Real Time Dynamics of Dissipative Quantum Systems.

Michael P. Zwolak, Gil Refael

Joachim Ankerhold, Hermann Grabert

F. Hebenstreit, Debasish Banerjee, M. Hornung +3 more

We study the real-time evolution of large open quantum spin systems in two spatial dimensions, whose dynamics is entirely driven by a dissipative coupling to the environment. We consider different dissipative processes and investigate the real-time evolution from an ordered phase of the Heisenberg or XY model towards a disordered phase at late times, disregarding unitary Hamiltonian dynamics. The corresponding Kossakowski-Lindblad equation is solved via an efficient cluster algorithm. We find that the symmetry of the dissipative process determines the time scales, which govern the approach towards a new equilibrium phase at late times. Most notably, we find a slow equilibration if the dissipative process conserves any of the magnetization Fourier modes. In these cases, the dynamics can be interpreted as a diffusion process of the conserved quantity.

Andrei D. Zaikin, Dmitry S. Golubev

This chapter describes the analysis of the effect of dissipation on quantum properties of double-well systems. The simple qualitative observation suggests that interaction with a dissipative bath can significantly alter physical properties of a quantum mechanical particle in a double-well potential. The chapter provides the description of real-time dynamics of the double-well systems in the presence of linear Ohmic dissipation. It shows that dissipation yields total loss of coherence and, hence, real-time dynamics of the system remains incoherent at all times. Drastic simplifications occur if one assumes that the average time the system remains in a state described by the diagonal density matrix strongly exceeds the time it spends in the off-diagonal state. The collective charge variable is canonically conjugate to that of the phase, thus also describing quantum states of a macroscopically large number of electron degrees of freedom.

Lit-Deh Chang

D. Mesterházy, F. Hebenstreit

We address the real-time dynamics of lattice quantum spin models coupled to single or multiple Markovian dissipative reservoirs using the method of closed hierarchies of correlation functions. This approach allows us to solve a number of quantum spin models exactly in arbitrary dimensions, which is illustrated explicitly with two examples of driven-dissipative systems. We investigate their respective nonequilibrium steady states as well as the full real-time evolution on unprecedented system sizes. Characteristic time scales are derived analytically, which allows us to understand the nontrivial finite-size scaling of the dissipative gap. The corresponding scaling exponents are confirmed by solving numerically for the full real-time evolution of two-point correlation functions.