We explore the connection between chaos, thermalization and ergodicity in a linear chain of $N$ interacting dipoles. Starting from the ground state, and considering chains of different numbers of dipoles, we introduce single site excitations with energy $ΔK$. The time evolution of the chaoticy of the system and the energy localization along the chain is analyzed by computing, up to very long times, the statistical average of the finite time Lyapunov exponent $λ(t)$ and of the participation ratio $Π(t)$. For small $ΔK$, the evolution of $λ(t)$ and $Π(t)$ indicates that the system becomes chaotic at roughly the same time as $Π(t)$ reaches a steady state. For the largest values of $ΔK$, the system becomes chaotic at an extremely early stage in comparison with the energy relaxation times. We find that this fact is due to the presence of chaotic breathers that keep the system far from equipartition and ergodicity. Finally, we show that the asymptotic values attained by the participation ratio $Π(t)$ fairly corresponds to thermal equilibrium.
We show that the known bound on the growth rate of the out-of-time-order four-point correlator in chaotic many-body quantum systems follows directly from the general structure of operator matrix elements in systems that obey the eigenstate thermalization hypothesis. This ties together two key paradigms of thermal behavior in isolated many-body quantum systems.
We present a detailed analysis of the connection between chaos and the onset of thermalization in the spin-boson Dicke model. This system has a well-defined classical limit with two degrees of freedom, and it presents both regular and chaotic regions. Our studies of the eigenstate expectation values and the distributions of the off-diagonal elements of the number of photons and the number of excited atoms validate the diagonal and off-diagonal eigenstate thermalization hypothesis (ETH) in the chaotic region, thus ensuring thermalization. The validity of the ETH reflects the chaotic structure o…
A profound quest of statistical mechanics is the origin of irreversibility - the arrow of time. New stimulants have been provided, thanks to unprecedented degree of control reached in experiments with isolated quantum systems and rapid theoretical developments of manybody localization in disordered interacting systems. The proposal of (many-body) eigenstate thermalization (ET) for these systems reinforces the common belief that either interaction or extrinsic randomness is required for thermalization. Here, we unveil a quantum thermalization mechanism challenging this belief. We find that, pro…
We study the quantum dynamics of the kicked Dicke model(KDM) in terms of the Floquet operator and analyze the connection between the chaos and thermalization in this context. The Hamiltonian map is constructed by taking the classical limit of the Heisenberg equation of motion suitably to study the corresponding phase space dynamics which shows a crossover from regular to chaotic motion by tuning the kicking strength. The fixed point analysis and calculation of the Lyapunov exponent(LE) provides us a complete picture of the onset of chaos in phase space dynamics. We carry out the spectral analy…
Exactly solvable models that exhibit quantum signatures of classical chaos are both rare as well as important - more so in view of the fact that the mechanisms for ergodic behavior and thermalization in isolated quantum systems and its connections to non-integrability are under active investigation. In this work, we study quantum systems of few qubits collectively modeled as a kicked top, a textbook example of quantum chaos. In particular, we show that the 3 and 4 qubit cases are exactly solvable and yet, interestingly, can display signatures of ergodicity and thermalization. Deriving analytic…
Coined discrete-time quantum walks are studied using simple deterministic dynamical systems as coins whose classical limit can range from being integrable to chaotic. It is shown that a Loschmidt echo like fidelity plays a central role and when the coin is chaotic this is approximately the characteristic function of a classical random walker. Thus the classical binomial distribution arises as a limit of the quantum walk and the walker exhibits diffusive growth before eventually becoming ballistic. The coin-walker entanglement growth is shown to be logarithmic in time as in the case of many-bod…
Semiclassical scaling of eigenstate thermalization in single-particle chaotic systems
University of Science and Technology of China（中国科学技术大学）；Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Wilczek Quantum Center, Shanghai Institute for Advanced Studies（复旦张肇韦量子中心，上海高等研究院）；CAS Key Laboratory of Microscale Magnetic Resonance（中国科学院微观磁学共振重点实验室）
Dynamical thermalization, Rayleigh-Jeans condensate, vortexes and wave collapse in quantum chaos fibers and fluid of light
Comisión Nacional de Energía Atómica（阿根廷国家原子能委员会）；Université Paris-Sud, CNRS（巴黎南大学，法国国家科学研究中心）；Université de Toulouse, CNRS, UPS（图卢兹大学，法国国家科学研究中心，图卢兹第三大学）
We study numerically the problem of dynamical thermalization of interacting cold fermionic atoms placed in an isolated Sinai-oscillator trap. This system is characterized by a quantum chaos regime for one-particle dynamics. We show that for a many-body system of cold atoms the interactions, with a strength above a certain quantum chaos border given by the Aberg criterion, lead to the Fermi-Dirac distribution and relaxation of many-body initial states to the thermalized state in absence of any contact with a thermostate. We discuss the properties of this dynamical thermalization and its links w…
We study numerically the evolution of Bose-Einstein condensate in the Sinai oscillator trap described by the Gross-Pitaevskii equation in two dimensions. In the absence of interactions this trap mimics the properties of Sinai billiards where the classical dynamics is chaotic and the quantum evolution is described by generic properties of quantum chaos and random matrix theory. We show that, above a certain border, the nonlinear interactions between atoms lead to the emergence of dynamical thermalization which generates the statistical Bose-Einstein distribution over eigenmodes of the system wi…
Most studies on the problem of equilibration of the Fermi-Pasta-Ulam-Tsingou (FPUT) system have focused on equipartition of energy being attained amongst the normal modes of the corresponding harmonic system. In the present work, we instead discuss the equilibration problem in terms of local variables, and consider initial conditions corresponding to spatially localized energy. We estimate the time-scales for equipartition of space localized degrees of freedom and find significant differences with the times scales observed for normal modes. Measuring thermalization in classical systems necessa…
We study a one-dimensional gas of hard rods trapped in a harmonic potential, which breaks integrability of the hard-rod interaction in a non-uniform way. We explore the consequences of such broken integrability for the dynamics of a large number of particles and find three distinct regimes: initial, chaotic, and stationary. The initial regime is captured by an evolution equation for the phase-space distribution function. For any finite number of particles, this hydrodynamics breaks down and the dynamics become chaotic after a characteristic time scale determined by the inter-particle distance …
We study the energy transfer in a classical dipole chain of $N$ interacting rigid rotating dipoles. The underlying high--dimensional potential energy landscape is analyzed in particular by determining the equilibrium points and their stability in the common plane of rotation. Starting from the minimal energy configuration, the response of the chain to excitation of a single dipole is investigated. Using both the linearized and the exact Hamiltonian of the dipole chain, we detect an approximate excitation energy threshold between a weakly and a strongly nonlinear dynamics. In the weakly nonline…
We study the chaotic behavior of multidimensional Hamiltonian systems in the presence of nonlinearity and disorder. It is known that any localized initial excitation in a large enough linear disordered system spreads for a finite amount of time and then halts forever. This phenomenon is called Anderson localization (AL). What happens to AL when nonlinearity is introduced is an interesting question which has been considered in several studies over the past decades. However, the characteristics and the asymptotic fate of such evolutions still remain an issue of intense debate due to their comput…
