Application of second quantization methods to the classical statistical mechanics (II)

Towards the topological quantization of classical mechanics

We consider the method of topological quantization for conservative systems with a finite number of degrees of freedom. Maupertuis’ formalism for classical mechanics provides an appropriate scenario which permit us to adapt the method of topological quantization, originally formulated for gravitational field configurations. We show that any conservative system in classical mechanics can be asso...

A Quantum Approach to Classical Statistical Mechanics

We present a new approach to study the thermodynamic properties of d-dimensional classical systems by reducing the problem to the computation of ground state properties of a d-dimensional quantum model. This classical-to-quantum mapping allows us to deal with standard optimization methods, such as simulated and quantum annealing, on an equal basis. Consequently, we extend the quantum annealing ...

The classical - statistical limit of quantum mechanics

The classical-statistical limit of quantum mechanics is studied. It is proved that the limit ~ → 0 is the good limit for the operators algebra but it si not so for the state compact set. In the last case decoherence must be invoked to obtain the classical-statistical limit.

Application of Numerical Methods in the Analysis of Mat Foundations and Limitations of Classical Methods

Application of Numerical Methods in the Analysis of Mat Foundations and Limitations of Classical Methods