridge University Press, Cambridge, 1996).
98. A. Zee, Quantum Field Theory in a Nutshell, 2nd ed. (Princeton University Press, Princeton, 2010).
99. A. Sommerfeld, Atomic Structure and Spectral Lines, Vol. 1 (E. P. Dutton and Company Inc., New York, 1934).
100. C. G. Darwin, Proc. Roy. Soc. A 124, 375 (1929).
101. D. L. Patey, J. Hist. Ideas 47, 139 (1986). https://doi.org/10.2307/2709600
102. A. Pais, Rev. Mod. Phys. 51, 863 (1979). https://doi.org/10.1103/RevModPhys.51.863
103. N. D. Mermin, Phys. Today 78 (January), 28 (2025). https://doi.org/10.1063/pt.hsjm.vbey
104. Z. Savitsky, Science 390, 978 (2025). https://doi.org/10.1126/science.aee3888
105. L. Pitaevskii, Phenomenology and microscopic theory: Theoretical foundations, in Superconductivity. Vol. 1: Conventional and Unconventional Superconductors, edited by K. H. Bennemann and J. B. Ketterson (Springer, Berlin, 2008), p. 27.
106. A. S. Alexandrov, Theory of Superconductivity: From Weak to Strong Coupling (IOP, Philadelphia, 2003).
107. J. E. Hirsch, Physica C 525–526, 44 (2016). https://doi.org/10.1016/j.physc.2016.03.020
108. J. E. Hirsch, Physica C 635, 1354747 (2025). https://doi.org/10.1016/j.physc.2025.1354747
109. A. V. Nikulov, Physica C 638, 1354791 (2025). https://doi.org/10.1016/j.physc.2025.1354791
110. H. L. Callendar, Proc. Phys. Soc. Lond. 23, 153 (1910). https://doi.org/10.1088/1478-7814/23/1/315
111. R. J. Morris, Brit. J. Hist. Sci. 6, 1 (1972). https://doi.org/10.1017/S000708740001195X
112. C. V. Fuchs and T. Filk, Physics 4, 920 (2022). https://doi.org/10.3390/physics4030060
113. V. L. Ginzburg and L. D. Landau, Zh. Eksp. Teor. Fiz. 20, 1064 (1950).
114. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge, 1995).
115. R. Loudon, The Quantum Theory of Light, 3rd ed. (Oxford University Press, New York, 2000).
116. The Nature of Light: What Is a Photon?, edited by C. Roychoudhuri, A. F. Kracklauer, and K. Creath (CRC Press, Boca Raton, 2008).
117. R. LaPierre, Getting Started in Quantum Optics (Springer, Cham, 2022).
118. A. Hobson, Fields and Their Quanta: Making Sense of Quantum Foundations (Springer, Cham, 2024).
119. M. Faraday, Phil. Trans. R. Soc. Lond. 142, 25 (1852).
120. W. Berkson, Fields of Force: The Development of a World View From Faraday to Einstein (Routledge, London,1974).
121. A. I. Akhiezer and S. V. Peletminskii, Theory of Fundamental Interactions (Naukova Dumka, Kyiv, 1993) (in Russian).
122. S. Weinberg, The Quantum Theory of Fields, Vol. 3, Supersymmetry (Cambridge University Press, Cambridge, 2000).
123. C. M. Will, Theory and Experiment in Gravitational Physics (Cambridge University Press, Cambridge, 2018).
124. S. Saunders, Analysis 66, 52 (2006). https://doi.org/10.1093/analys/66.1.52
125. C. Friebe, M. Kuhlmann, H. Lyre, P. M. Näger, O. Passon, and M. Stöckler, The Philosophy of Quantum Physics (Springer, Cham, 2018).
126. A. M. Gabovich and V. I. Kuznetsov, Stud. Hist. Philos. Sci. Technol. 34, 3 (2025).
127. B. Hanfstingl, C. Mitterer, and K. Abbas, Z. Psychol. 233, 261 (2025).
128. T. S. Kuhn, The Structure of Scientific Revolution (The University of Chicago Press, Chicago, 1996).
129. K. Shrader-Frechette, Phil. Sci. 44, 409 (1977). https://doi.org/10.1086/288757
130. R. E. Hendrick and A. Murphy, Phil. Sci. 48, 454 (1981). https://doi.org/10.1086/289010
131. V. L. Ginzburg, The Physics of a Lifetime: Reflections on the Problems and Personalities of 20th Century Physics (Springer, Berlin, 2001).
132. A. Krauss, Proc. Roy. Soc. A 480, 20240141 (2024). https://doi.org/10.1098/rspa.2024.0141
133. R. Kidd, J. Ardini, and A. Anton, Amer. J. Phys. 57, 27 (1989).
134. T. Arabatzis, Representing Electrons: A Biographical Approach to Theoretical Entities (The University of Chicago Press, Chicago, 2005).
135. H. Chang, Erkenn 75, 413 (2011). https://doi.org/10.1007/s10670-011-9340-9
136. A. Zajonc, Catching the Light (Oxford University Press, New York, 1995).
137. O. Passon, Physik in der Schule 63, 44 (2014).
138. J. Spałek, Stud. Hist. Scient. 19, 423 (2020). https://doi.org/10.4467/2543702XSHS.20.013.12569
139. M. Pizzochero, J. Gen. Philos. Sci. 56, 625 (2025). https://doi.org/10.1007/s10838-024-09714-4
140. A. I. Akhiezer and V. B. Berestetskii, Quantum Electrodynamics (Interscience Publishers, New York, 1965).
141. A. I. Akhiezer and V. B. Berestetskii, Quantum Electrodynamics (Nauka, Moscow, 1981) (in Russian).
142. I. Bialynicki-Birula, Photon wave function, in Progress in Optics, XXXVI, edited by E. Wolf (Elsevier, Amsterdam, 1996), p. 245.
