Bulletin of the American Physical Society
APS March Meeting 2019
Volume 64, Number 2
Monday–Friday, March 4–8, 2019; Boston, Massachusetts
Session H55: The Subtle Road to Equilibrium  or Not?Focus

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Sponsoring Units: GSNP Chair: David Campbell, Boston Univ Room: BCEC 254B 
Tuesday, March 5, 2019 2:30PM  3:06PM 
H55.00001: The subtle road to equilibrium  or not? Invited Speaker: Carlo Danieli The influence that deviations from equilibrium have on the ergodic equipartitioned dynamics of classical and quantum systems has been widely investigated in the recent years. 
Tuesday, March 5, 2019 3:06PM  3:18PM 
H55.00002: Lyapunov exponents, ergodization time and outoftimeorder correlators in chaotic manyparticle systems from Loschmidt echoes Andrei Tarkhov, Sandro Marcel Wimberger, Boris V. Fine We propose an experimentally realizable method to demonstrate Lyapunov instability and to estimate ergodization time in chaotic manyparticle systems by monitoring equilibrium noise of virtually any observable quantity before and after time reversal of dynamics (Loschmidt echo). In the quantum regime, the quantity of interest for the method is a counterpart of outoftimeorder correlators (OTOCs). The ergodization time is defined as the characteristic time required to extract the largest Lyapunov exponent from a system’s dynamics. The proposal focuses specifically on a lattice of coupled BoseEinstein condensates in the classical regime describable by the discrete GrossPitaevskii equation. We support our theoretical analysis by direct numerical simulations demonstrating that the largest Lyapunov exponent and the ergodization time can indeed be extracted from the Loschmidt echo routine. 
Tuesday, March 5, 2019 3:18PM  3:30PM 
H55.00003: Quantum versus classical thermalization in manybody isolated systems Felix Izrailev In view of recent studies of the thermalization occurring in manybody isolated systems, we discuss the onset of relaxation towards a steadystate equilibrium, paying main attention to the systems with finite number of interacting particles. We have found that in the models of randomly interacting fermions and bosons, the effective number of components in the wave packets increases exponentially in time, provided the eigenstates are strongly chaotic in the Hilbert space defined by noninteracting particles. Our semianalytical approach allows one to obtain the estimates for the rate of this increase and for the characteristic time of the saturation which can be considered as the time for a complete thermalization. Special interest has been payed to the correlations between occupation numbers, that increase in time during the scrambling of wave packets in Hilbert space. These correlations are responsible for the onset of the BoseEinstein and FermiDirac distributions. We discuss the relevance of the exponentially fast quantum dynamics to the KolmogorovSinai entropy characterizing degree of chaos in the corresponding classical systems. 
Tuesday, March 5, 2019 3:30PM  3:42PM 
H55.00004: Behavior and Breakdown of HigherOrder FermiPastaUlamTsingou Recurrences Salvatore Pace, David K Campbell We investigate numerically the existence and stability of higherorder recurrences (HoRs), including superrecurrences, supersuperrecurrences, etc., in the alpha and beta FermiPastaUlamTsingou (FPUT) lattices for initial conditions in the fundamental normal mode. Our results represent a considerable extension of the pioneering work of Tuck and Menzel on superrecurrences. For fixed lattice sizes, we observe and study apparent singularities in the periods of these HoRs, speculated to be caused by nonlinear resonances. These singularities depend very sensitively on the initial energy. We compare the mechanisms by which the superrecurrences in the two model's breakdown as the initial energy and respective nonlinear parameters are increased. The breakdown of superrecurrences in the betaFPUT lattice is associated with the destruction of the socalled metastable state and hence is associated with relaxation towards equilibrium. For the alphaFPUT lattice, we find this is not the case and show that the superrecurrences break down while the lattice is still metastable. We close with comments on the generality of our results for different lattice sizes. 
Tuesday, March 5, 2019 3:42PM  3:54PM 
H55.00005: Aperiodically driven integrable systems and their emergent steady states Diptiman Sen, Sourav Nandy, Arnab Sen For periodically driven closed quantum manybody systems, it is known 
Tuesday, March 5, 2019 3:54PM  4:06PM 
H55.00006: Dynamical Glass Phase and Ergodization Times in Josephson Junction Chains Mithun Thudiyangal, Carlo Danieli, Yagmur Kati, Sergej Flach Models of Josephson junction chains turn integrable in the limit of large energy densities or small Josephson energies. Close to these limits the Josephson coupling between the superconducting grains induces a short range nonintegrable network. We compute distributions of finite time averages of grain charges and extract the ergodization time $T_E$ which controls their convergence to ergodic $\delta$distributions. We relate $T_E$ to the statistics of fluctuation times of the charges, which are dominated by fat tails. $T_E$ is growing anomalously fast upon approaching the integrable limit, as compared to the Lyapunov time $T_{\Lambda}$  the inverse of the largest Lyapunov exponent  reaching astonishing ratios $T_E/ T_{\Lambda} \ge 10^8$. The microscopic reason for the observed dynamical glass phase is routed in a growing number of grains evolving over long times in a regular almost integrable fashion due to the low probability of resonant interactions with the nearest neighbors. We conjecture that the observed dynamical glass phase is a generic property of Josephson junction networks irrespective of their space dimensionality. 
