Large deviations and dynamical phase transitions

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• Robert Jack (Bath)
• Thursday 19 January 2017, 13:45-15:00
• Theory Library.

If you have a question about this talk, please contact Mike Gunn.

In ergodic systems, observables that are integrated over long times \tau converge (almost surely) to their equilbrium values, as \tau tends to infinity. We use large deviation theory to investigate the (small) probability that such observables have non-typical values. We show that by restricting to particular (non-typical) values of the observable, unusual dynamical phase transitions can be observed, even in simple systems such as the classical one-dimensional Ising model [1]. These phase transitions are also related to quantum phase transitions, and can be analysed in operator or path-integral formalisms, although in some cases the relevant operators are non-Hermitian. We discuss the implications of these phase transitions for the classical models [2], including relationships with metastable states and optimal control theory [3].

[1] R. L. Jack and P. Sollich, Prog. Theor. Phys. Supp. 184, 304 (2010) [2] See for example L. O. Hedges, R. L. Jack, J. P. Garrahan and D. Chandler, Science 323, 1309 (2009). [3] R. L. Jack and P. Sollich, Eur. Phys. J.: Special Topics 224, 2351 (2015)

This talk is part of the Theoretical Physics Seminars series.

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