143. I. Bialynicki-Birula and Z. Bialynicki-Birula, Phys. Rev. A 79, 032112 (2009). https://doi.org/10.1103/PhysRevA.79.032112
144. O. Passon, Physics 4, 880 (2022). https://doi.org/10.3390/physics4030057
145. D. Dragoman, Ann. NY Acad. Sci. 1549, 11 (2025). https://doi.org/10.1111/nyas.15378
146. I. Bialynicki-Birula, Phys. Rev. Lett. 80, 5247 (1998). https://doi.org/10.1103/PhysRevLett.80.5247
147. K. W. Chan, C. K. Law, and J. H. Eberly, Phys. Rev. Lett. 88, 100402 (2002). https://doi.org/10.1103/PhysRevLett.88.100402
148. P. Saari, M. Menert, and H. Valtna, Opt. Commun. 246, 445 (2005). https://doi.org/10.1016/j.optcom.2004.11.020
149. P. Saari, “Photon localization revisited,” in Quantum Optics and Laser Experiments, edited by S. Lyagushyn, (InTech, Rijeka, 2011), p. 49.
150. J. J. Thomson, J. Inst. Electr. Eng. 64, 721 (1926).
151. J. J. Thomson, Proc. R. Soc. Edinburgh 46, 90 (1927). https://doi.org/10.1017/S0370164600021933
152. O. Reiser, J. Philosoph. 25, 309 (1928). https://doi.org/10.2307/2014916
153. R. B. Lindsay, Sci. Monthly 26, 299 (1928).
154. E. U. Condon, Science 68, 193 (1928). https://doi.org/10.1126/science.68.1757.193
155. E. U. Condon and P. M. Morse, Quantum Mechanics (McGraw-Hill, New York, 1929).
156. A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777 (1935). https://doi.org/10.1103/PhysRev.47.777
157. J. S. Bell, Physics 1, 195 (1964). https://doi.org/10.1103/PhysicsPhysiqueFizika.1.195
158. D. J. Wineland, Rev. Mod. Phys. 85, 1103 (2013). https://doi.org/10.1103/RevModPhys.85.1103
159. S. Haroche, Rev. Mod. Phys. 85, 1083 (2013). https://doi.org/10.1103/RevModPhys.85.1083
160. A. J. Leggett, Annu. Rev. Condens. Matter Phys. 11, 1 (2020). https://doi.org/10.1146/annurev-conmatphys-031119-050704
161. H. Lüth, Quantum Physics in the Nanoworld: Schrödinger’s Cat and the Dwarfs (Springer, Berlin, 2013).
162. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).
163. W. Heisenberg, Z. Phys. 43, 172 (1927). https://doi.org/10.1007/BF01397280
164. L. D. Landau and E. M. Lifshits, Quantum Mechanics: Nonrelativistic Theory (Nauka, Moscow, 1989) (in Russian).
165. E. H. Kennard, Z. Phys. 44, 326 (1927). https://doi.org/10.1007/BF01391200
166. H. Weyl, The Theory of Groups and Quantum Mechanics (Dover Publications, New York, 1928).
167. L. E. Ballentine, Quantum Mechanics: A Modern Development, 2nd ed. (World Scientific, Singapore, 2015).
168. E. N. Economou, A Short Journey From Quarks to the Universe (Springer, Berlin, 2011).
169. A. I. M. Rae, Quantum Physics: A Beginner’s Guide (A One World Book, Oxford, 2005).
170. What is the Electron?, edited by V. Simulik (Apeiron, Montreal, 2005).
171. L. de la Peña, A. M. Cetto, and A. Valdés-Hernández, The Emerging Quantum: The Physics Behind Quantum Mechanics (Springer, Cham, 2015).
172. R. Dick, Advanced Quantum Mechanics: Materials and Photons (Springer, New York, 2012).
173. F. Bloch, Z. Phys. 52, 555 (1929).
174. L. D. Landau, Zh. Eksp. Teor. Fiz. 30, 1058 (1956) [Sov. Phys. JETP 3, 920 (1957)].
175. Google Scholar
176. M. I. Kaganov and I. M. Lifshits, Quasiparticles (Mir, Moscow, 1979).
177. J. Callaway, Quantum Theory of the Solid State (Academic Press, San Diego, 1991).
178. M. Imada, A. Fujimori, and Y. Tokura, Rev. Mod. Phys. 70, 1040 (1998). https://doi.org/10.1103/RevModPhys.70.1039
179. G. Kotliar, S. Y. Savrasov, K. Haule, V. S. Oudovenko, O. Parcollet, and C. A. Marianetti, Rev. Mod. Phys. 78, 865 (2006). https://doi.org/10.1103/RevModPhys.78.865
180. E. S. Corchero, Realistic Interpretation of Quantum Mechanics (Cambridge Scholars Publishing, Newcastle upon Tyne, 2022).
181. G. Viehhauser and T. Weidberg, Detectors in Particle Physics: A Modern Introduction, (CRC Press, Boca Raton, 2024).
182. C. T. R. Wilson, Proc. Roy. Soc. A 85, 285 (1911).
183. C. T. R. Wilson, Proc. Roy. Soc. A 87, 277 (1912).
184. M. Leone and N. Robotti, Eur. J. Phys. 25, 781 (2004). https://doi.org/10.1088/0143-0807/25/6/010
185. G. Gamow, Z. Phys. 51, 204 (1928). https://doi.org/10.1007/BF01343196
186. Google ScholarCrossref
187. G. Gamow, Nature 122, 805 (1928). https://doi.org/10.1038/122805b0
188. R. W. Gurney and E. U. Condon, Nature 122, 439 (1928). https://doi.org/10.1038/122439a0
189. R. W. Gurney and E. U. Condon, Phys. Rev. 33, 127 (1929). https://doi.org/10.1103/PhysRev.33.127
190. N. F. Mott, Proc. Roy. Soc. A 126, 79 (1929).
191. Yu. A. Berezhnoi, Lectures on Quantum Mechanics (Maister-Klas, Kyiv, 2008).
192. R. Figari and A. Teta, Arch. Hist. Exact Sci. 67, 215 (2013). https://doi.org/10.1007/s00407-012-0111-z
193. Ya. I. Frenkel, Usp. Fiz. Nauk 44, 110 (1951). https://doi.org/10.3367/UFNr.0044.195105j.0110
194. M. Born, Z. Phys. 38, 803 (1926). https://doi.org/10.1007/BF01397184
195. M. Schlosshauer, Decoherence and the Quantum-to-Classical Transition (Springer, Berlin, 2008).
196. J. Millen and B. A. Stickler, Contemp. Phys. 61, 155 (2020). https://doi.org/10.1080/00107514.2020.1854497
197. V. L. Ginzburg and L. P. Pitaevskii, Zh. Eksp. Teor. Fiz. 34, 1240 (1958) [Sov. Phys. JETP 7, 858 (1958)].
198. F. London, Superfluids. Vol. I. Macroscopic Theory of Superconductivity, 2nd Revised Edition with a new Epilogue “Theoretical Developments 1950–1960,” edited by M. J. Buckingham (Dover Publications, New York, 1961).
