Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
134 tokens/sec
GPT-4o
9 tokens/sec
Gemini 2.5 Pro Pro
47 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

First Principles Numerical Demonstration of Emergent Decoherent Histories (2304.10258v4)

Published 20 Apr 2023 in quant-ph, cond-mat.stat-mech, and gr-qc

Abstract: Within the histories formalism the decoherence functional is a formal tool to investigate the emergence of classicality in isolated quantum systems, yet an explicit evaluation of it from first principles has not been reported. We provide such an evaluation for up to five-time histories based on exact numerical diagonalization of the Schr\"odinger equation. We find a robust emergence of decoherence for slow and coarse observables of a generic random matrix model and extract a finite size scaling law by varying the Hilbert space dimension over four orders of magnitude. Specifically, we conjecture and observe an exponential suppression of coherent effects as a function of the particle number of the system. This suggests a solution to the preferred basis problem of the many worlds interpretation (or the set selection problem of the histories formalism) within a minimal theoretical framework -- without relying on environmentally induced decoherence, quantum Darwinism, Markov approximations, low-entropy initial states or ensemble averages.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (131)
  1. H. Everett, “”Relative State” Formulation of Quantum Mechanics,” Rev. Mod. Phys. 29, 454–462 (1957).
  2. B. S. De Witt, “Quantum Mechanics and Reality,” Phys. Today 23, 30 (1970).
  3. L. Vaidman, “The Stanford Encyclopedia of Philosophy,”  (2021) Chap. Many-Worlds Interpretation of Quantum Mechanics, fall 2021 ed.
  4. B. Carr, ed., Universe or Multiverse? (Cambridge University Press, Cambridge, 2007).
  5. D. Wallace, The Emergent Multiverse: Quantum Theory According to the Everett Interpretation (Oxford University Press, Oxford, 2012).
  6. S. Carroll, “Solo: The Philosophy of the Multiverse,” Podcast at www.preposterousuniverse.com (2022).
  7. “Everything Everywhere All at Once,” Movie directed by D. Kwan and D. Scheinert (2022).
  8. N. Gisin, “The Multiverse Pandemic,” arXiv 2210.05377  (2022).
  9. M. Tegmark, ‘‘Parallel universes,” Sci. Am. 288, 40–51 (2003).
  10. K. Barad, Meeting the universe halfway: Quantum physics and the entanglement of matter and meaning (Duke University Press, 2007).
  11. R. B. Griffiths, “Consistent histories and the interpretation of quantum mechanics,” J. Stat. Phys. 36, 219–272 (1984).
  12. R. Omnès, “Consistent interpretations of quantum mechanics,” Rev. Mod. Phys. 64, 339–382 (1992).
  13. H. F. Dowker and J. J. Halliwell, “Quantum mechanics of history: The decoherence functional in quantum mechanics,” Phys. Rev. D 46, 1580–1609 (1992).
  14. M. Gell-Mann and J. B. Hartle, “Classical equations for quantum systems,” Phys. Rev. D 47, 3345–3382 (1993).
  15. J. J. Halliwell, “A Review of the Decoherent Histories Approach to Quantum Mechanics,” Ann. (N.Y.) Acad. Sci. 755, 726–740 (1995).
  16. F. Dowker and A. Kent, “On the consistent histories approach to quantum mechanics,” J. Stat. Phys. 82 (1996), 10.1007/BF02183396.
  17. R. B. Griffiths, Consistent Quantum Theory (Cambridge University Press, Cambridge, 2002).
  18. M. Gell-Mann and J. B. Hartle, “Quasiclassical coarse graining and thermodynamic entropy,” Phys. Rev. A 76, 022104 (2007).
  19. R. B. Griffiths, “The Stanford Encyclopedia of Philosophy,”  (2019) Chap. The Consistent Histories Approach to Quantum Mechanics, summer 2019 ed.
  20. J. P. Paz and W. H. Zurek, “Environment-induced decoherence, classicality, and consistency of quantum histories,” Phys. Rev. D 48, 2728–2738 (1993).
  21. F. Dowker and A. Kent, “Properties of Consistent Histories,” Phys. Rev. Lett. 75, 3038–3041 (1995).
  22. C. J. Riedel, W. H. Zurek,  and M. Zwolak, “Objective past of a quantum universe: Redundant records of consistent histories,” Phys. Rev. A 93, 032126 (2016).
  23. W. H. Zurek, “Decoherence, einselection, and the quantum origins of the classical,” Rev. Mod. Phys. 75, 715–775 (2003).
