The study of nonequilibrium dissipative quantum dynamics and applications to energy transport and quantum information processes

I. Prigogine

Junran Kong, Yuwei Lu, Huan Liu +2 more

Nonequilibrium energy transport serves as one of fundamental problems in quantum thermodynamics and quantum technologies. Driven quantum master equation in the dressed picture provides an efficient way of investigating nonequilibrium energy flow in general driven-dissipative quantum systems, where the systems are simultaneously driven by the finite thermodynamic bias and coherent driving field. The validity and general applicability of driven quantum master equation is confirmed by comparing with Floquet master equation, by analyzing energy currents in generic spin and boson models. The additional driving phase reserved in system-reservoir interactions, will apparently modify microscopic energy exchange processes. The steady-state energy currents are dramatically enhanced, in particular near the resonant regimes. In contrast, the traditional dressed master equation yields distinct behaviors of the energy currents. We hope that the driven quantum master equation may provide an efficient utility for the control of quantum transport and thermodynamic performances in driven-dissipative nanodevices.

Ilya Prigogine

Chengyun Hua, Lucas Lindsay, Yuya Shinohara +1 more

Nonequilibrium dynamics in spin systems is a topic currently under intense investigation as it provides fundamental insights into thermalization, universality, and exotic transport phenomena. While most of the studies have been focused on ideal closed quantum many-body systems such as ultracold atomic quantum gases and one-dimensional spin chains, driven-dissipative Bose gases in steady states away from equilibrium in classical systems also lead to intriguing nonequilibrium physics. In this work, we theoretically investigate out-of-equilibrium dynamics of magnons in a gapped Heisenberg quantum antiferromagnet based on Boltzmann transport theory. We show that, by treating scattering terms beyond the relaxation-time approximation in the Boltzmann transport equation, energy and particle number conservation mandate that nonequilibrium magnons cannot relax to equilibrium, but decay to other nonequilibrium stationary states. The only decay channel for these stationary states back to equilibrium is through the nonconserving interactions (i.e., changing particle number and/or energy within the magnon system) such as boundary or magnon-phonon scattering. At low temperatures, these nonconserving interactions are much slower processes than intrinsic magnon-magnon interaction in a gapped spin system. Using magnon-phonon interaction as a quintessential type of nonconserving interaction, we then propose that nonequilibrium steady states of magnons can be maintained and tailored using periodic driving at frequencies faster than relaxation due to phonon interactions. These findings reveal a class of classical material systems that are suitable platforms to study nonequilibrium statistical physics and macroscopic phenomena such as classical Bose-Einstein condensation of quasiparticles and magnon supercurrents that are relevant for spintronic applications.

Xiao-Kan Guo, Zhiqiang Huang

In this paper, we study the quantum information-geometric structure underlying short-time nonequilibrium relaxation in quantum Markov dynamics, and derive bounds on the nonequilibrium correction to the short-time relaxation curvature. These bounds generalize the information-geometric structure underlying Auconi's classical nonequilibrium relaxation inequality to quantum Markov dynamics. We consider the von Neumann relative entropy as quantum divergence, and parametrize perturbations through the Kubo-Mori map, which converts the second-order expansion of the relative entropy into the Bogoliubov-Kubo-Mori (BKM) inner product at all temperatures. For a quantum Markov semigroup with full-rank stationary state, the induced tangent-space generator admits a canonical decomposition into a BKM-symmetric and a BKM-antisymmetric part, and the leading nonequilibrium curvature correction takes the exact form of the expectation of the commutator between the dissipative and the transport part of the generator. This correction is bounded by the product of a BKM-symmetric dissipative activity and a transport-sector activity. The bound is verified on a noncommuting qubit model and a driven-dissipative qutrit, and the full chain is confirmed numerically on a two-dimensional Fokker-Planck steady state. In the high-temperature and overdamped limit the quantum formula reduces to the position-space Fokker-Planck expression and reproduces Auconi's entropy-production bound with the correct temperature factor.

Ilya Prigogine