Starting from Bloch equation for a canonical ensemble, we deduce a set of hierarchy equations for the reduced statistical density operator for an identical many-body system with two-body interaction. They provide a law according to which the reduced density operator varies in temperature. By definition of the reduced density operator in Fock space for a grand canonical ensemble, we also obtain ...

Starting from Bloch equation for a canonical ensemble, we deduce a set of hierarchy equations for the reduced statistical density operator for an identical many-body system with two-body interaction. They provide a law according to which the reduced density operator varies in temperature. By definition of the reduced density operator in Fock space for a grand canonical ensemble, we also obtain ...

The Preisach operator and its variants have been successfully used in the modeling of a physical system with hysteresis. In an application, one has to determine the density function describing the Preisach operator from measurements. In our earlier work, we described a regularization method to obtain an approximation to the density function with limited measurements. In this paper, we describe ...

A new derivation of quantum stochastic differential equation for the evolution operator in the low density limit is presented. We use the distribution approach and derive a new algebra for quadratic master fields in the low density limit by using the energy representation. We formulate the stochastic golden rule in the low density limit case for a system coupling with Bose field via quadratic i...

The kinetic energy of a multi-particle system is described by the one-particle density matrix τ(x,y). Alongside γ(x,y) it one key objects in quantum-mechanical approximation schemes. We prove asymptotic formula λk∼(Bk)−2, B⩾0, as k→∞, for eigenvalues λk self-adjoint operator T⩾0 with kernel