Thermalisation

In physics, thermalisation (or thermalization) is the process of physical bodies reaching thermal equilibrium through mutual interaction. In general, the natural tendency of a system is towards a state of equipartition of energy and uniform temperature that maximizes the system's entropy. Thermalisation, thermal equilibrium, and temperature are therefore important fundamental concepts within statistical physics, statistical mechanics, and thermodynamics; all of which are a basis for many other specific fields of scientific understanding and engineering application.

Examples of thermalisation include:

• the achievement of equilibrium in a plasma. ^[1]
• the process undergone by high-energy neutrons as they lose energy by collision with a moderator. ^[2]
• the process of heat or phonon emission by charge carriers in a solar cell, after a photon that exceeds the semiconductor band gap energy is absorbed. ^[3]

The hypothesis, foundational to most introductory textbooks treating quantum statistical mechanics, ^[4] assumes that systems go to thermal equilibrium (thermalisation). The process of thermalisation erases local memory of the initial conditions. The eigenstate thermalisation hypothesis is a hypothesis about when quantum states will undergo thermalisation and why.

Not all quantum states undergo thermalisation. Some states have been discovered which do not (see below), and their reasons for not reaching thermal equilibrium are unclear as of March 2019 ^[update] .

Theoretical description

The process of equilibration can be described using the H-theorem or the relaxation theorem, ^[5] see also entropy production.

Systems resisting thermalisation

Classical systems

Broadly-speaking, classical systems with non-chaotic behavior will not thermalise. Systems with many interacting constituents are generally expected to be chaotic, but this assumption sometimes fails. A notable counter example is the Fermi–Pasta–Ulam–Tsingou problem, which displays unexpected recurrence and will only thermalise over very long time scales. ^[6] Non-chaotic systems which are pertubed by weak non-linearities will not thermalise for a set of initial conditions, with non-zero volume in the phase space, as stated by the KAM theorem, although the size of this set decreases exponentially with the number of degrees of freedom. ^[7] Many-body integrable systems, which have an extensive number of conserved quantities, will not thermalise in the usual sense, but will equilibrate according to a generalized Gibbs ensemble. ^{[8] [9]}

Quantum systems

Some such phenomena resisting the tendency to thermalize include (see, e.g., a quantum scar): ^[10]

• Conventional quantum scars, ^{[11] [12] [13] [14]} which refer to eigenstates with enhanced probability density along unstable periodic orbits much higher than one would intuitively predict from classical mechanics.
• Perturbation-induced quantum scarring: ^{[15] [16] [17] [18] [19]} despite the similarity in appearance to conventional scarring, these scars have a novel underlying mechanism stemming from the combined effect of nearly-degenerate states and spatially localized perturbations, ^{[15] [19]} and they can be employed to propagate quantum wave packets in a disordered quantum dot with high fidelity. ^[16]
• Many-body quantum scars.
• Many-body localisation (MBL), ^[20] quantum many-body systems retaining memory of their initial condition in local observables for arbitrary amounts of time. ^{[21] [22]}

Other systems that resist thermalisation and are better understood are quantum integrable systems ^[23] and systems with dynamical symmetries. ^[24]

