Quantization of dissipative dynamical systems

K. Hajra

In the framework of stochastic quantization the quantum theory of an open system is envisaged here. A hydrodynamical model has been suggested for the motion of a quantum particle in the presence of frictional dissipative force. Finally, a comparison is made between quantum conservative and nonconservative systems.

N. Emir Anuar

We present a formalism for which a dissipative system is given by a variational principle. The formalism applies to dynamical systems where its trajectory is monotonic. Subsequently, we derive its Lagrangian and Hamiltonian. From the Hamiltonian, we quantize canonically the classical particle in a viscous media. We study the free quantum particle in a viscous media and the dissipative quantum tunnelling. It is found that the dissipation influences tunnelling probability by a factor that closely resembles the result of Caldeira and Leggett.

Vasily Evgenevich Tarasov

In this paper a generalization of Weyl quantization which maps a dynamical operator in a function space to a dynamical superoperator in an operator space is suggested. Quantization of dynamical operator, which cannot be represented as Poisson bracket with some function, is considered. The usual Weyl quantization of observables can be derived as a specific case of suggested quantization if dynamical operator is an operator of multiplication on a function. This approach allows to define consistent Weyl quantization of non-Hamiltonian and dissipative systems. Examples of the harmonic oscillator with friction and a system which evolves by Fokker-Planck-type equation are considered.

Mohsen Razavy