199. V. L. Ginzburg, Usp. Fiz. Nauk 167, 429 (1997) [Phys. Usp. 40, 407 (1997)]. https://doi.org/10.3367/UFNr.0167.199704f.0429
200. V. L. Ginzburg, On Superconductivity and Superfluidity: A Scientific Autobiography (Springer, Berlin, 2009).
201. L. D. Landau and E. M. Lifshits, Statistical Physics, Part 1 (Nauka, Moscow, 1976) (in Russian).
202. E. M. Lifshits and L. P. Pitaevskii, Statistical Physics, Part 2 (Nauka, Moscow, 1978) (in Russian).
203. A. J. Leggett, The order parameter as a macroscopic quantum wavefunction, in Connectivity and Superconductivity, edited by J. Berger and J. Rubinstein (Springer, Berlin, 2000), p. 230.
204. M. Planck, Ann. Phys. 309, 553 (1901). https://doi.org/10.1002/andp.19013090310
205. B. C. Reed, Quantum Mechanics: An Enhanced Primer, 2nd ed. (Springer, Cham, 2022).
206. P. A. M. Dirac, The Principles of Quantum Mechanics (Clarendon Press, Oxford, 1958).
207. R. P. Feynman, QED: the Strange Theory of Light and Matter (Princeton University Press, Princeton, 1985).
208. P. Jordan, Die Physik und das Geheimnis des Organischen Lebens (Friedr. Vieweg und Sohn, Braunschweig, 1941).
209. W. Heitler, The Quantum Theory of Radiation (Dover Publications, New York, 1954).
210. V. A. Fock, Selected Works: Quantum Mechanics and Quantum Field Theory (CRC Press, Boca Raton, 2004).
211. C. M. Caves and P. D. Drummond, Rev. Mod. Phys. 66, 481 (1994). https://doi.org/10.1103/RevModPhys.66.481
212. B. M. Garraway and K.-A. Suominen, Rep. Prog. Phys. 58, 365 (1995). https://doi.org/10.1088/0034-4885/58/4/001
213. B. Lounis and M. Orrit, Rep. Prog. Phys. 68, 1129 (2005). https://doi.org/10.1088/0034-4885/68/5/R04
214. B. J. Smith and M. G. Raymer, New J. Phys. 9, 414 (2007). https://doi.org/10.1088/1367-2630/9/11/414
215. H. P. Specht, J. Bochmann, M. Mücke, B. Weber, E. Figueroa, D. L. Moehring, and G. Rempe, Nat. Phot. 3, 469 (2009). https://doi.org/10.1038/nphoton.2009.115
216. R. J. Glauber, Phys. Rev. 131, 2766 (1963). https://doi.org/10.1103/PhysRev.131.2766
217. P. Carruthers and M. M. Nieto, Rev. Mod. Phys. 40, 411 (1968). https://doi.org/10.1103/RevModPhys.40.411
218. M. Sargent III, M. O. Scully, and W. E. Lamb, Jr., Laser Physics, Reading, Mass. (Addison-Wesley Publishing Company, 1974).
219. E. Schrödinger, Naturwissenschaften 14, 664 (1926). https://doi.org/10.1007/BF01507634
220. J. Clauser and M. Horne, Phys. Rev. D 9, 853 (1974). https://doi.org/10.1103/PhysRevD.9.853
221. M. D. Crisp and E. T. Jaynes, Phys. Rev. 179, 1253 (1969). https://doi.org/10.1103/PhysRev.179.1253
222. C. R. Stroud, Jr. and E. T. Jaynes, Phys. Rev. A 1, 106 (1970). https://doi.org/10.1103/PhysRevA.1.106
223. E. T. Jaynes, Survey of the present status of neoclassical radiation theory, in Coherence and Quantum Optics. Proceedings of the Third Rochester Conference on Coherence and Quantum Optics, edited by L. Mandel and E. Wolf (Plenum Press, New York, 1973), p. 35.
224. G. I. Taylor, Proc. Cambridge Philos. Soc. 15, 114 (1909).
225. P. Grangier, G. Roger, and A. Aspect, EPL 1, 173 (1986). https://doi.org/10.1209/0295-5075/1/4/004
226. Z.-Y. J. Ou, Multi-Photon Quantum Interference (Springer, New York, 2007).
227. H. Paul, Rev. Mod. Phys. 58, 209 (1986). https://doi.org/10.1103/RevModPhys.58.209
228. V. Weisskopf and E. Wigner, Z. Phys. 63, 54 (1930). https://doi.org/10.1007/BF01336768
229. V. Weisskopf and E. Wigner, Z. Phys. 65, 18 (1930). https://doi.org/10.1007/BF01397406
230. W. E. Lamb, Jr., Appl. Phys. B 60, 77 (1995). https://doi.org/10.1007/BF01135846
231. Ya. M. Gel’fer, V. L. Lyuboshitz, and M. I. Podgoretskii, Gibbs Paradox and Particle Identity in Quantum Mechanics (Nauka, Moscow, 1975) (in Russian).