  24. M. Schlosshauer, “Quantum decoherence,” Phys. Rep. 831, 1–57 (2019).
  25. W. H. Zurek, “Quantum Darwinism,” Nature Phys. 5 (2009), doi.org/10.1038/nphys1202.
  26. W. H. Zurek, “Quantum Theory of the Classical: Einselection, Envariance, Quantum Darwinism and Extantons,” Entropy 24, 1520 (2022).
  27. J. Finkelstein, “Definition of decoherence,” Phys. Rev. D 47, 5430–5433 (1993).
  28. S. Saunders, “Decoherence, relative states, and evolutionary adaptation,” Found. Phys. 23, 1553–1585 (1993).
  29. L. Diósi, N Gisin, J. Halliwell,  and I. C. Percival, “Decoherent Histories and Quantum State Diffusion,” Phys. Rev. Lett. 74, 203–207 (1995).
  30. T. A. Brun, “Quantum Jumps as Decoherent Histories,” Phys. Rev. Lett. 78, 1833–1837 (1997).
  31. T. Yu, “Decoherence and localization in quantum two-level systems,” Physica A 248, 393–418 (1998).
  32. L. Vaidman, “On schizophrenic experiences of the neutron or why we should believe in the many‐worlds interpretation of quantum theory,” Int. Stud. Phil. Sci. 12, 245 (1998).
  33. T. A. Brun, “Continuous measurements, quantum trajectories, and decoherent histories,” Phys. Rev. A 61, 042107 (2000).
  34. A. Albrecht, R. Baunach,  and A. Arrasmith, “Einselection, equilibrium, and cosmology,” Phys. Rev. D 106, 123507 (2022).
  35. A. Touil, F. Anza, S. Deffner,  and J. P. Crutchfield, “Branching States as The Emergent Structure of a Quantum Universe,” arXiv: 2208.05497  (2022).
  36. P. Strasberg, “Classicality with(out) decoherence: Concepts, relation to Markovianity, and a random matrix theory approach,” SciPost Phys. 15, 024 (2023).
  37. F. A. Pollock, C. Rodríguez-Rosario, T. Frauenheim, M. Paternostro,  and K. Modi, “Operational Markov condition for quantum processes,” Phys. Rev. Lett. 120, 040405 (2018).
  38. L. Li, M. J. W. Hall,  and H. M. Wiseman, “Concepts of quantum non-Markovianity: A hierarchy,” Phys. Rep. 759, 1–51 (2018).
  39. S. Milz and K. Modi, “Quantum Stochastic Processes and Quantum non-Markovian Phenomena,” PRX Quantum 2, 030201 (2021).
  40. R. Dümcke, “Convergence of multitime correlation functions in the weak and singular coupling limits,” J. Math. Phys. 24, 311 (1983).
  41. G. W. Ford and R. F. O’Connell, “There is no quantum regression theorem,” Phys. Rev. Lett. 77, 798–801 (1996).
  42. P. Figueroa-Romero, K. Modi,  and F. A. Pollock, “Almost markovian processes from closed dynamics,” Quantum 3, 136 (2019).
  43. P. Figueroa-Romero, F. A. Pollock,  and K. Modi, “Markovianization with approximate unitary designs,” Commun. Phys. 4, 127 (2021).
  44. P. Strasberg, A. Winter, J. Gemmer,  and J. Wang, “Classicality, Markovianity, and local detailed balance from pure-state dynamics,” Phys. Rev. A 108, 012225 (2023).
  45. N. Van Kampen, “Quantum statistics of irreversible processes,” Physica 20, 603–622 (1954).
  46. T. A. Brun and J. J. Halliwell, “Decoherence of hydrodynamic histories: A simple spin model,” Phys. Rev. D 54, 2899–2912 (1996).
  47. J. J. Halliwell, “Decoherent histories and hydrodynamic equations,” Phys. Rev. D 58, 105015 (1998).
  48. J. J. Halliwell, “Decoherent Histories and the Emergent Classicality of Local Densities,” Phys. Rev. Lett. 83, 2481–2485 (1999a).
  49. E. A. Calzetta and B. L. Hu, “Influence action and decoherence of hydrodynamic modes,” Phys. Rev. D 59, 065018 (1999).
  50. J. J. Halliwell, “Decoherence of histories and hydrodynamic equations for a linear oscillator chain,” Phys. Rev. D 68, 025018 (2003).
  51. J. Halliwell, “Many Worlds? Everett, Quantum Theory, and Reality,”  (Oxford University Press, Oxford, 2010) Chap. Macroscopic Superpositions, Decoherent Histories, and the Emergence of Hydrodynamic Behaviour, pp. 99–118.
