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Register a new userChaos and the dynamics of information in dissipative electronic systems
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The dynamics of chaotic systems are, by definition, exponentially sensitive to initial conditions and may appear rather random. In this work, we explore relations between the chaotic dynamics of an observable and the dynamics of information (entropy) contained in this observable, focussing on a disordered metal coupled to a dissipative, e.g. phononic, bath. The chaotic dynamics is characterised by Lyapunov exponents $lambda$, the rates of growth of out-of-time order correlators (OTOCs), quantities of the form $langle[hat A(t),hat B(0)]^{2}rangleproptoexp(2lambda t)$, where $hat A$ and $hat B$ are the operators of, e.g., the total current of electrons in a metallic quantum dot. We demonstrate that the Lyapunov exponent $lambda$ matches the rate of decay of information stored in the observable $langle hat A(t)rangle$ after applying a small perturbation with a small classical uncertainty. This relation suggests a way to measure Lyapunov exponents in experiment. We compute both the Lyapunov exponent and the rate of decay of information microscopically in a disordered metal in the presence of a bosonic bath, which may, in particular, represent interactions in the system. For a sufficiently short range of the correlations in the bath, the exponent has the form $lambda=lambda_{0}-1/tau$, where $lambda_{0}$ is the (temperature-independent) Lyapunov exponent in the absence of the bath and $1/tau$ is the inelastic scattering rate. Our results demonstrate also the existence of a transition between chaotic and non-chaotic behaviour at $lambda_{0}=1/tau$, which may be triggered, e.g., by changing the temperature of the bath.
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Periodically driven quantum systems host a range of non-equilibrium phenomena which are unrealizable at equilibrium. Discrete time-translational symmetry in a periodically driven many-body system can be spontaneously broken to form a discrete time crystal, a putative quantum phase of matter. We present the observation of discrete time crystalline order in a driven system of paramagnetic $P$ -donor impurities in isotopically enriched $^{28}Si$ cooled below $10$ K. The observations exhibit a stable subharmonic peak at half the drive frequency which remains pinned even in the presence of pulse error, a signature of DTC order. We propose a theoretical model based on the paradigmatic central spin model which is in good agreement with experimental observations, and investigate the role of dissipation in the stabilisation of the DTC. Both experiment and theory indicate that the order in this system is primarily a dissipative effect, and which persists in the presence of spin-spin interactions. We present a theoretical phase diagram as a function of interactions and dissipation for the central spin model which is consistent with the experiments. This opens up questions about the interplay of coherent interaction and dissipation for time-translation symmetry breaking in many-body Floquet systems.
In this work, we study the driven-dissipative dynamics of a coherently-driven spin ensemble with a squeezed, superradiant decay. This decay consists of a sum of both raising and lowering collective spin operators with a tunable weight. The model presents different critical non-equilibrium phases with a gapless Liouvillian that are associated to particular symmetries and that give rise to distinct kinds of non-ergodic dynamics. In Ref. [1] we focus on the case of a strong-symmetry and use this model to introduce and discuss the effect of dissipative freezing, where, regardless of the system size, stochastic quantum trajectories initialized in a superposition of different symmetry sectors always select a single one of them and remain there for the rest of the evolution. Here, we deepen this analysis and study in more detail the other type of non-ergodic physics present in the model, namely, the emergence of non-stationary dynamics in the thermodynamic limit. We complete our description of squeezed superradiance by analysing its metrological properties in terms of spin squeezing and by analysing the features that each of these critical phases imprint on the light emitted by the system.
A method of determining the temperature of the nonradiative reservoir in a microcavity exciton-polariton system is developed. A general relation for the homogeneous polariton linewidth is theoretically derived and experimentally used in the method. In experiments with a GaAs microcavity under nonresonant pulsed excitation, the reservoir temperature dynamics is extracted from the polariton linewidth. Within the first nanosecond the reservoir temperature greatly exceeds the lattice temperature and determines the dynamics of the major processes in the system. It is shown that, for nonresonant pulsed excitation of GaAs microcavities, the polariton Bose-Einstein condensation is typically governed by polariton-phonon scattering, while interparticle scattering leads to condensate depopulation.
In this note we study chaos in generic quantum systems with a global symmetry generalizing seminal work [arXiv : 1503.01409] by Maldacena, Shenker and Stanford. We conjecture a bound on instantaneous chaos exponent in a thermodynamic ensemble at temperature $T$ and chemical potential $mu$ for the continuous global symmetry under consideration. For local operators which could create excitation up to some fixed charge, the bound on chaos (Lyapunov) exponent is independent of chemical potential $lambda_L leq frac{2 pi T}{ hbar} $. On the other hand when the operators could create excitation of arbitrary high charge, we find that exponent must satisfy $lambda_L leq frac{2 pi T}{(1-|frac{mu}{mu_c}|) hbar} $, where $mu_c$ is the maximum value of chemical potential for which the thermodynamic ensemble makes sense. As specific examples of quantum mechanical systems we consider conformal field theories. In a generic conformal field theory with internal $U(1)$ symmetry living on a cylinder the former bound is applicable, whereas in more interesting examples of holographic two dimensional conformal field theories dual to Einstein gravity, we argue that later bound is saturated in presence of a non-zero chemical potential for rotation.
It is known that entanglement can be converted to work in quantum composite systems. In this paper we consider a quench protocol for two initially independent reservoirs $A$ and $B$ described by the quantum thermal states. For a free fermion model at low temperatures, the von Neumann entropy of each reservoir increases once the reservoirs are coupled. At the moment of decoupling there is an energy transfer to the system in the amount set by the von Neumann entropy accumulated during joint evolution of $A$ and $B$. This energy transfer appears as work produced by the quench to decouple the reservoirs. Once the reservoirs are disconnected, the information about their mutual correlations $-$ von Neumann entropy $-$ is stored in the energy increment of each reservoir. This result provides a possibility of a direct readout of quantum correlations at low temperature.
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