232. R. J. Sciamanda, Amer. J. Phys. 37, 1128 (1969). https://doi.org/10.1119/1.1975229
233. J. C. Garrison and R. Y. Chiao, Quantum Optics (Oxford University Press, New York, 2008).
234. J. L. Bromberg, Arch. Hist. Exact Sci. 61, 243 (2016). https://doi.org/10.1007/s00407-015-0166-8
235. Y. Imry, Introduction to Mesoscopic Physics (Oxford University Press, Oxford,2002).
236. A. Bachtold, J. Moser, and M. I. Dykman, Rev. Mod. Phys. 94, 045005 (2022). https://doi.org/10.1103/RevModPhys.94.045005
237. A. J. Leggett, Contemp. Phys. 25, 583 (1984). https://doi.org/10.1080/00107518408210731
238. P. W. Anderson, Science 177, 393 (1972).
239. Y. Holovatch, R Kenna, and S. Thurner, Eur. J. Phys. 38, 023002 (2017). https://doi.org/10.1088/1361-6404/aa5a87
240. C. Henry, J.-P. Minier, and S. Brambilla, Phys. Rep. 1007, 1 (2023). https://doi.org/10.1016/j.physrep.2022.12.005
241. D. Dieks and A. Lubberdink, J. Gen. Philos. Sci. 53, 259 (2022). https://doi.org/10.1007/s10838-020-09510-w
242. L. B. Okun, Usp. Fiz. Nauk 170, 1366 (2000) [Phys. Usp. 43, 1270 (2000)]. https://doi.org/10.3367/UFNr.0170.200012j.1366
243. C. A. Bennett, Principles of Physical Optics, 2nd ed. (John Wiley and Sons, Hoboken, New York, 2022).
244. D. Pines, Elementary Excitations in Solids: Lectures on Protons, Electrons, and Plasmons (W. A. Benjamin, New York, 1963).
245. N. C. Lindquist, P. Nagpal, K. M. McPeak, D. J. Norris, and S.-H. Oh, Rep. Prog. Phys. 75, 036501 (2012). https://doi.org/10.1088/0034-4885/75/3/036501
246. S. K. Ghosh and T. Pal, Chem. Rev. 107, 4797 (2007). https://doi.org/10.1021/cr0680282
247. I. Chakraborty and T. Pradeep, Chem. Rev. 117, 8208 (2017). https://doi.org/10.1021/acs.chemrev.6b00769
248. W. Natanson, “On the statistical theory of radiation,” in Bulletin International de l’Académie des Sciences de Cracovie, Classe des Sciences mathématiques et naturelles. Série A: Sciences mathématiques/Anzeiger der Akademie der Wissenschaften in Krakau. Mathematisch-Naturwissenschaftliche Klasse. Reihe A: Mathematische Wissenschaften, Kraków (1911), p. 134.
249. W. Natanson, Zasady Teoryi Promieniowania (Wydawnictwo Redakcji Prac Matematyczno-Fizycznych, Warszawa, 1913).
250. P. Debye, Ann. Phys. 338, 1427 (1910). https://doi.org/10.1002/andp.19103381617
251. N. Nagasawa, Stud. Hist. Scient. 17, 391 (2018). https://doi.org/10.4467/2543702XSHS.18.014.9334
252. M. Kokowski, Stud. Hist. Scient. 18, 327 (2019). https://doi.org/10.4467/2543702XSHS.19.012.11018
253. S. Bose, Z. Phys. 26, 178 (1924). https://doi.org/10.1007/BF01327326
254. A. Einstein, Sitzungsber. Preuss. Akad. Wiss. 22, 261 (1924).
255. E. Schrödinger, Statistical Thermodynamics (Cambridge University Press, Cambridge, 1948).
256. E. Fermi, Collected Papers (Note e Memorie). Vol. I. Italy, 1921–1938 (The University of Chicago Press, Chicago, 1962).
257. P. A. M. Dirac, Proc. Roy. Soc. A 112, 661 (1926).
258. W. Pauli, Phys. Rev. 58, 716 (1940). https://doi.org/10.1103/PhysRev.58.716
259. W. Pauli, Prog. Theor. Phys. 5, 526 (1950). https://doi.org/10.1143/ptp/5.4.526
260. C. Santori, D. Fattal, J. Vucković, G. S. Solomon, and Y. Yamamoto, Nature 419, 594 (2002). https://doi.org/10.1038/nature01086
261. P. Bertet, A. Auffeves, P. Maioli, S. Osnaghi, T. Meunier, M. Brune, J. M. Raimond, and S. Haroche, Phys. Rev. Lett. 89, 200402 (2002). https://doi.org/10.1103/PhysRevLett.89.200402
262. H. G. Barros, A. Stute, T. E. Northup, C. Russo, P. O. Schmidt, and R. Blatt, New J. Phys. 11, 103004 (2009). https://doi.org/10.1088/1367-2630/11/10/103004
