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Dynamical freezing of relaxation to equilibrium
##manager.scheduler.building##: Edificio San Jose
##manager.scheduler.room##: Aula Magna
Date: 2019-07-10 06:30 PM – 06:45 PM
Last modified: 2019-06-13
Abstract
Slow processes in physics are typically related to the existence of high (free) energy barriers, which require strong fluctuations, or to nearly integrable regions in the phase space, which determine a slow onset of equipartition. In this talk [1] we intend to discuss a different mechanism, whose generality is an open question, leading to the dynamical freezing of relaxation in a discrete lattice. This phenomenon might occur when the appearance of intrinsic localized excitations is accompanied by a fast rotation which tend to decouple the breather from the lattice. We analyze this mechanism in the Discrete Nonlinear Schroedinger Equation (DNLSE), which models propagation in nonlinear discrete media with negligible dissipation (e.g., arrays of optical waveguides).
DNLSE is known to display a high energy (negative temperature) regime, where breathers spontaneously emerge but dynamics is almost frozen so that they do not coarsen to attain the equilibrium state characterized by one single breather sitting on top of a random background [2]. In addition of this, the fast rotation of breathers would naively produce a power-law relaxation [3] whilst dynamics is essentially blocked [4]. Our first result is that slow dynamics appear at positive temperatures as well if we study the relaxation of a tall breather. The second result is that slow relaxation is due to the presence of an adiabatic invariant, which freezes the dynamics. Consequently, relaxation proceeds via rare events, where energy is suddenly released towards the background. We conjecture that this exponentially slow relaxation is a key ingredient contributing to the non-ergodic behavior recently observed in the negative temperature region of the DNLSE [5].
[1] S. Iubini, L. Chirondojan, G.-L. Oppo, A. Politi, P. Politi, Phys. Rev. Lett. 122, 084102 (2019)
[2] B. Rumpf, Phys. Rev. E 69, 016618 (2004).
[3] S. Iubini, A. Politi, P. Politi, J. Stat. Mech. 073201 (2017)
[4] S. Iubini, R. Franzosi, R. Livi, G.-L. Oppo, and A. Politi, New Journal of Physics 15, 023032 (2013)
[5] T. Mithun, Y. Kati, C. Danieli, and S. Flach, Phys. Rev. Lett. 120, 184101 (2018)
DNLSE is known to display a high energy (negative temperature) regime, where breathers spontaneously emerge but dynamics is almost frozen so that they do not coarsen to attain the equilibrium state characterized by one single breather sitting on top of a random background [2]. In addition of this, the fast rotation of breathers would naively produce a power-law relaxation [3] whilst dynamics is essentially blocked [4]. Our first result is that slow dynamics appear at positive temperatures as well if we study the relaxation of a tall breather. The second result is that slow relaxation is due to the presence of an adiabatic invariant, which freezes the dynamics. Consequently, relaxation proceeds via rare events, where energy is suddenly released towards the background. We conjecture that this exponentially slow relaxation is a key ingredient contributing to the non-ergodic behavior recently observed in the negative temperature region of the DNLSE [5].
[1] S. Iubini, L. Chirondojan, G.-L. Oppo, A. Politi, P. Politi, Phys. Rev. Lett. 122, 084102 (2019)
[2] B. Rumpf, Phys. Rev. E 69, 016618 (2004).
[3] S. Iubini, A. Politi, P. Politi, J. Stat. Mech. 073201 (2017)
[4] S. Iubini, R. Franzosi, R. Livi, G.-L. Oppo, and A. Politi, New Journal of Physics 15, 023032 (2013)
[5] T. Mithun, Y. Kati, C. Danieli, and S. Flach, Phys. Rev. Lett. 120, 184101 (2018)