Tuesday, March 5, 2019 4:06PM  4:18PM 
H55.00007: NonGibbs states on a BoseHubbard Lattice Alexander Cherny, Thomas Engl, Sergej Flach We study the equilibrium properties of the repulsive quantum BoseHubbard model at high temperatures in arbitrary dimensions, with and without disorder. In its microcanonical setting the model conserves energy and particle number. The microcanonical dynamics is characterized by a pair of two densities: energy density ε and particle number density n. The macrocanonical Gibbs distribution also depends on two parameters: the inverse nonnegative temperature β and the chemical potential μ. We prove the existence of nonGibbs states, that is, pairs (ε,n) which can not be mapped onto (β,μ). The separation line in the density control parameter space between Gibbs and nonGibbs states ε∼n^{2} corresponds to infinite temperature β=0. The nonGibbs phase can not be cured into a Gibbs one within the standard Gibbs formalism using negative temperatures. 
Tuesday, March 5, 2019 4:18PM  4:30PM 
H55.00008: Probing the mobility edge in an interacting model using MPS Nicholas Pomata, Sriram Ganeshan, TzuChieh Wei The quasiperiodic Generalized AubryAndré model is known to exhibit a mobility edge in the noninteracting limit for a certain range of disorder strengths. However, there is not much known about the interacting version of the model. We use the ShiftInvert Matrix Product State method of Yu, Pekker, and Clark to study this system with sizes from 32 to 128 sites, computing excited states for different disorder realizations (produced by varying the phase in the quasiperiodic potentials). Our goal is to determine where manybody localized states are absent or present, starting from the singleparticle mobility edge. 
Tuesday, March 5, 2019 4:30PM  4:42PM 
H55.00009: Effective ergodicity breaking phase transition in a drivendissipative system Sakib Matin, Harvey Gould, W. Klein The growing interest in nonequilibrium systems has prompted question of what equilibrium methods can be extended to nonequilibrium systems. We discuss a nonequilibrium phase transition in the OlamiFederChristensen model that is characterized by critical exponents which obey scaling laws from equilibrium statistical mechanics. Below the critical noise, the sites are trapped in different limit cycles. The probability distributions of different trajectories are distinct and highlight the nonergodic nature of the phase. Above the critical noise all sites converge to the same time average and the system is effectively ergodic. We use tools from the study of glassy systems and nonlinear dynamics to illuminate various properties of this nonequilibrium phase transition. Our results show a promising start to extending the methods of equilibrium statistical mechanics to a new class of nonequilibrium systems. 
Tuesday, March 5, 2019 4:42PM  4:54PM 
H55.00010: Investigating manybody mobility edges in isolated quantum systems Xing Bo Wei, Chen Cheng, Gao Xianlong, Rubem Mondaini The existence of manybody mobility edges in closed quantum systems has been the focus of intense debate after the emergence of the description of the manybody localization phenomenon. Here we propose that this issue can be settled in experiments by investigating the time evolution of local degrees of freedom, tailored for specific energies and intial states. An interacting model of spinless fermions with exponentially longranged tunneling amplitudes, whose noninteracting version known to display singleparticle mobility edges, is used as the starting point upon which nearestneighbor interactions are included. We verify the manifestation of manybody mobility edges by using numerous probes, directly comparing it with the predictions of the Eigenstate Thermalization Hypothesis (ETH). Our results indicate the coexistence of regions with finite measure when approaching the thermodynamic limit where thermalization and localization are manifest, suggesting that one cannot explain their appearance as merely being a result of finitesize effects. 
Tuesday, March 5, 2019 4:54PM  5:06PM 
H55.00011: Rogue Fluctuations in FermiPastaUlamTsingou Systems Surajit Sen, Rahul Kashyap Rogue waves, also referred to as freak waves, are large, short lived waves in the oceans and have been the subject of intense research due to their destructive nature. We consider discrete strongly nonlinear systems with FermiPastaUlamTsingou type potentials by means of extensive simulations. We define rogue fluctuations in these systems as large and persistent kinetic energy fluctuations with finite lifetimes in these systems at late enough times. Our simulations suggest that rogue fluctuations are generic to strongly nonlinear systems. We also observe from our simulations that rogue fluctuations show features which are reminiscent of rogue waves in the oceans, providing evidence that they are natural candidates for analogs of rogue waves in discrete systems [1]. Effects arising from the presence of phonons in these systems are also explored. 
Tuesday, March 5, 2019 5:06PM  5:18PM 
H55.00012: Quantum coherence in the ergodic and manybody localized phase Sayandip Dhara, Alioscia Hamma, Eduardo R Mucciolo We use quantum coherence as a tool to study the structure of the eigenstates of disordered and interacting quantum many body systems. In particular, we numerically calculate several different measures of quantum coherence for the excited eigenstates to be able to capture the signatures of the ergodic and the manybody localized phase in these finite systems. It is apparent that the different measures of coherence show different behaviour with the increasing disorder strength. We also investigate how the unitary evolution affects quantum coherence in several disordered spin chains. Starting from a maximal coherent state in the computational basis, we study the dynamics of decoherence in both the ergodic and the manybody localized phase. We show that coherence can capture many important features of quantum dynamical phases and offers important computational advantages. 
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