IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v504y2018icp130-154.html
   My bibliography  Save this article

Aspects of non-equilibrium in classical and quantum systems: Slow relaxation and glasses, dynamical large deviations, quantum non-ergodicity, and open quantum dynamics

Author

Listed:
  • Garrahan, Juan P.

Abstract

In these four lectures I describe basic ideas and methods applicable to both classical and quantum systems displaying slow relaxation and non-equilibrium dynamics. The first half of these notes considers classical systems, and the second half, quantum systems. In Lecture 1, I briefly review the glass transition problem as a paradigm of slow relaxation and dynamical arrest in classical many-body systems. I discuss theoretical perspectives on how to think about glasses, and in particular how to model them in terms of kinetically constrained dynamics. In Lecture 2, I describe how via large deviation methods it is possible to define a statistical mechanics of trajectories which reveals the dynamical phase structure of systems with complex relaxation such as glasses. Lecture 3 is about closed (i.e. isolated) many-body quantum systems. I review thermalisation and many-body localisation, and consider the possibility of slow thermalisation and quantum non-ergodicity in the absence of disorder, thus connecting with some of the ideas of the first lecture. Lecture 4 is about open quantum systems, that is, quantum systems interacting with an environment. I review the description of open quantum dynamics within the Markovian approximation in terms of quantum master equations and stochastic quantum trajectories, and explain how to extend the dynamical large deviation method to study the statistical properties of ensembles of quantum jump trajectories. My overall aim is to draw analogies between classical and quantum non-equilibrium and find connections in the way we think about problems in these areas.

Suggested Citation

  • Garrahan, Juan P., 2018. "Aspects of non-equilibrium in classical and quantum systems: Slow relaxation and glasses, dynamical large deviations, quantum non-ergodicity, and open quantum dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 504(C), pages 130-154.
    • Handle: RePEc:eee:phsmap:v:504:y:2018:i:c:p:130-154
    DOI: 10.1016/j.physa.2017.12.149
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437117313985
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2017.12.149?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Marcos Rigol & Vanja Dunjko & Maxim Olshanii, 2008. "Thermalization and its mechanism for generic isolated quantum systems," Nature, Nature, vol. 452(7189), pages 854-858, April.
    2. Galit Shmueli & Thomas P. Minka & Joseph B. Kadane & Sharad Borle & Peter Boatwright, 2005. "A useful distribution for fitting discrete data: revival of the Conway–Maxwell–Poisson distribution," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(1), pages 127-142, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Matsuyama, Kazue, 2021. "Loss of ergodicity in a quantum hopping model of a dense many body system with repulsive interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 584(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gauss Cordeiro & Josemar Rodrigues & Mário Castro, 2012. "The exponential COM-Poisson distribution," Statistical Papers, Springer, vol. 53(3), pages 653-664, August.
    2. Mevin B. Hooten & Michael R. Schwob & Devin S. Johnson & Jacob S. Ivan, 2023. "Multistage hierarchical capture–recapture models," Environmetrics, John Wiley & Sons, Ltd., vol. 34(6), September.
    3. Can Zhou & Yan Jiao & Joan Browder, 2019. "How much do we know about seabird bycatch in pelagic longline fisheries? A simulation study on the potential bias caused by the usually unobserved portion of seabird bycatch," PLOS ONE, Public Library of Science, vol. 14(8), pages 1-19, August.
    4. Darcy Steeg Morris & Kimberly F. Sellers, 2022. "A Flexible Mixed Model for Clustered Count Data," Stats, MDPI, vol. 5(1), pages 1-18, January.
    5. Joseph B. Kadane & Ramayya Krishnan & Galit Shmueli, 2006. "A Data Disclosure Policy for Count Data Based on the COM-Poisson Distribution," Management Science, INFORMS, vol. 52(10), pages 1610-1617, October.
    6. Imelda Trejo & Nicolas W Hengartner, 2022. "A modified Susceptible-Infected-Recovered model for observed under-reported incidence data," PLOS ONE, Public Library of Science, vol. 17(2), pages 1-23, February.
    7. Fernando Bonassi & Rafael Stern & Cláudia Peixoto & Sergio Wechsler, 2015. "Exchangeability and the law of maturity," Theory and Decision, Springer, vol. 78(4), pages 603-615, April.
    8. Lord, Dominique & Mannering, Fred, 2010. "The statistical analysis of crash-frequency data: A review and assessment of methodological alternatives," Transportation Research Part A: Policy and Practice, Elsevier, vol. 44(5), pages 291-305, June.
    9. Dexter Cahoy & Elvira Di Nardo & Federico Polito, 2021. "Flexible models for overdispersed and underdispersed count data," Statistical Papers, Springer, vol. 62(6), pages 2969-2990, December.
    10. Krivitsky, Pavel N., 2017. "Using contrastive divergence to seed Monte Carlo MLE for exponential-family random graph models," Computational Statistics & Data Analysis, Elsevier, vol. 107(C), pages 149-161.
    11. Stefan Birnkammer & Alvise Bastianello & Michael Knap, 2022. "Prethermalization in one-dimensional quantum many-body systems with confinement," Nature Communications, Nature, vol. 13(1), pages 1-9, December.
    12. Robert E. Gaunt & Satish Iyengar & Adri B. Olde Daalhuis & Burcin Simsek, 2019. "An asymptotic expansion for the normalizing constant of the Conway–Maxwell–Poisson distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(1), pages 163-180, February.
    13. Subrata Chakraborty & S. H. Ong, 2017. "Mittag - Leffler function distribution - a new generalization of hyper-Poisson distribution," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-17, December.
    14. Sellers, Kimberly F. & Raim, Andrew, 2016. "A flexible zero-inflated model to address data dispersion," Computational Statistics & Data Analysis, Elsevier, vol. 99(C), pages 68-80.
    15. Kimberly F. Sellers & Andrew W. Swift & Kimberly S. Weems, 2017. "A flexible distribution class for count data," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-21, December.
    16. Aamir Saghir & Zhengyan Lin, 2014. "Control chart for monitoring multivariate COM-Poisson attributes," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(1), pages 200-214, January.
    17. Durga Bhaktavatsala Rao Dasari & Sen Yang & Arnab Chakrabarti & Amit Finkler & Gershon Kurizki & Jörg Wrachtrup, 2022. "Anti-Zeno purification of spin baths by quantum probe measurements," Nature Communications, Nature, vol. 13(1), pages 1-10, December.
    18. Zhou, Can & Jiao, Yan & Browder, Joan, 2019. "K-aggregated transformation of discrete distributions improves modeling count data with excess ones," Ecological Modelling, Elsevier, vol. 407(C), pages 1-1.
    19. Saralees Nadarajah, 2009. "Useful moment and CDF formulations for the COM–Poisson distribution," Statistical Papers, Springer, vol. 50(3), pages 617-622, June.
    20. Bilal Barakat, 2017. "Generalised count distributions for modelling parity," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 36(26), pages 745-758.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:504:y:2018:i:c:p:130-154. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.