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Register a new userQuantum Work Relations and Response Theory in $mathcal{PT}$-Symmetric Quantum Systems
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Authors
Bo-Bo Wei
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In this work, we show that a universal quantum work relation for a quantum system driven arbitrarily far from equilibrium extend to $mathcal{PT}$-symmetric quantum system with unbroken $mathcal{PT}$ symmetry, which is a consequence of microscopic reversibility. The quantum Jarzynski equality, linear response theory and Onsager reciprocal relations for the $mathcal{PT}$-symmetric quantum system are recovered as special cases of the universal quantum work relation in $mathcal{PT}$-symmetric quantum system. In the regime of broken $mathcal{PT}$ symmetry, the universal quantum work relation does not hold as the norm is not preserved during the dynamics.
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A universal quantum work relation is proved for isolated time-dependent Hamiltonian systems in a magnetic field as the consequence of microreversibility. This relation involves a functional of an arbitrary observable. The quantum Jarzynski equality is recovered in the case this observable vanishes. The Green-Kubo formula and the Casimir-Onsager reciprocity relations are deduced thereof in the linear response regime.
Thermodynamics and information theory have been intimately related since the times of Maxwell and Boltzmann. Recently it was shown that the dissipated work in an arbitrary non-equilibrium process is related to the R{e}nyi divergences between two states along the forward and reversed dynamics. Here we show that the relation between dissipated work and Renyi divergences generalizes to $mathcal{PT}$-symmetric quantum mechanics with unbroken $mathcal{PT}$ symmetry. In the regime of broken $mathcal{PT}$ symmetry, the relation between dissipated work and Renyi divergences does not hold as the norm is not preserved during the dynamics. This finding is illustrated for an experimentally relevant system of two-coupled cavities.
Recent work by Teifel and Mahler [Eur. Phys. J. B 75, 275 (2010)] raises legitimate concerns regarding the validity of quantum nonequilibrium work relations in processes involving moving hard walls. We study this issue in the context of the rapidly expanding one-dimensional quantum piston. Utilizing exact solutions of the time-dependent Schru007fodinger equation, we find that the evolution of the wave function can be decomposed into static and dynamic components, which have simple semiclassical interpretations in terms of particle-piston collisions. We show that nonequilibrium work relations remains valid at any finite piston speed, provided both components are included, and we study explicitly the work distribution for this model system.
Fluctuation dissipation theorems connect the linear response of a physical system to a perturbation to the steady-state correlation functions. Until now, most of these theorems have been derived for finite-dimensional systems. However, many relevant physical processes are described by systems of infinite dimension in the Gaussian regime. In this work, we find a linear response theory for quantum Gaussian systems subject to time dependent Gaussian channels. In particular, we establish a fluctuation dissipation theorem for the covariance matrix that connects its linear response at any time to the steady state two-time correlations. The theorem covers non-equilibrium scenarios as it does not require the steady state to be at thermal equilibrium. We further show how our results simplify the study of Gaussian systems subject to a time dependent Lindbladian master equation. Finally, we illustrate the usage of our new scheme through some examples. Due to broad generality of the Gaussian formalism, we expect our results to find an application in many physical platforms, such as opto-mechanical systems in the presence of external noise or driven quantum heat devices.
Parity-time (PT) non-Hermitian (NH) system has significant effects on observable in a great variety of physical phenomena in NH physics. However, the PT-symmetric NH quantum system at finite temperature (the so-called thermal PT system) has never been addressed. In this letter, based on a controlled open quantum system coupling two separated environments, we proposed a design to realize a thermal PT system. After solving quantum master equation in the Gorini-KossakowskiSudarshan-Lindblad form, the unexpected, abnormal, universal properties of NH thermal states (the unique final states under time evolution) are explored, for example, the non-Boltzmann/Gibbs distribution, high-temperature non-thermalization effect, etc. To understand the anomalous behaviours in thermal PT system, we developed the quantum Liouvillian statistical theory-the generalization of usual quantum statistical theory to finite-temperature NH systems. With its help, we derived the analytical results of thermodynamic properties. In addition, we found that at exceptional point (EP) a continuous thermodynamic phase transition occurs, of which there exists zero temperature anomaly. This discovery will open a door to novel physics for NH systems at finite temperature.
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