Quantization of stationary Gaussian random processes and their generalizations

A. I. Oksak

Russian Correspondence Institute for Textile and Light Industry, Moscow, Russia

Abstract: We consider quantization of stationary Gaussian random processes whose physical counterparts are states of open systems in equilibrium with the environment. For this, we propose a formalism and its physical interpretation in accordance with the concept of Hamiltonian modeling. The method is universal and includes the known models as particular cases. We also consider extending the method applicability domain to linear systems with infrared singularities of two-point functions. In particular, fractal Brownian motions constitute a family of reference models in this class.

Keywords: open system, Hamiltonian modeling, Gaussian flow, quasifree state of the algebra of canonical commutation relations, fractal Brownian motion.

Received: 04.04.2012
Revised: 12.07.2012

DOI: 10.4213/tmf8341

 English version: Theoretical and Mathematical Physics, 2012, 173:3, 1743–1775

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