Eigenstate thermalization for observables that break Hamiltonian symmetries and its counterpart in interacting integrable systems

Many-Body Localization Dynamics from Gauge Invariance

“…Since the number of matrix elements is very large even at small system sizes, we and observables in the infinite temperature regime [165,134,166,167,19]. Most interestingly, Gaussianity of the off-diagonal matrix elements has now started to be considered an identifier of quantum chaos [32,134,167,19].…”

“…In all instances, the statistical matrix appears to have some common features. The matrix elements R nm at a given energy Ē and frequency ω obey Gaussian statistics [165,134,166,32,167,19], in contrast with non-ergodic systems [195][196][197].…”

Eigenstate thermalization in dual-unitary quantum circuits: Asymptotics of spectral functions

“…These questions are interrelated and have been investigated in many studies with most of them focusing on the Hamiltonian (continuous-time) case rather than Floquet systems. For instance, the distribution of both diagonal and off-diagonal matrix elements has been confirmed to be generically well described by a Gaussian distribution in the quantum ergodic (or quantum chaotic) regime, whose variance decreases exponentially when increasing the system size [20][21][22][23][24][25][26][27][28][29]. For these distributions the ratio of the variance of diagonal and off-diagonal matrix elements agrees with random matrix predictions [22,23,29,30].…”

“…For instance, the distribution of both diagonal and off-diagonal matrix elements has been confirmed to be generically well described by a Gaussian distribution in the quantum ergodic (or quantum chaotic) regime, whose variance decreases exponentially when increasing the system size [20][21][22][23][24][25][26][27][28][29]. For these distributions the ratio of the variance of diagonal and off-diagonal matrix elements agrees with random matrix predictions [22,23,29,30]. Deviations from the Gaussian nature of the distribution have been found when the system under consideration approaches the integrable or localized regime [22,28,29,31,32] as well as for specific nonlocal operators [33].…”

Typicality of nonequilibrium (quasi-)steady currents

“…In the future we will consider adding an intermediate system between the baths so as to study conditions for the emergence of a (quasi-)steady current within this intermediate system. Furthermore, it would be important to consider whether the conditions for the emergence of the (quasi-)steady current can be loosened, for example considering also integrable baths [55,[62][63][64][65][66]]. In this section we derive the perturbative current expression (Eq.…”