263. A. Kuhn and D. Ljunggren, Contemp. Phys. 51, 289 (2010). https://doi.org/10.1080/00107511003602990
264. L. de Broglie, J. Phys. Radium 8, 225 (1927). https://doi.org/10.1051/jphysrad:0192700805022500
265. D. Bohm, Phys. Rev. 85, 166 (1952). https://doi.org/10.1103/PhysRev.85.166
266. D. Bohm, Phys. Rev. 85, 180 (1952). https://doi.org/10.1103/PhysRev.85.180
267. M. Faraday, Phil. Mag. 3, 401 (1852). https://doi.org/10.1080/14786445208647033
268. M. Faraday, Phil. Mag. 13, 225 (1857). https://doi.org/10.1080/14786445708642290
269. Ya. I. Frenkel, Usp. Fiz. Nauk 42, 69 (1950). https://doi.org/10.3367/UFNr.0042.195009e.0069
270. E. Schrödinger, Sitzber. preuss. Akad. Wiss, Phys.-Math. Klasse 24, 418 (1930).
271. W. Greiner, Relativistic Quantum Mechanics: Wave Equations (Springer, Berlin, 2000).
272. H. P. Robertson, Phys. Rev. 34, 163 (1929). https://doi.org/10.1103/PhysRev.34.163
273. A. N. Tawfik and A. M. Diab, Rep. Prog. Phys. 78, 126001 (2015). https://doi.org/10.1088/0034-4885/78/12/126001
274. M. N. Bera, A. Acín, M. Kuś, M. W. Mitchell, and M. Lewenstein, Rep. Prog. Phys. 80, 124001 (2017). https://doi.org/10.1088/1361-6633/aa8731
275. A. M. Gabovich, V. I. Kuznetsov, and A. I. Voitenko, Low Temp. Phys. 50, 925 (2024) [Fiz. Nizk. Temp. 50, 1031 (2024)]. https://doi.org/10.1063/10.0030409
276. E. Rutherford, Phil. Mag. 21, 669 (1911). https://doi.org/10.1080/14786440508637080
277. E. Rutherford, Radioactive Substances and Their Radiations (Cambridge University Press, Cambridge, 1913).
278. M. Faraday, Experimental Researches in Electricity (J. M. Dent and Sons, London, 1922).
279. M. Jonson, Solid State Commun. 33, 743 (1980). https://doi.org/10.1016/0038-1098(80)90821-2
280. R. A. Young, Solid State Commun. 45, 263 (1983). https://doi.org/10.1016/0038-1098(83)90477-5
281. A. M. Gabovich, V. M. Rosenbaum, and A. I. Voitenko, Surf. Sci. 186, 523 (1987). https://doi.org/10.1016/S0039-6028(87)80392-8
282. P. Guéret, A. Baratoff, and E. Marclay, EPL 3, 367 (1987). https://doi.org/10.1209/0295-5075/3/3/019
283. D. V. Averin, Phys. Rev. B 50, 8934 (1994). https://doi.org/10.1103/PhysRevB.50.8934
284. U. S. Sainadh, R. T. Sang, and I. V. Litvinyuk, J. Phys. Photonics 2, 042002 (2020). https://doi.org/10.1088/2515-7647/aba009
285. Single Charge Tunneling: Coulomb Blockade Phenomena in Nanostructures, edited by H. Grabert and M. H. Devoret (Plenum Press, New York, 1992).
286. K. K. Likharev, Proc. IEEE 87, 606 (1999). https://doi.org/10.1109/5.752518
287. J. R. Waldram, Rep. Prog. Phys. 39, 751 (1976). https://doi.org/10.1088/0034-4885/39/8/002
288. K. K. Likharev, Rev. Mod. Phys. 51, 101 (1979). https://doi.org/10.1103/RevModPhys.51.101
289. Yu. Makhlin, G. Schön, and A. Shnirman, Rev. Mod. Phys. 73, 357 (2001). https://doi.org/10.1103/RevModPhys.73.357
290. J. von Delft and D. C. Ralph, Phys. Rep. 345, 61 (2001). https://doi.org/10.1016/S0370-1573(00)00099-5
291. A. A. Golubov, M. Yu. Kupriyanov, and E. Il’ichev, Rev. Mod. Phys. 76, 411 (2004). https://doi.org/10.1103/RevModPhys.76.411
292. Fundamentals and Frontiers of the Josephson Effect edited by, F. Tafuri (Springer, Cham, 2019).
293. R. Y. Chiao and A. M. Steinberg, “Tunneling times and superluminality,” in Progress in Optics, XXXVII, edited by E. Wolf (Elsevier, Amsterdam, 1997), p. 345.
294. V. S. Olkhovsky, E. Recami, and J. Jakiel, Phys. Rep. 398, 133 (2004). https://doi.org/10.1016/j.physrep.2004.06.001
295. V. S. Olkhovsky, Usp. Fiz. Nauk 181, 859 (2011) [Phys. Usp. 54, 829 (2011)]. https://doi.org/10.3367/UFNr.0181.201108d.0859
296. A. Hobson, Tales of the Quantum: Understanding Physics’ Most Fundamental Theory (Oxford University Press, Oxford, 2017).
297. S. Weinberg, Lectures on Quantum Mechanics (Cambridge University Press, Cambridge, 2012).
298. S. Weinberg, Facing Up: Science and Its Cultural Adversaries (Harvard University Press, Cambridge Massachusetts, 2001).
299. F. Wilczek, Phys. Today 52 (November), 11 (1999).
300. T. Banks, Quantum Mechanics: An Introduction (CRC Press, Boca Raton, 2018).
301. S. Bose, I. Fuentes, A. A. Geraci, S. M. Khan, S. Qvarfort, M. Rademacher, M. Rashid, M. Toroš, H. Ulbricht, and C. C. Wanjura, Rev. Mod. Phys. 97, 015003 (2025). https://doi.org/10.1103/RevModPhys.97.015003
302. D. W. Snoke, Interpreting Quantum Mechanics: Modern Foundations (Cambridge University Press, Cambridge, 2024).
303. M. Born, Z. Phys. 37, 863 (1926). https://doi.org/10.1007/BF01397477
304. O. Darrigol, Arch. Hist. Exact Sci. 58, 21 (2003) https://doi.org/10.1007/s00407-003-0070-5
305. P. Behroozi, K. Cordray, W. Griffin, and F. Behroozi, Amer. J. Phys. 75, 407 (2007). https://doi.org/10.1119/1.2710482
306. K. Y. Bliokh, Contemp. Phys. 65, 219 (2024). https://doi.org/10.1080/00107514.2025.2506860
307. R. L. Willett, Adv. Phys. 46, 447 (1997). https://doi.org/10.1080/00018739700101528
308. X.-L. Qi and S.-C. Zhang, Rev. Mod. Phys. 83, 1057 (2011). https://doi.org/10.1103/RevModPhys.83.1057
309. P. Wölfle, Rep. Prog. Phys. 81, 032501 (2018). https://doi.org/10.1088/1361-6633/aa9bc4
310. T. Giamarchi, Quantum Physics in One Dimension (Clarendon Press, Oxford, 2003).
311. B. Edegger, V. N. Muthukumar, and C. Gros, Adv. Phys. 56, 927 (2007). https://doi.org/10.1080/00018730701627707
312. D. M. Forrester, RSC Adv. 5, 5442 (2015). https://doi.org/10.1039/C4RA11227J
313. E. H. Lieb and R. Seiringer, The Stability of Matter in Quantum Mechanics (Cambridge University Press, Cambridge, 2009).
