Stochastic Quantization and Critical Dynamics

Б.В. Медведев

Martin C. Gutzwiller

L. Garrido, D. Luri�, Maxi San Miguel

Patrizia Ruggiero, Marco Zannetti

The stochastic quantization of Nelson is extended to the finite-temperature equilibrium states and is applied to the study of the quantum effects in the critical dynamics of the time-dependent Ginzburg-Landau model in the large-$n$ limit. A temperature-dependent (non-Markovian) stochastic process for the order parameter is derived which contains the crossover from the ground-state dynamics dominated by the quantum fluctuations, to classical critical dynamics in the neighborhood of the finite-temperature critical points. The crossover is exhibited by means of the effective dynamical critical exponent.

Ichiro Ohba

Patrizia Ruggiero, Marco Zannetti

In the framework of stochastic quantization the stochastic process is derived for the harmonic oscillator in equilibrium with a thermal bath. This allows one to treat the quantum and thermal fluctuations within the same scheme of stochastic differential equations. As an application of the theory the quantum-classical crossover is computed in the dynamical critical exponent of the Van Hove model.