  52. N. G. van Kampen, B. DeWitt, S. Goldstein, J. Bricmont, R. B. Griffiths,  and R. Omnès, “Quantum Histories, Mysteries, and Measurements,” Phys. Today 53, 76 (2000).
  53. N. G. van Kampen, “The scandal of quantum mechanics,” Am. J. Phys. 76, 989 (2008).
  54. J. Gemmer and R. Steinigeweg, “Entropy increase in k𝑘kitalic_k-step Markovian and consistent dynamics of closed quantum systems,” Phys. Rev. E 89, 042113 (2014).
  55. D. Schmidtke and J. Gemmer, “Numerical evidence for approximate consistency and Markovianity of some quantum histories in a class of finite closed spin systems,” Phys. Rev. E 93, 012125 (2016).
  56. C. Nation and D. Porras, “Taking snapshots of a quantum thermalization process: Emergent classicality in quantum jump trajectories,” Phys. Rev. E 102, 042115 (2020).
  57. L. Diósi, “Anomalies of Weakened Decoherence Criteria for Quantum Histories,” Phys. Rev. Lett. 92, 170401 (2004).
  58. A. Smirne, D. Egloff, M. G. Díaz, M. B. Plenio,  and S. F. Hulega, “Coherence and non-classicality of quantum Markov processes,” Quantum Sci. Technol. 4, 01LT01 (2018).
  59. P. Strasberg and M. G. Díaz, “Classical quantum stochastic processes,” Phys. Rev. A 100, 022120 (2019).
  60. S. Milz, F. Sakuldee, F. A. Pollock,  and K. Modi, “Kolmogorov extension theorem for (quantum) causal modelling and general probabilistic theories,” Quantum 4, 255 (2020a).
  61. P. Strasberg, Quantum Stochastic Thermodynamics: Foundations and Selected Applications (Oxford University Press, Oxford, 2022).
  62. P. Szańkowski and Ł. Cywiński, “Objectivity of classical quantum stochastic processes,” arXiv: 2304.07110  (2023).
  63. C. Emary, N. Lambert,  and F. Nori, “Leggett-Garg inequalities,” Rep. Prog. Phys. 77, 039501 (2014).
  64. A. Albrecht, “Investigating decoherence in a simple system,” Phys. Rev. D 46, 5504–5520 (1992).
  65. J. J. Halliwell, “Somewhere in the universe: Where is the information stored when histories decohere?” Phys. Rev. D 60, 105031 (1999b).
  66. P. J. Dodd and J. J. Halliwell, “Decoherence and records for the case of a scattering environment,” Phys. Rev. D 67, 105018 (2003).
  67. J. B. Hartle, “Decoherent Histories Quantum Mechanics Starting with Records of What Happens,” arXiv 1608.04145  (2016).
  68. A. Schmid, “Repeated measurements on dissipative linear quantum systems,” Ann. Phys. 173, 103–148 (1987).
  69. J. J. Halliwell, “Approximate decoherence of histories and ’t Hooft’s deterministic quantum theory,” Phys. Rev. D 63, 085013 (2001).
  70. Y. Subaşı and B. L. Hu, “Quantum and classical fluctuation theorems from a decoherent histories, open-system analysis,” Phys. Rev. E 85, 011112 (2012).
  71. R. Omnès, “Logical reformulation of quantum mechanics. IV. Projectors in semiclassical physics.” J. Stat. Phys. 57, 357–382 (1989).
  72. M. M. Wilde, Quantum Information Theory, 2nd ed. (Cambridge University Press, Cambridge, 2019).
  73. M. Srednicki, “The approach to thermal equilibrium in quantized chaotic systems,” J. Phys. A 32, 1163–1175 (1999).
  74. J. M. Deutsch, “Eigenstate thermalization hypothesis,” Rep. Prog. Phys. 81, 082001 (2018).
  75. E. Wigner, “Random matrices in physics,” SIAM Reviews 9, 1–23 (1967).
  76. T. A. Brody, J. Flores, J. B. French, P. A. Mello, A. Pandey,  and S. S. M. Wong, “Random-matrix physics: spectrum and strength fluctuations,” Rev. Mod. Phys. 53, 385–479 (1981).
  77. J. M. Deutsch, “Quantum statistical mechanics in a closed system,” Phys. Rev. A 43, 2046–2049 (1991).
  78. C. W. J. Beenakker, “Random-matrix theory of quantum transport,” Rev. Mod. Phys. 69, 731–808 (1997).
  79. T. Guhr, Müller-Groeling A,  and H. A.Weidenmüller, “Random-matrix theories in quantum physics: common concepts,” Phys. Rep. 299, 189–425 (1998).