314. S. Blundell, Magnetism in Condensed Matter (Oxford University Press, Oxford, 2001).
315. Handbook of Magnetism and Magnetic Materials, edited by M. Coey and S. S. P. Parkin (Springer, Cham, 2021).
316. S. Chen, Y. Zhang, S. Koo, H. Tian, C. Yam, G. Chen, and M. A. Ratner, J. Phys. Chem. Lett. 5, 2748 (2014). https://doi.org/10.1021/jz5007143
317. O. Penrose and L. Onsager, Phys. Rev. 104, 576 (1956). https://doi.org/10.1103/PhysRev.104.576
318. C. N. Yang, Rev. Mod. Phys. 34, 694 (1962). https://doi.org/10.1103/RevModPhys.34.694
319. A. M. Gabovich, A. I. Voitenko, and M. Ausloos, Phys. Rep. 367, 583 (2002). https://doi.org/10.1016/S0370-1573(02)00029-7
320. L. P. Gor’kov, Zh. Eksp. Teor. Fiz. 34, 735 (1958) [Sov. Phys. JETP 7, 505 (1958)].
321. L. P. Gor’kov. Zh. Eksp. Teor. Fiz. 36, 1918 (1959) [Sov. Phys. JETP 9, 1364 (1959)].
322. M. Cyrot, Rep. Prog. Phys. 36, 103 (1973). https://doi.org/10.1088/0034-4885/36/2/001
323. V. V. Schmidt, Introduction to the Physics of Superconductors (MCCME, Moscow, 2000) (in Russian).
324. A. Damascelli, Z. Hussain, and Z.-X. Shen, Rev. Mod. Phys. 75, 473 (2003). https://doi.org/10.1103/RevModPhys.75.473
325. D. N. Basov and T. Timusk, Rev. Mod. Phys. 77, 721 (2005). https://doi.org/10.1103/RevModPhys.77.721
326. P. A. Lee, N. Nagaosa, and X.-G. Wen, Rev. Mod. Phys. 78, 17 (2006). https://doi.org/10.1103/RevModPhys.78.17
327. T. P. Devereaux and R. Hackl, Rev. Mod. Phys. 79, 175 (2007). https://doi.org/10.1103/RevModPhys.79.175
328. D. N. Basov, R. D. Averitt, D. van der Marel, M. Dressel, and K. Haule, Rev. Mod. Phys. 83, 471 (2011). https://doi.org/10.1103/RevModPhys.83.471
329. J. A. Sobota, Y. He, and Z.-X. Shen, Rev. Mod. Phys. 93, 025006 (2021). https://doi.org/10.1103/RevModPhys.93.025006
330. H. Won and K. Maki, Phys. Rev. B 49, 1397 (1994). https://doi.org/10.1103/PhysRevB.49.1397
331. C. C. Tsuei and J. R. Kirtley, Rev. Mod. Phys. 72, 969 (2000). https://doi.org/10.1103/RevModPhys.72.969
332. H. Hilgenkamp and J. Mannhart, Rev. Mod. Phys. 74, 485 (2002). https://doi.org/10.1103/RevModPhys.74.485
333. A. V. Balatsky, I. Vekhter, and J-X. Zhu, Rev. Mod. Phys. 78, 373 (2006). https://doi.org/10.1103/RevModPhys.78.373
334. L. Savary and L. Balents, Rep. Prog. Phys. 80, 016502 (2017). https://doi.org/10.1088/0034-4885/80/1/016502
335. M. Smidman, M. B. Salamon, H. Q. Yuan, and D. F. Agterberg, Rep. Prog. Phys. 80, 036501 (2017). https://doi.org/10.1088/1361-6633/80/3/036501
336. J. Linder and A. V. Balatsky, Rev. Mod. Phys. 91, 045005 (2019). https://doi.org/10.1103/RevModPhys.91.045005
337. S. K. Lewin, C. E. Frank, S. Ran, J. Paglione, and N. P. Butch, Rep. Prog. Phys. 86, 114501 (2023). https://doi.org/10.1088/1361-6633/acfb93
338. M. Smidman, O. Stockert, E. M. Nica, Y. Liu, H. Yuan, Q. Si, and F Steglich, Rev. Mod. Phys. 95, 031002 (2023). https://doi.org/10.1103/RevModPhys.95.031002
339. A. B. Pippard, Physica 19, 765 (1953). https://doi.org/10.1016/S0031-8914(53)80085-6
340. R. Holm and W. Meissner, Z. Phys. 74, 715 (1932). https://doi.org/10.1007/BF01340420
341. P. G. De Gennes, Superconductivity of Metals and Alloys (W. A. Benjamin, New York, 1966).
342. W. L. McMillan, Phys. Rev. 175, 537 (1968). https://doi.org/10.1103/PhysRev.175.537
343. W. L. McMillan, Phys. Rev. 175, 559 (1968). https://doi.org/10.1103/PhysRev.175.559
344. E. L. Wolf and G. B. Arnold, Phys. Rep. 91, 31 (1982). https://doi.org/10.1016/0370-1573(82)90061-8
345. G. Deutscher, Rev. Mod. Phys. 77, 109 (2005). https://doi.org/10.1103/RevModPhys.77.109
346. I. Giaever, Rev. Mod. Phys. 46, 245 (1974). https://doi.org/10.1103/RevModPhys.46.245
347. G. E. Blonder, M. Tinkham, and T. M. Klapwijk, Phys. Rev. B 25, 4515 (1982). https://doi.org/10.1103/PhysRevB.25.4515
348. B. D. Josephson, Phys. Lett. 1, 251 (1962). https://doi.org/10.1016/0031-9163(62)91369-0
349. I. O. Kulik and A. N. Omel’yanchuk, Sov. J. Low Temp. Phys. 3, 459 (1977) [Fiz. Nizk. Temp. 3, 945 (1977)]. https://doi.org/10.1063/10.0029534
350. I. O. Kulik and I. K. Yanson, Josephson Effect in Superconducting Tunnel Structures (Coronet, New York, 1971).
351. A. K. Jain, K. K. Likharev, J. E. Lukens, and J. E. Sauvageau, Phys. Rep. 109, 309 (1984). https://doi.org/10.1016/0370-1573(84)90002-4
352. K. K. Likharev, Dynamics of Josephson Junctions and Circuits (Gordon and Breach, New York, 1986).
353. A. V. Svidzinsky, Spatially-Nonhomogeneous Problems of the Superconductivity Theory (Nauka, Moscow, 1982) (in Russian).
