We characterize all Gaussian dynamical semigroups in continuous-variables quantum systems of $n$ -bosonic modes which have a thermal Gibbs state as a stationary solution. This is performed through an explicit relation between the diffusion and dissipation matrices, which characterize the semigroup dynamics, and the covariance matrix of the thermal equilibrium state. We also show that Alicki's quantum detailed-balance condition, based on a Gelfand-Naimark-Segal inner product, allows the determination of the temperature dependence of the diffusion and dissipation matrices and the identification of different Gaussian dynamical semigroups which share the same thermal equilibrium state.We characterize all Gaussian dynamical semigroups in continuous-variables quantum systems of $n$-bosonic modes which have a thermal Gibbs state as a stationary solution. This is performed through an explicit relation between the diffusion and dissipation matrices, which characterize the semigroup dynamics, and the covariance matrix of the thermal equilibrium state. We also show that Alicki's quantum detailed-balance condition, based on a Gelfand-Naimark-Segal inner product, allows the determination of the temperature dependence of the diffusion and dissipation matrices and the identification of different Gaussian dynamical semigroups which share the same thermal equilibrium state.

arXiv:2207.05151Physical Review ADec 15, 20227 citations

A density-matrix approach to thermal equilibrium states

Stella M. Peltier

The European Physical Journal AJun 1, 19870 citations

Quantum Nonequilibrium Dynamics: Transport, Entanglement, and Thermalization

HyungWon Kim

We study three aspects of quantum nonequilibrium dynamics; (1) transport of conserved quantities, (2) entanglement spreading, and (3) construction of local operators which slowly relax to thermal equilibrium. Motivated by recent progresses in ultracold atom experiments, we first analyze transport phenomena of a population imbalanced two-component fermi gas with arbitrary strength of inter-species interaction in three dimension. Using the Boltzmann kinetic equation at dilute regime, we obtain the transport coefficients of linear responses to gradients of temperature and chemical potential imbalance. We identify the magneto-caloric effects, and determine how these effects depend on interaction strength and population imbalance. Then, we propose an experimental protocol to observe these effects in an experiment with ultracold atoms. Next, we study entanglement spreading in a one-dimensional quantum Ising chain with longitudinal and transverse fields, which is diffusive and nonintegrable. Fully diagonalizing the Hamiltonian matrix, we explicitly show that the entanglement spreading is ballistic, thus faster than diffusive transport of conserved quantities. We provide a local spreading picture of entanglement entropy in terms of logarithmic negativity. Then, we discuss a role of energy conservation in entanglement spreading through analyzing a Floquet system. Lastly, we construct local operators that relax slowly to equilibrium with the same one-dimensional Hamiltonian. By showing that the Hamiltonian satisfies the eigenstate thermalization hypothesis, we first conclude that this model relaxes local operators to thermal equilibrium. Then, we systematically construct local operators that relax slower than conventional diffusive modes.We study three aspects of quantum nonequilibrium dynamics; (1) transport of conserved quantities, (2) entanglement spreading, and (3) construction of local operators which slowly relax to thermal equilibrium. Motivated by recent progresses in ultracold atom experiments, we first analyze transport phenomena of a population imbalanced two-component fermi gas with arbitrary strength of inter-species interaction in three dimension. Using the Boltzmann kinetic equation at dilute regime, we obtain the transport coefficients of linear responses to gradients of temperature and chemical potential imbalance. We identify the magneto-caloric effects, and determine how these effects depend on interaction strength and population imbalance. Then, we propose an experimental protocol to observe these effects in an experiment with ultracold atoms. Next, we study entanglement spreading in a one-dimensional quantum Ising chain with longitudinal and transverse fields, which is diffusive and nonintegrable. Fully diagonalizing the Hamiltonian matrix, we explicitly show that the entanglement spreading is ballistic, thus faster than diffusive transport of conserved quantities. We provide a local spreading picture of entanglement entropy in terms of logarithmic negativity. Then, we discuss a role of energy conservation in entanglement spreading through analyzing a Floquet system. Lastly, we construct local operators that relax slowly to equilibrium with the same one-dimensional Hamiltonian. By showing that the Hamiltonian satisfies the eigenstate thermalization hypothesis, we first conclude that this model relaxes local operators to thermal equilibrium. Then, we systematically construct local operators that relax slower than conventional diffusive modes.

Jan 1, 20141 citation

We characterize all Gaussian dynamical semigroups in continuous-variables quantum systems of

n

-bosonic modes which have a thermal Gibbs state as a stationary solution. This is performed through an explicit relation between the diffusion and dissipation matrices, which characterize the semigroup dynamics, and the covariance matrix of the thermal equilibrium state. We also show that Alicki's quantum detailed-balance condition, based on a Gelfand-Naimark-Segal inner product, allows the determination of the temperature dependence of the diffusion and dissipation matrices and the identification of different Gaussian dynamical semigroups which share the same thermal equilibrium state.