  80. F. Haake, Quantum Signatures of Chaos (Springer-Verlag, Berlin Heidelberg, 2010).
  81. P. Reimann and L. Dabelow, “Refining Deutsch’s approach to thermalization,” Phys. Rev. E 103, 022119 (2021).
  82. C. Bartsch, R. Steinigeweg,  and J. Gemmer, “Occurrence of exponential relaxation in closed quantum systems,” Phys. Rev. E 77, 011119 (2008).
  83. P. Strasberg and J. Schindler, “Shearing Off the Tree: Emerging Branch Structure and Born’s Rule in an Equilibrated Multiverse,” arXiv: 2310.06755  (2023).
  84. M. Srednicki, “Chaos and quantum thermalization,” Phys. Rev. E 50, 888–901 (1994).
  85. J. J. Halliwell, “Commuting position and momentum operators, exact decoherence, and emergent classicality,” Phys. Rev. A 72, 042109 (2005).
  86. M. B. Hastings, “Making Almost Commuting Matrices Commute,” Commun. Math. Phys. 291, 321 (2009).
  87. Y. Ogata, “Approximating macroscopic observables in quantum spin systems with commuting matrices,” J. Funct. Anal. 264, 2005–2033 (2013).
  88. N. Y. Halpern, P. Faist, J. Oppenheim,  and A. Winter, “Microcanonical and resource-theoretic derivations of the thermal state of a quantum system with noncommuting charges,” Nat. Comm. 7, 12051 (2016).
  89. A. Stokes and A. Nazir, “Gauge ambiguities imply Jaynes-Cummings physics remains valid in ultrastrong coupling QED,” Nat. Commun. 10, 499 (2019).
  90. A. Stokes and A. Nazir, “Implications of gauge freedom for nonrelativistic quantum electrodynamics,” Rev. Mod. Phys. 94, 045003 (2022).
  91. A. Kent, “Consistent Sets Yield Contrary Inferences in Quantum Theory,” Phys. Rev. Lett. 78, 2874–2877 (1997).
  92. R. B. Griffiths and J. B. Hartle, “Comment on “Consistent Sets Yield Contrary Inferences in Quantum Theory”,” Phys. Rev. Lett. 81, 1981–1981 (1998).
  93. A. Kent, “Kent Replies:,” Phys. Rev. Lett. 81, 1982–1982 (1998).
  94. R. Penrose, The Emperor’s New Mind (Oxford University Press, Oxford, 1989).
  95. J. L. Lebowitz, “Boltzmann’s Entropy and Time’s Arrow,” Phys. Today 46, 32 (1993).
  96. H. Price, Time’s Arrow and Archimedes’ Point (Oxford University Press, New York, 1996).
  97. H. Price, “Contemporary Debates in Philosophy of Science,”  (Blackwell, 2004) Chap. On the Origins of the Arrow of Time: Why there is Still a Puzzle about the Low-Entropy Past, pp. 219–239.
  98. C. Callender, “Contemporary Debates in Philosophy of Science,”  (Blackwell, 2004) Chap. There Is No Puzzle about the Low Entropy Past, pp. 240–255.
  99. J. B. Hartle and S. W. Hawking, “Wave function of the Universe,” Phys. Rev. D 28, 2960–2975 (1983).
  100. S.W. Hawking, “The quantum state of the universe,” Nucl. Phys. B 239, 257–276 (1984).
  101. F. J. Tipler, “Interpreting the wave function of the universe,” Phys. Rep. 137, 231–275 (1986a).
  102. V. Mukhanov, Physical Foundations of Cosmology (Cambridge University Press, Cambridge, 2005).
  103. J.-L. Lehners, “Review of the no-boundary wave function,” Phys. Rep. 1022, 1–82 (2023), review of the No-Boundary Wave Function.
  104. F. J. Tipler, “Quantum concepts of space and time,”  (Oxford University Press, New York, 1986) Chap. The many-worlds interpretation of quantum mechanics in quantum cosmology, pp. 1–204.
  105. I. E. Farquhar and P. T. Landsberg, “On the Quantum-Statistical Ergodic and H-Theorems,” Proc. R. Soc. Lond. A 239, 134–144 (1957).
  106. P. Bocchieri and A. Loinger, “Ergodic Theorem in Quantum Mechanics,” Phys. Rev. 111, 668–670 (1958).
  107. S. Popescu, A. J. Short,  and A. Winter, “Entanglement and the foundations of statistical mechanics,” Nat. Phys. 2, 754 – 758 (2006).
