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Register a new userScaling behavior of the stationary states arising from dissipation at continuous quantum transitions
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We study the critical behavior of the nonequilibrium dynamics and of the steady states emerging from the competition between coherent and dissipative dynamics close to quantum phase transitions. The latter is induced by the coupling of the system with a Markovian bath, such that the evolution of the systems density matrix can be effectively described by a Lindblad master equation. We devise general scaling behaviors for the out-of-equilibrium evolution and the stationary states emerging in the large-time limit for generic initial conditions, in terms of the parameters of the Hamiltonian providing the coherent driving and those associated with the dissipative interactions with the environment. Our framework is supported by numerical results for the dynamics of a one-dimensional lattice fermion gas undergoing a quantum Ising transition, in the presence of dissipative mechanisms which include local pumping and decay of particles.
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We describe how to characterize dynamical phase transitions in open quantum systems from a purely dynamical perspective, namely, through the statistical behavior of quantum jump trajectories. This approach goes beyond considering only properties of the steady state. While in small quantum systems dynamical transitions can only occur trivially at limiting values of the controlling parameters, in many-body systems they arise as collective phenomena and within this perspective they are reminiscent of thermodynamic phase transitions. We illustrate this in open models of increasing complexity: a three-level system, a dissipative version of the quantum Ising model, and the micromaser. In these examples dynamical transitions are accompanied by clear changes in static behavior. This is however not always the case, and in general dynamical phase behavior needs to be uncovered by observables which are strictly dynamical, e.g. dynamical counting fields. We demonstrate this via the example of a class of models of dissipative quantum glasses, whose dynamics can vary widely despite having identical (and trivial) stationary states.
In this Letter we show that the time reversal asymmetry of a stationary time series provides information about the entropy production of the physical mechanism generating the series, even if one ignores any detail of that mechanism. We develop estimators for the entropy production which can detect non-equilibrium processes even when there are no measurable flows in the time series.
We investigate the effects of dissipation on the quantum dynamics of many-body systems at quantum transitions, especially considering those of the first order. This issue is studied within the paradigmatic one-dimensional quantum Ising model. We analyze the out-of-equilibrium dynamics arising from quenches of the Hamiltonian parameters and dissipative mechanisms modeled by a Lindblad master equation, with either local or global spin operators acting as dissipative operators. Analogously to what happens at continuous quantum transitions, we observe a regime where the system develops a nontrivial dynamic scaling behavior, which is realized when the dissipation parameter $u$ (globally controlling the decay rate of the dissipation within the Lindblad framework) scales as the energy difference $Delta$ of the lowest levels of the Hamiltonian, i.e., $usim Delta$. However, unlike continuous quantum transitions where $Delta$ is power-law suppressed, at first-order quantum transitions $Delta$ is exponentially suppressed with increasing the system size (provided the boundary conditions do not favor any particular phase).
We analyze the scaling behavior of the fidelity, and the corresponding susceptibility, emerging in finite-size many-body systems whenever a given control parameter $lambda$ is varied across a quantum phase transition. For this purpose we consider a finite-size scaling (FSS) framework. Our working hypothesis is based on a scaling assumption of the fidelity in terms of the FSS variables associated to $lambda$ and to its variation $delta lambda$. This framework entails the FSS predictions for continuous transitions, and meanwhile enables to extend them to first-order transitions, where the FSS becomes qualitatively different. The latter is supported by analytical and numerical analyses of the quantum Ising chain along its first-order quantum transition line, driven by an external longitudinal field.
We study the decoherence properties of a two-level (qubit) system homogeneously coupled to an environmental many-body system at a quantum transition, considering both continuous and first-order quantum transitions. In particular, we consider a d-dimensional quantum Ising model as environment system. We study the dynamic of the qubit decoherence along the global quantum evolution starting from pure states of the qubit and the ground state of the environment system. This issue is discussed within dynamic finite-size scaling frameworks. We analyze the dynamic finite-size scaling of appropriate qubit-decoherence functions. At continuous quantum transitions, they develop power laws of the size of the environment system, with a substantial enhancement of the growth rate of the qubit decoherence with respect to the case the environment system is in normal noncritical conditions. The enhancement of the qubit decoherence growth rate appears much larger at first-order quantum transitions, leading to exponential laws when increasing the size of the environment system.
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