Slow heating in a quantum coupled kicked rotors system

Abstract

We consider a finite-size periodically driven quantum system of coupled kicked rotors which exhibits two distinct regimes in parameter space: a dynamically-localized one with kinetic-energy saturation in time and a chaotic one with unbounded energy absorption (dynamical delocalization). We provide numerical evidence that the kinetic energy grows subdiffusively in time in a parameter region close to the boundary of the chaotic dynamically-delocalized regime. We map the different regimes of the model via a spectral analysis of the Floquet operator and investigate the properties of the Floquet states in the subdiffusive regime. We observe an anomalous scaling of the average inverse participation ratio (IPR) analogous to the one observed at the critical point of the Anderson transition in a disordered system. We interpret the behavior of the IPR and the behavior of the asymptotic-time energy as a mark of the breaking of the eigenstate thermalization in the subdiffusive regime. Then we study the distribution of the kinetic-energy-operator off-diagonal matrix elements. We find that in presence of energy subdiffusion they are not Gaussian and we propose an anomalous random matrix model to describe them.PACS numbers: Valid PACS appear here arXiv:1907.00002v1 [cond-mat.quant-gas] Slow heating in a quantum coupled kicked rotors system ‡ This is rigorously true in the case of a driven system. In the autonomous case, the eigenstates of the Hamiltonian behave as the eigenstates of a random banded matrix [13], in order to ensure energy conservation.

Nonergodic behavior of the clean Bose-Hubbard chain

“…4. This is consistent with other findings in the literature [49,71]. We are not able to say if this is a finite-size effect and further research is needed.…”

“…Moreover, for J ∈ [0.03, 0.2], we see that γ = γ log (considering also the errorbars). This is sufficient to say that in this interval of J the IPR distribution is broad, opposite to the narrow one valid in the ergodic case [71] (at least for the sizes we can numerically reach). We note that the value J ∼ 1, where γ attains the ergodic value is somewhat larger than the value where the average level spacing ratio attains the Wigner-Dyson value in Fig.…”

“…There are many examples of this behavior in the literature, and they can correspond to multifractal behavior [67][68][69] or many-body localization [70]. We remark that extended nonergodic phases can have an average level-spacing ratio near to the Wigner-Dyson one [49,71]. We show our numerical results in Fig.…”

Quasi-localization dynamics in a Fibonacci quantum rotor

“…As for example, it has been observed that the dynamics of a QKR driven with three incommensurate frequencies can be mapped to the three dimensional Anderson problem and thus can exhibit both dynamical localization as well as diffusive growth in its kinetic energy [22]. Similarly, the localiza- * sourav.offc@gmail.com tion as well as delocalization behavior has been reported in coupled systems of multiple kicked rotors [23][24][25][26][27][28][29]. Finally, the robustness of the dynamically localized phase when subjected to a multitude of perturbations such as noise and environment induced dissipation effects have also been actively investigated [13][14][15][30][31][32][33][34][35].…”

Fragility to quantum fluctuations of classical Hamiltonian period doubling

“…( 2) and they are taken in increasing order [49]. If r 0.5269 the level-spacing distribution is of the COE type and the dynamics is ergodic (the Floquet states are like eigenstates of a random matrix) while if r 0.386 the level-spacing distribution is of the Poisson type and the model is integrable (see for instance [50]). We can evaluate r for the Hamiltonian in Eq.…”