  108. A. Shimony, “Role of the Observer in Quantum Theory,” American Journal of Physics 31, 755–773 (1963).
  109. S. M. Carroll and J. Chen, “Spontaneous Inflation and the Origin of the Arrow of Time,” arXiv:hep-th/0410270  (2004).
  110. J. Barbour, T. Koslowski,  and F. Mercati, “Identification of a Gravitational Arrow of Time,” Phys. Rev. Lett. 113, 181101 (2014).
  111. J. M. Deutsch and A. Aguirre, “State-to-State Cosmology: A New View on the Cosmological Arrow of Time and the Past Hypothesis,” Found. Phys. 52, 82 (2022).
  112. Stephen M. Barnett, “Quantum retrodiction,” in Quantum Information and Coherence, edited by Erika Andersson and Patrik Öhberg (Springer International Publishing, Cham, 2014) pp. 1–30.
  113. A. Albrecht and L. Sorbo, “Can the universe afford inflation?” Phys. Rev. D 70, 063528 (2004).
  114. S. M. Carroll, “Current Controversies in Philosophy of Science ,”  (Routledge, New York, 2020) Chap. Why Boltzmann Brains Are Bad, p. 14.
  115. M. P. Müller, “Law without law: from observer states to physics via algorithmic information theory,” Quantum 4, 301 (2020).
  116. C. J. Isham, “Quantum logic and the histories approach to quantum theory,” J. Math. Phys. 35, 2157–2185 (1994), https://pubs.aip.org/aip/jmp/article-pdf/35/5/2157/8164052/2157_1_online.pdf .
  117. C. J. Isham and N. Linden, “Information entropy and the space of decoherence functions in generalized quantum theory,” Phys. Rev. A 55, 4030–4040 (1997).
  118. Y. Aharonov, P. G. Bergmann,  and J. L. Lebowitz, “Time Symmetry in the Quantum Process of Measurement,” Phys. Rev. 134, B1410–B1416 (1964).
  119. L. Vaidman, “Many Worlds? Everett, Quantum Theory, and Reality,”  (Oxford University Press, Oxford, 2010) Chap. Time Symmetry and the Many‐Worlds Interpretation, pp. 582–596.
  120. D. Deutsch, “Many Worlds? Everett, Quantum Theory, and Reality,”  (Oxford University Press, Oxford, 2010) Chap. Apart from Universes, pp. 542–552.
  121. S. Aaronson, Quantum Computing since Democritus (Cambridge University Press, Cambridge, 2013).
  122. L. He and W.-g. Wang, “Statistically preferred basis of an open quantum system: Its relation to the eigenbasis of a renormalized self-Hamiltonian,” Phys. Rev. E 89, 022125 (2014).
  123. E. Calzetta and J. J. Gonzalez, “Chaos and semiclassical limit in quantum cosmology,” Phys. Rev. D 51, 6821–6828 (1995).
  124. N. J. Cornish and E. P. S. Shellard, ‘‘Chaos in Quantum Cosmology,” Phys. Rev. Lett. 81, 3571–3574 (1998).
  125. E. Calzetta, “Chaos, decoherence and quantum cosmology,” Class. Quant. Grav. 29, 143001 (2012).
  126. J. Berjon, E. Okon,  and D. Sudarsky, “Critical review of prevailing explanations for the emergence of classicality in cosmology,” Phys. Rev. D 103, 043521 (2021).
  127. N. Dowling, P. Figueroa-Romero, F. A. Pollock, P. Strasberg,  and K. Modi, “Relaxation of Multitime Statistics in Quantum Systems,” Quantum 7, 1027 (2023a).
  128. A. Aguirre and M. Tegmark, “Born in an infinite universe: A cosmological interpretation of quantum mechanics,” Phys. Rev. D 84, 105002 (2011).
  129. L. Vaidman, “Derivations of the Born Rule,” in Quantum, Probability, Logic: The Work and Influence of Itamar Pitowsky, edited by M. Hemmo and O. Shenker (Springer International Publishing, Cham, 2020) Chap. Derivations of the Born Rule, pp. 567–584.
  130. A. Albrecht and D. Phillips, “Origin of probabilities and their application to the multiverse,” Phys. Rev. D 90, 123514 (2014).
  131. F. Del Santo and N. Gisin, “Physics without determinism: Alternative interpretations of classical physics,” Phys. Rev. A 100, 062107 (2019).
Citations (5)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now
X Twitter Logo Streamline Icon: https://streamlinehq.com

Tweets

Youtube Logo Streamline Icon: https://streamlinehq.com

YouTube