References

1. "Collisions and Thermalization". sdphca.ucsd.edu. Retrieved 2018-05-14.
2. "NRC: Glossary -- Thermalization". www.nrc.gov. Retrieved 2018-05-14.
3. Andersson, Olof; Kemerink, Martijn (December 2020). "Enhancing Open-Circuit Voltage in Gradient Organic Solar Cells by Rectifying Thermalization Losses". Solar RRL. 4 (12): 2000400. doi: 10.1002/solr.202000400 . ISSN   2367-198X. S2CID   226343918.
4. Sakurai JJ. 1985. Modern Quantum Mechanics. Menlo Park, CA: Benjamin/Cummings
5. Reid, James C.; Evans, Denis J.; Searles, Debra J. (2012-01-11). "Communication: Beyond Boltzmann's H-theorem: Demonstration of the relaxation theorem for a non-monotonic approach to equilibrium" (PDF). The Journal of Chemical Physics. 136 (2): 021101. Bibcode:2012JChPh.136b1101R. doi:10.1063/1.3675847. hdl: 1885/16927 . ISSN   0021-9606. PMID   22260556.
6. Gallavotti, Giovanni, ed. (2008). The Fermi-Pasta-Ulam Problem - A Status Report. Lecture Notes in Physics. Vol. 728. Berlin, Heidelberg: Springer Berlin Heidelberg. doi:10.1007/978-3-540-72995-2. ISBN   978-3-540-72994-5.
7. Dumas, H. Scott (2014). The KAM Story – A Friendly Introduction to the Content, History, and Significance of Classical Kolmogorov–Arnold–Moser Theory. [Hackensack], New Jersey: World Scientific Publishing Company Incorporated. ISBN   978-981-4556-58-3.
8. Doyon, Benjamin; Hübner, Friedrich; Yoshimura, Takato (2024-06-17). "New Classical Integrable Systems from Generalized TT-Deformations". Physical Review Letters. 132 (25): 251602. arXiv: 2311.06369 . doi:10.1103/PhysRevLett.132.251602. ISSN   0031-9007. PMID   38996253.
9. Spohn, Herbert (2020). "Generalized Gibbs Ensembles of the Classical Toda Chain". Journal of Statistical Physics. 180 (1–6): 4–22. arXiv: 1902.07751 . doi:10.1007/s10955-019-02320-5. ISSN   0022-4715.
10. "Quantum Scarring Appears to Defy Universe's Push for Disorder". Quanta Magazine. March 20, 2019. Retrieved March 24, 2019.
11. Heller, Eric J. (1984-10-15). "Bound-State Eigenfunctions of Classically Chaotic Hamiltonian Systems: Scars of Periodic Orbits". Physical Review Letters. 53 (16): 1515–1518. Bibcode:1984PhRvL..53.1515H. doi:10.1103/PhysRevLett.53.1515.
12. Kaplan, L (1999-01-01). "Scars in quantum chaotic wavefunctions". Nonlinearity. 12 (2): R1 –R40. doi:10.1088/0951-7715/12/2/009. ISSN   0951-7715. S2CID   250793219.
13. Kaplan, L.; Heller, E. J. (1998-04-10). "Linear and Nonlinear Theory of Eigenfunction Scars". Annals of Physics. 264 (2): 171–206. arXiv: chao-dyn/9809011 . Bibcode:1998AnPhy.264..171K. doi:10.1006/aphy.1997.5773. ISSN   0003-4916. S2CID   120635994.
14. Heller, Eric (5 June 2018). The Semiclassical Way to Dynamics and Spectroscopy. Princeton University Press. ISBN   978-1-4008-9029-3. OCLC   1104876980.
15. Keski-Rahkonen, J.; Ruhanen, A.; Heller, E. J.; Räsänen, E. (2019-11-21). "Quantum Lissajous Scars". Physical Review Letters. 123 (21): 214101. arXiv: 1911.09729 . Bibcode:2019PhRvL.123u4101K. doi:10.1103/PhysRevLett.123.214101. PMID   31809168. S2CID   208248295.
16. Luukko, Perttu J. J.; Drury, Byron; Klales, Anna; Kaplan, Lev; Heller, Eric J.; Räsänen, Esa (2016-11-28). "Strong quantum scarring by local impurities". Scientific Reports. 6 (1): 37656. arXiv: 1511.04198 . Bibcode:2016NatSR...637656L. doi:10.1038/srep37656. ISSN   2045-2322. PMC   5124902 . PMID   27892510.
17. Keski-Rahkonen, J.; Luukko, P. J. J.; Kaplan, L.; Heller, E. J.; Räsänen, E. (2017-09-20). "Controllable quantum scars in semiconductor quantum dots". Physical Review B. 96 (9): 094204. arXiv: 1710.00585 . Bibcode:2017PhRvB..96i4204K. doi:10.1103/PhysRevB.96.094204. S2CID   119083672.
18. Keski-Rahkonen, J; Luukko, P J J; Åberg, S; Räsänen, E (2019-01-21). "Effects of scarring on quantum chaos in disordered quantum wells". Journal of Physics: Condensed Matter. 31 (10): 105301. arXiv: 1806.02598 . Bibcode:2019JPCM...31j5301K. doi:10.1088/1361-648x/aaf9fb. ISSN   0953-8984. PMID   30566927. S2CID   51693305.
19. Keski-Rahkonen, Joonas (2020). Quantum Chaos in Disordered Two-Dimensional Nanostructures. Tampere University. ISBN   978-952-03-1699-0.
20. Nandkishore, Rahul; Huse, David A.; Abanin, D. A.; Serbyn, M.; Papić, Z. (2015). "Many-Body Localization and Thermalization in Quantum Statistical Mechanics". Annual Review of Condensed Matter Physics. 6: 15–38. arXiv: 1404.0686 . Bibcode:2015ARCMP...6...15N. doi:10.1146/annurev-conmatphys-031214-014726. S2CID   118465889.
21. Choi, J.-y.; Hild, S.; Zeiher, J.; Schauss, P.; Rubio-Abadal, A.; Yefsah, T.; Khemani, V.; Huse, D. A.; Bloch, I.; Gross, C. (2016). "Exploring the many-body localization transition in two dimensions". Science. 352 (6293): 1547–1552. arXiv: 1604.04178 . Bibcode:2016Sci...352.1547C. doi:10.1126/science.aaf8834. PMID   27339981. S2CID   35012132.
22. Wei, Ken Xuan; Ramanathan, Chandrasekhar; Cappellaro, Paola (2018). "Exploring Localization in Nuclear Spin Chains". Physical Review Letters. 120 (7): 070501. arXiv: 1612.05249 . Bibcode:2018PhRvL.120g0501W. doi:10.1103/PhysRevLett.120.070501. PMID   29542978. S2CID   4005098.
23. Caux, Jean-Sébastien; Essler, Fabian H. L. (2013-06-18). "Time Evolution of Local Observables After Quenching to an Integrable Model". Physical Review Letters. 110 (25): 257203. arXiv: 1301.3806 . Bibcode:2013PhRvL.110y7203C. doi: 10.1103/PhysRevLett.110.257203 . PMID   23829756. S2CID   3549427.
24. Buča, Berislav; Tindall, Joseph; Jaksch, Dieter (2019-04-15). "Non-stationary coherent quantum many-body dynamics through dissipation". Nature Communications. 10 (1): 1730. arXiv: 1804.06744 . Bibcode:2019NatCo..10.1730B. doi:10.1038/s41467-019-09757-y. ISSN   2041-1723. PMC   6465298 . PMID   30988312.