Formulation of Quantum Statistics

Raj K. Pathria, Paul D. Beale

Gustavo V. López

The classical and quantum Statistical Mechanics is straightforwardly formulated in the configuration space (x, v), and an example of a system is given to make the comparison with the formulation of the Statistical Mechanics in the phase space (x, p). It is shown that the advantage of using configuration space for system with their interaction force depends explicitly on the velocity of the bodies. In addition, for these types of systems it is shown that their partition function can be well defined in the configuration space but it is not defined in the phase space, or they can bring about different results, bringing the possibility of experimental verification of the formulation of Statistical Mechanics in the configuration space.

シロウ イシカワ, Shiro Ishikawa, 史郎 石川

9.1 Statistical measurements (W∗-algebraic formulation) 9.2 The relation among systems (Proclaimʷ∗2 in SMTʷ∗) 9.3 Quantum mechanics in B(L²(R)) 9.4 The method of moments 9.5 Principal components analysis in MT

Keith S. Stowe

Shigeji Fujita, Kei Ito, Salvador Godoy

Nikola Burić, Istok P. Mendaš, Duska B Popovic +2 more

General statistical ensembles in the Hamiltonian formulation of hybrid quantum-classical systems are analyzed. It is argued that arbitrary probability densities on the hybrid phase space must be considered as the class of possible physically distinguishable statistical ensembles of hybrid systems. Nevertheless, statistical operators associated with the hybrid system and with the quantum subsystem can be consistently defined. Dynamical equations for the statistical operators representing the mixed states of the hybrid system and its quantum subsystem are derived and analyzed. In particular, these equations irreducibly depend on the total probability density on the hybrid phase space.