Aspects of nonequilibrium dynamics of dissipation and relaxation in quantum field theory

Shuai Yin, Chung-Yu Lo, Pochung Chen

We study the scaling behavior of the relaxation dynamics to thermal equilibrium when a quantum system is near the quantum critical point. In particular, we investigate systems whose relaxation dynamics is described by a Lindblad master equation. We find that the universal scaling behavior not only appears in the equilibrium stage at the long-time limit but also manifests in the nonequilibrium relaxation process. While the critical behavior is dictated by the low-lying energy levels of the Hamiltonian, the dissipative part in the Lindblad equation also plays important roles in two aspects: First, the dissipative part makes the high-energy levels decay fast, after which the universal behavior controlled by the low-lying modes emerges. Second, the dissipation rate gives rise to a time scale that affects the scaling behavior. We confirm our theory by solving the Lindblad equation for the one-dimensional transverse-field Ising model.

Gert Aarts A

Da-Shin Lee

Chaudhuri, J R, Deb, B, Shankar, Ray D

We extend the quantum theory of dissipation in the context of system-reservoir model, where the reservoir in question is kept in a nonequilibrium condition. Based on a systematic separation of time scales involved in the dynamics, appropriate generalizations of the fluctuation-dissipation and Einstein's relations have been pointed out. We show that the Wigner-Weisskopf decay of the system mode results in a rate constant which depending on the relaxation of nonequilibrium bath is dynamically modified. We also calculate the time-dependent spectra of a cavity mode with a suitable gain when the cavity is kept in contact with a nonequilibrium bath.

Ivan A. Kalashnikov, Pavel Vladimirovich Prudnikov

Renormalization-group approach is applied to investigate the short-time nonequilibriumcritical behavior of pure and diluted spin systems with nonmagnetic point-like impurities.The dissipative relaxation dynamics with non-conserved order parameter is considered. For thefirst time the description of the order parameter growth induced by the initial nonequilibriumstate of system is carried out at fixed dimension d = 3 without use of ε-expansion.

Esteban A. Calzetta, B. L. Hu