354. A. V. Svidzinsky, Microscopic Theory of Superconductivity (Volyn’ State University, Luts’k, 2011) (in Ukrainian).
355. C. Kallin and J. Berlinsky, Rep. Prog. Phys. 79, 054502 (2016). https://doi.org/10.1088/0034-4885/79/5/054502
356. A. F. Andreev, Zh. Eksp. Teor. Fiz. 46, 1823 (1964) [Sov. Phys. JETP 19, 1228 (1964)].
357. D. Saint-James, J. Phys. (Paris) 25, 899 (1964). https://doi.org/10.1051/jphys:019640025010089900
358. S. Kashiwaya and Y. Tanaka, Rep. Prog. Phys. 63, 1641 (2000). https://doi.org/10.1088/0034-4885/63/10/202
359. T. Löfwander, V. S. Shumeiko, and G. Wendin, Supercond. Sci. Technol. 14, R53 (2001). https://doi.org/10.1088/0953-2048/14/5/201
360. C. T. Black, D. C. Ralph, and M. Tinkham, Phys. Rev. Lett. 76, 688 (1996). https://doi.org/10.1103/PhysRevLett.76.688
361. I. O. Kulik and R. I. Shekhter, Zh. Eksp. Teor. Fiz. 68, 623 (1975) [Sov. Phys. JETP 41, 308 (1975)].
362. K. A. Matveev, M. Gisselfalt, L. I. Glazman, M. Jonson, and R. I. Shekhter, Phys. Rev. Lett. 70, 2940 (1993). https://doi.org/10.1103/PhysRevLett.70.2940
363. T. A. Fulton, P. L. Gammel, D. J. Bishop, L. N. Dunkleberger, and G. J. Dolan, Phys. Rev. Lett. 63, 1307 (1989). https://doi.org/10.1103/PhysRevLett.63.1307
364. A. M. van den Brink, G. Schön, and L. J. Geerligs, Phys. Rev. Lett. 67, 3030 (1991). https://doi.org/10.1103/PhysRevLett.67.3030
365. D. C. Ralph, C. T. Black, and M. Tinkham, Phys. Rev. Lett. 78, 4087 (1997). https://doi.org/10.1103/PhysRevLett.78.4087
366. Yu. V. Nazarov and Ya. M. Blanter, Quantum Transport: Introduction to Nanoscience (Cambridge University Press, Cambridge, 2009).
367. A. Larkin and A. Varlamov, Theory of Fluctuations in Superconductors (Oxford University Press, New York, 2009).
368. L. J. Geerligs, V. F. Anderegg, J. Romijn, and J. E. Mooij, Phys. Rev. Lett. 65, 377 (1990). https://doi.org/10.1103/PhysRevLett.65.377
369. M. T. Tuominen, J. M. Hergenrother, T. S. Tighe, and M. Tinkham, Phys. Rev. Lett. 69, 1997 (1992). https://doi.org/10.1103/PhysRevLett.69.1997
370. D. J. van Woerkom, A. Geresdi, and L. P. Kouwenhoven, Nat. Phys. 11, 547 (2015). https://doi.org/10.1038/nphys3342
371. P. Aynajian, E. H. da Silva Neto, B. B. Zhou, S. Misra, R. E. Baumbach, Z. Fisk, J. Mydosh, J. D. Thompson, E. D. Bauer, and A. Yazdani, J. Phys. Soc. Jpn. 83, 061008 (2014). https://doi.org/10.7566/JPSJ.83.061008
372. K. Hasselbach, J. R. Kirtley, and P. Lejay, Phys. Rev. B 46, 5826 (1992). https://doi.org/10.1103/PhysRevB.46.5826
373. G. Deutscher and P. Nozières, Phys. Rev. B 50, 13557 (1994). https://doi.org/10.1103/PhysRevB.50.13557
374. A. J. Leggett, Prog. Theor. Phys. Suppl. N 69, 80 (1980). https://doi.org/10.1143/PTPS.69.80
375. J. Clarke, A. N. Clelland, M. H. Devoret, D. Esteve, and J. M. Martinis, Science 239, 992 (1988). https://doi.org/10.1126/science.239.4843.992
376. Yu. M. Ivanchenko and L. A. Zil’berman, Zh. Eksp. Teor. Fiz. 55, 2395 (1968) [Sov. Phys. JETP 28, 1272 (1969)].
377. A. O. Caldeira and A. J. Leggett, Phys. Rev. Lett. 46, 211 (1981). https://doi.org/10.1103/PhysRevLett.46.211
378. K. K. Likharev, Physica B 108, 1079 (1981). https://doi.org/10.1016/0378-4363(81)90843-3
379. A. J. Leggett, “Quantum tunnelling of a macroscopic variable,” in Quantum Tunnelling in Condensed Media, edited by, Yu. M. Kagan and A. J. Leggett, (North-Holland, Amsterdam, 1992), p. 1.
380. D. Massarotti, L. Longobardi, L. Galletti, D. Stornaiuolo, D. Montemurro, G. Pepe, G. Rotoli, A. Barone, and F. Tafuri, Low Temp. Phys. 38, 263 (2012) [Fiz. Nizk. Temp. 38, 336 (2012)]. https://doi.org/10.1063/1.3699625
381. M. R. Ebert, D. C. Ohnmacht, W. Belzig, and J. C. Cuevas, Phys. Rev. B 112, 195430 (2025). https://doi.org/10.1103/phvj-vfnx
382. D. Massarotti and F. Tafuri, “Current-Voltage characteristics,” in Fundamentals and Frontiers of the Josephson Effect, edited by F. Tafuri (Springer, Cham, 2019), p. 235.
