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Register a new userPhysics of PT-Symmetric Quantum Systems at Finite Temperature
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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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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.
We consider the Haldane model, a 2D topological insulator whose phase is defined by the Chern number. We study its phases as temperature varies by means of the Uhlmann number, a finite temperature generalization of the Chern number. Because of the relation between the Uhlmann number and the dynamical transverse conductivity of the system, we evaluate also the conductivity of the model. This analysis does not show any sign of a phase transition induced by the temperature, nonetheless it gives a better understanding of the fate of the topological phase with the increase of the temperature, and it provides another example of the usefulness of the Uhlmann number as a novel tool to study topological properties at finite temperature.
The Quantum Monte Carlo method for spin 1/2 fermions at finite temperature is formulated for dilute systems with an s-wave interaction. The motivation and the formalism are discussed along with descriptions of the algorithm and various numerical issues. We report on results for the energy, entropy and chemical potential as a function of temperature. We give upper bounds on the critical temperature T_c for the onset of superfluidity, obtained by studying the finite size scaling of the condensate fraction. All of these quantities were computed for couplings around the unitary regime in the range -0.5 le (k_F a)^{-1} le 0.2, where a is the s-wave scattering length and k_F is the Fermi momentum of a non-interacting gas at the same density. In all cases our data is consistent with normal Fermi gas behavior above a characteristic temperature T_0 > T_c, which depends on the coupling and is obtained by studying the deviation of the caloric curve from that of a free Fermi gas. For T_c < T < T_0 we find deviations from normal Fermi gas behavior that can be attributed to pairing effects. Low temperature results for the energy and the pairing gap are shown and compared with Green Function Monte Carlo results by other groups.
By rearrangements of waveguide arrays with gain and losses one can simulate transformations among parity-time (PT-) symmetric systems not affecting their pure real linear spectra. Subject to such transformations, however, the nonlinear properties of the systems undergo significant changes. On an example of an array of four waveguides described by the discrete nonlinear Schrodinger equation with dissipation and gain, we show that the equivalence of the underlying linear spectra implies similarity of neither structure nor stability of the nonlinear modes in the arrays. Even the existence of one-parametric families of nonlinear modes is not guaranteed by the PT symmetry of a newly obtained system. Neither the stability is directly related to the PT symmetry: stable nonlinear modes exist even when the spectrum of the linear array is not purely real. We use graph representation of PT-symmetric networks allowing for simple illustration of linearly equivalent networks and indicating on their possible experimental design.
We generalize techniques previously used to compute ground-state properties of one-dimensional noninteracting quantum gases to obtain exact results at finite temperature. We compute the order-n Renyi entanglement entropy to all orders in the fugacity in one, two, and three spatial dimensions. In all spatial dimensions, we provide closed-form expressions for its virial expansion up to next-to-leading order. In all of our results, we find explicit volume scaling in the high-temperature limit.
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