QUANTUM GENERALIZED LANGEVIN EQUATION APPROACH TO MULTI-DIMENSIONAL DYNAMICS

A. Lavagno

Crispin W. Gardiner

Tsuyoshi Otobe, Hiromichi Nakazato, Keisuke Okano +2 more

We investigate the critical short-time scaling of the two-dimensional lattice ϕ4 field theory with a Langevin dynamics. Starting from a "hot" initial configuration but with a small magnetization, the critical initial increase of the magnetization is observed, through which we determine the critical point. From the short-time relaxation dynamics of various quantities at the critical point obtained, the dynamic critical exponents θ, z and the static exponent β/ν are evaluated. In executing a Langevin simulation, an appropriate discretization method with respect to the time degree of freedom becomes essentially important to be adopted and we show that the well-known second-order form of discretized Langevin equation works well to investigate the short-time dynamics.

Crispin W. Gardiner, P. Zoller

Gian Paolo Beretta

In this paper, we outline the main features of the nonlinear quantum evolution equation proposed by the present author. Such an equation may be used as a model of reduced subsystem dynamics to complement various historical and contemporary efforts to extend linear Markovian theories of dissipative phenomena and relaxation based on master equations, Lindblad and Langevin equations, to the nonlinear and far nonequilibrium domain. It may also be used as the fundamental dynamical principle in theories that attempt to unite mechanics and thermodynamics, such as the Hatsopoulos–Gyftopoulos unified theory which motivated the original development of this well-behaved general nonlinear equation for the evolution of the density operator capable of generating irreversible deterministic relaxation to thermodynamic equilibrium from any far nonequilibrium state even for an isolated system.

Mauricio Domingues Coutinho-Neto, Alexandra Viel, Uwe Manthe