Nonequilibrium dynamics of a noisy quantum Ising chain: Statistics of work and prethermalization after a sudden quench of the transverse field

Abstract

We discuss the non-equilibrium dynamics of a Quantum Ising Chain (QIC) following a quantum quench of the transverse field and in the presence of a gaussian time dependent noise. We discuss the probability distribution of the work done on the system both for static and dynamic noise. While the effect of static noise is to smooth the low energy threshold of the statistic of the work, appearing for sudden quenches, a dynamical noise protocol affects also the spectral weight of such features. We also provide a detailed derivation of the kinetic equation for the Green's functions on the Keldysh contour and the time evolution of observables of physical interest, extending previously reported results (J. Marino, A. Silva, Phys. Rev. B 86, 060408 (2012)), and discussing the extension of the concept of prethermalization which can be used to study noisy quantum many body hamiltonians driven out-of-equilibrium.

Quench action and large deviations: Work statistics in the one-dimensional Bose gas

“…(44) has been defined with a rescaling by the system size L and not by the number of Bosons N as in Eq. (34). The two definitions are clearly equivalent since N = DL and the density D is assumed to be fixed.…”

“…In this respect, a natural quantity which can be investigated is the work done upon changing some of the system's parameters [26][27][28][29], as, e.g., in a quantum quench [30,31]. Crucially, its statistics has now proven to encode important information on the internal dynamics of the system [28,[32][33][34][35][36][37] and to display interesting features such as, most prominently, an emergent universal behavior [38], in quenches near a critical point [39][40][41]. Furthermore, the statistics of the work is a valuable tool for studying dynamical phase transitions [42][43][44] and for detecting them [42,43,45].…”

Overlap distributions for quantum quenches in the anisotropic Heisenberg chain

“…The work distribution is thus simply a continuous version of the distribution of squared overlaps, with the zero of the energy shifted by E i . The work statistics in non-equilibrium processes in various quantum many-body systems is a topic of much recent interest [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37]. Another quantity of wide current interest, closely related to the overlap distribution and work distribution, is the return probability,…”

Quench echo and work statistics in integrable quantum field theories

“…Study of the return amplitude in a finite system described by a Conformal Field Theory reveals that in a certain timeto-system-size limit the reduced density matrix of the system approaches exponentially a thermal one, as well as the complicate structure of quantum revivals [84]. The Loschmidt echo has been calculated in the context of quantum quench and related problems in several other studies relative to spin chains, conformal field theories and other models that are essentially equivalent to non-interacting ones [85][86][87][88][89][90][91][92][93][94][95][96][97][98][99].…”