Quantum quench in matrix models: dynamical phase transitions, selective equilibration and the Generalized Gibbs Ensemble

Abstract

Quantum quench dynamics is considered in a one dimensional unitary matrix model with a single trace potential. This model is integrable and has been studied in the context of noncritical string theory. We find dynamical phase transitions, and study the role of the quantum critical point. In course of the time evolutions, we find evidence of selective equilibration for a certain class of observables. The equilibrium is governed by the Generalized Gibbs Ensemble (GGE) and differs from the standard Gibbs ensemble. We compute the production of entropy which is O(N) for large N matrices. An important feature of the equilibration is the appearance of an energy cascade, reminiscent of the Richardson cascade in turbulence, where we find flow of energy from initial long wavelength modes to progressively shorter wavelength excitations. We discuss possible implication of the equilibration and of GGE in string theories and higher spin theories. In another related study, we compute time evolutions in a double trace unitary matrix model, which arises as an effective theory of D2 branes in IIA string theory in the confinement phase. We find similar equilibrations and dynamical transitions in this matrix model. The dynamical transitions are related to Gregory-Laflamme transitions in string theory and are potentially connected with the issue of appearance of naked singularities.

Quantum quench and thermalization of one-dimensional Fermi gas via phase-space hydrodynamics

“…Fully exact time-dependence and subsequent results on thermalization were obtained for free scalars and Fermions in 1+1 dimensions for mass quenches ending at zero mass in [14].In this paper, we will discuss quantum quench in a free Fermi gas in one space dimension, by using a large-N technique 4 . This subject was dealt with earlier in a paper [17] by two of the present authors, where it was shown how moments of the Fermion density approached thermalization from particular sudden quenches. Apart from studies of thermalization, several other dynamical aspects, such as the onset of shock fronts, have been studied in large-N non-interacting as well as interacting Fermi gases [18,19,20,21,22] (see also the Appendix A) ; finite-N corrections have been studied in [23].The importance of the large-N limit is that the Fermions are described by a semiclassical fluid in the phase space.…”

“…where we have used (17). Since the second terms would be suppressed at large t through the p integral due to the oscillation, we would obtain…”

“…Thus, it is tempting to think that thermalization can be understood somehow in terms of the equations of conventional hydrodynamics, which would be of significant interest. However, conventional hydrodynamics of the Fermions typically breaks down way before we reach asymptotic times because of formation of shock fronts [17,18,19,20,21,23]. (See Figure 9 also.)…”

Bell violation in the sky

“…See Refs. [59][60][61][62][63][64][65][66] for more details in this direction. In this context we are interested in this specific type of mass parametrization as the corresponding equivalent version of Schrödinger quantum mechanical problem can easily solvable.…”

“…In the standard WKB approximation the total solution can be recast in the following form: 66) where D 1 and D 2 are two arbitrary integration constants, which depend on the choice of the initial condition during WKB approximation at early and late time scale. In the present context u k (η) andū k (η) are defined as…”