383. D. E. McCumber, J. Appl. Phys. 39, 3113 (1968). https://doi.org/10.1063/1.1656743
384. W. C. Stewart, Appl. Phys. Lett. 12, 277 (1968). https://doi.org/10.1063/1.1651991
385. H. A. Kramers, Physica 7, 284 (1940). https://doi.org/10.1016/S0031-8914(40)90098-2
386. M. Büttiker, E. P. Harris, and R. Landauer, Phys. Rev. B 28, 1268 (1983). https://doi.org/10.1103/PhysRevB.28.1268
387. P. Hänggi, P. Talkner, and M. Borkovec, Rev. Mod. Phys. 62, 251 (1990). https://doi.org/10.1103/RevModPhys.62.251
388. V. I. Mel’nikov, Phys. Rep. 209, 1 (1991). https://doi.org/10.1016/0370-1573(91)90108-X
389. A. I. Larkin and Yu. N. Ovchinnikov, Pis’ma Zh. Éksp. Teor. Fiz. 37, 322 (1983) [JETP Lett. 37, 382 (1983)].
390. H. Grabert and U. Weiss, Phys. Rev. Lett. 53, 1787 (1984). https://doi.org/10.1103/PhysRevLett.53.1787
391. A. O. Caldeira and A. J. Leggett, Ann. Phys. 149, 374 (1983). https://doi.org/10.1016/0003-4916(83)90202-6
392. K. K. Likharev, Usp. Fiz. Nauk 139, 169 (1983) [Sov. Phys. Usp. 26, 87 (1983)]. https://doi.org/10.3367/UFNr.0139.198301g.0169
393. I. M. Dmitrenko, V. A. Khlus, G. M. Tsoi, and V. I. Shnyrkov, Sov. J. Low Temp. Phys. 11, 77 (1985) [Fiz. Nizk. Temp. 11, 146 (1985)]. https://doi.org/10.1063/10.0031246
394. W. Den Boer and R. de Bruyn Ouboter, Physica B 98, 185 (1980). https://doi.org/10.1016/0378-4363(80)90075-3
395. D. Massarotti and F. Tafuri, “Phase dynamics and macroscopic quantum tunneling,” in Fundamentals and Frontiers of the Josephson Effect, edited by, F. Tafuri (Springer, Cham, 2019), p. 455.
396. J. M. Martinis, M. H. Devoret, and J. Clarke, Nat. Phys. 16, 234 (2020). https://doi.org/10.1038/s41567-020-0829-5
397. R. F. Voss and R. A. Webb, Phys. Rev. Lett. 47, 265 (1981). https://doi.org/10.1103/PhysRevLett.47.265
398. L. D. Jackel, J. P. Gordon, E. L. Hu, H. E. Howard, L. A. Fetter, D. M. Tennant, H. W. Epworth, and J. Kurkijärvi, Phys. Rev. Lett. 47, 697 (1981). https://doi.org/10.1103/PhysRevLett.47.697
399. R. H. Koch, D. J. Van Harlingen, and J. Clarke, Phys. Rev. Lett. 47, 1216 (1981). https://doi.org/10.1103/PhysRevLett.47.1216
400. I. M. Dmitrenko, G. M. Tsoi, and V. I. Shnyrkov, Sov. J. Low Temp. Phys. 8, 330 (1982) [Fiz. Nizk. Temp. 8, 660 (1982)]. https://doi.org/10.1063/10.0030726
401. J. M. Martinis, M. H. Devoret, and J. Clarke, Phys. Rev. Lett. 55, 1543 (1985). https://doi.org/10.1103/PhysRevLett.55.1543
402. S. Washburn, R. A. Webb, R. F. Voss, and S. M. Faris, Phys. Rev. Lett. 54, 2712 (1985). https://doi.org/10.1103/PhysRevLett.54.2712
403. D. B. Schwartz, B. Sen, C. N. Archie, and J. E. Lukens, Phys. Rev. Lett. 55, 1547 (1985). https://doi.org/10.1103/PhysRevLett.55.1547
404. M. H. Devoret, J. M. Martinis, and J. Clarke, Phys. Rev. Lett. 55, 1908 (1985). https://doi.org/10.1103/PhysRevLett.55.1908
405. J. M. Martinis, M. H. Devoret, and J. Clarke, Phys. Rev. B 35, 4682 (1987). https://doi.org/10.1103/PhysRevB.35.4682
406. O. G. Turutanov, Low Temp. Phys. 51, 1522 (2025) [Fiz. Nizk. Temp. 51, 1685 (2025)]. https://doi.org/10.1063/10.0039961
407. H. F. Olson, Dynamical Analogies (D. Van Nostrand, Inc, New York, 1944).
408. E. P. Pokatilov, M. D. Croitoru, V. M. Fomin, and J. T. Devreese, Phys. Status Solidi B 237, 244 (2003). https://doi.org/10.1002/pssb.200301785
409. A. Einstein, Collected Papers, Vol. 6. The Berlin Years: Writings, 1914–1917 (Princeton University Press, Princeton, 1997).
410. M. Beller, Phys. Today 51 (September), 29 (1998). https://doi.org/10.1063/1.882436
411. H. Chang, Centaurus 51, 239 (2009). https://doi.org/10.1111/j.1600-0498.2009.00150.x
412. B. W. Harrer, Amer. J. Phys. 85, 454 (2017). https://doi.org/10.1119/1.4979538
413. R. D. Johnson-Sheehan, J. Techn. Writing Commun. 27, 177 (1997). https://doi.org/10.2190/LXWH-UXTL-2BBT-PRM5
414. A. Kojevnikov, Hist. Stud. Phys. Biol. Sci. 44, 295 (1999).
415. H. Pulaczewska, Aspects of Metaphor in Physics (Max Niemeyer, Tübingen, 1999).
416. E. Leane, Rev. Engl. Stud. 52, 411 (2001). https://doi.org/10.1093/res/52.207.411
417. F. Corni, H. U. Fuchs, and E. Dumont, J. Phys. Conf. Ser. 1286, 012059 (2019). https://doi.org/10.1088/1742-6596/1286/1/012059
418. R. P. Crease, Phys. World 38 (September), 17 (2025).