Microscopic open systems

Steven M. Valone

Ensemble averages are an approximation technique for connecting macroscopic and microscopic properties of a system. For systems open with respect to exchange of particles with a bath, the microscopic states are those with integer numbers of particles. When a property of the open system is represented as an ensemble average over these microscopic states, self-consistency dictates several implications for the properties of both for open-system energy density functionals and the integer-state functionals describing the microscopic states. The first is that each integer-state energy density functional is a functional of the original type discovered by Levy. Another is that the dependence of the open-system functional on the ensemble density is linear whereas the dependence of the integer-state functional is decidedly nonlinear. Finally, the derivative discontinuity behavior with respect to particle number of some open-system density functionals appears to be connected to the long-range behavior of the effective external potentials of the integer-state functionals governing the interactions among subsystems in the ensemble.

L. A. Lugiato

Ilya Sinayskiy, Francesco Petruccione

A microscopic derivation of an open quantum walk of a three level system on a two node graph is presented.The explicit form of the "quantum coin" operators is derived.

Hiroki Majima, Akira Suzuki

A microscopic description of an open system is generally expressed by the Hamiltonian of the form: H tot = H sys + H environ + H sys − environ . We developed a microscopic theory of entropy and derived a general formula, so-called "entropy-Hamiltonian relation" (EHR), that connects the entropy of the system to the interaction Hamiltonian represented by H sys - environ for a nonequilibrium open quantum system. To derive the EHR formula, we mapped the open quantum system to the representation space of the Liouville-space formulation or thermo field dynamics (TFD), and thus worked on the representation space := ⊗ , where denotes the ordinary Hilbert space while the tilde Hilbert space conjugates to . We show that the natural transformation (mapping) of nonequilibrium open quantum systems is accomplished within the theoretical structure of TFD. By using the obtained EHR formula, we also derived the equation of motion for the distribution function of the system. We demonstrated that by knowing the microscopic description of the interaction, namely, the specific form of H sys − environ on the representation space , the EHR formulas enable us to evaluate the entropy of the system and to gain some information about entropy for nonequilibrium open quantum systems.

H. J. Carmichael