On the description of noise in quantum systems

A formalism of probability operators which generalizes the notion of density operator is introduced into the theory of noisy quantum systems. The Markov property and the connexion between Heisenberg and Schrödinger picture for systems undergoing an irreversible change are discussed in detail. The probability-operator treatment of noise is related to the Langevin method discussed byLax through a generalized Einstein-relation. The master equation for the quantum mechanical oscillator with linear damping is written down in a Fokker-Planck-type approximation. By means of the Einstein-relation the coefficients in the Fokker-Planck-equation are related to the parameters in the phenomenological equations.     

On the relativistic description of two-quark systems

We present a comparison of relativistic and nonrelativistic calculations of two quark systems in a potential model. It turns out that different presumptions concerning the confinement potential give better agreement in the relativistic approximation than the nonrelativistic approach although there is a certain disagreement with heavy quarkonium perhaps due to a simple potential chosen.     

Operator properties of generalized coherent state systems

The main properties of standard quantum mechanical coherent states and the two generalizations of Klauder and of Perelomov are reviewed. For a system of generalized coherent states in the latter sense, necessary and sufficient conditions for existence of a diagonal coherent stable representation for all Hilbert-Schmidt operators are obtained. The main ingredients are Clebsch-Gordan theory and induced representation theory.     

Quantum logical description of two-particle systems

The quantum logical way of simulating quantum systems by automata is considered for two-particle systems. As an example, the EPR experiment with two spin-1/2 particles is considered and the violation of Bell's inequalities is demonstrated. Some methodological implications of the proposed approach are discussed.     

Statistical description of nonequilibrium self-gravitating systems

Self-gravitating systems are non-equilibrium a priori. A new approach is proposed, which employs a non-equilibrium statistical operator that takes account inhomogeneous distribution of particles and temperature. The method involves a saddle-point procedure to find the dominant contributions to the partition function, thus obtaining all thermodynamic parameters of the system. Probable peculiar features in the behavior of the self-gravitating systems are considered for various conditions. The equation of state for self-gravitating systems has been determined. A new length of the statistical instability is obtained for a real gravitational system, as are parameters of the spatially inhomogeneous distribution of particles and temperature.     

Boson description of many-exciton systems in polar semiconductors

Using a unitary transformation the Hamiltonian of interacting polar excitons is established. Two representative states of the many-exciton systems, the biexciton and the dielectric excitonic liquid are discussed for the materials CdS, CuCl and CuBr.     

Phase space description of vignetting in optical systems

A general theory of vignetting in real optical systems has been developed. Considered a beam of light rays limited by a field stop, an aperture stop inside of the real optical system (aberration vignetting) and a stop outside of it (natural vignetting). It is shown that each of these 2D-stops can be replaced by a virtual 4D-phase stop, and the result stop for 4D-phase result stops is their intersection. In case of an axially-symmetrical optical system with circular stop openings all phase stops are solids of revolution and can be fully characterized by their meridional cross sections in a 3D-space, which can be easily drawn.     

Inclusion of the causality principle in the dynamical description of nonequilibrium systems

In the nonequilibrium-statistical-operator (NSO) method a correction to the Hamiltonian of a system is found, corresponding to a source in the Liouville equation, which destroys the invariance of this equation with respect to time reversal. Analysis of this correction enables one to conclude that the forces leading to the irreversible behavior of a system are of an essentially nonpotential nature. Inclusion of the causality principle in the Hamiltonian of a system also makes it possible to give a new representation of the NSO.     

On the exact mean-field description of continuous quantum systems in equilibrium

The thermodynamic limit of free energy density is investigated for quantum systems of n particles obeying Boltzmann, Fermi and Bose statistics, interacting via spin-independent 2-body bounded separable potentials and confined to a bounded region Λ ? R^v. The technique used exploits the Feynman-Kac theorem in finite volume and the saddle-point method of Tindemans and Capel. It is shown that the limiting free energy density of such systems is equal to that of a system of noninteracting particles subject to a mean field which is equal to the averaged 2-body interaction. The equations for the mean field of n particles obeying Boltzmann, Fermi or Bose statistics represent self-consistent field problems and their forms comply with the well-known theorems on mean occupation numbers of single-particle eigenstates of ideal quantum gases at inverse temperature β.     

A fully relativistic description of the hyperfine interaction in magnetic systems

Based on the spin-polarized version of the multiple scattering theory, a relativistically correct formulation for the Green’s function describing the electronic structure of magnetic metallic systems has been derived. By this way, orbital contributions to the magnetic moment and, for the first time, to the hyperfine fields, which are caused by an unquenching of the orbital momentum due to spin-orbit coupling, were accessible to a calculation. In the case of Fe, Co and Ni, it has been found, that the corresponding non-s-contributions to the hyperfine field of the conduction electrons stem nearly exclusively from the d-electrons, are positive and of the same order of magnitude as the s-part of the conduction band contribution to the total hyperfine field. In all three cases these large non-s-hyperfine fields compensate the relativistic enhancement of the (Fermi contact) s-hyperfine field compared to a non-relativistic calculation, leading to theoretical hyperfine fields which are below the experimental ones. At the moment, it cannot be decided whether this discrepancy is caused by the neglect of the non-s-contributions of the core electrons or shortcomings of the local spin density approximation.     

Hamiltonian description and quantization of dissipative systems

Dissipative systems are described by a Hamiltonian, combined with a “dynamical matrix” which generalizes the simplectic form of the equations of motion. Criteria for dissipation are given and the examples of a particle with friction and of the Lotka-Volterra model are presented. Quantization is first introduced by translating generalized Poisson brackets into commutators and anticommutators. Then a generalized Schrödinger equation expressed by a dynamical matrix is constructed and discussed.     

Coordinate-space Hartree-Fock-Bogoliubov description of superfluid Fermi systems

Properties of strongly interacting, two-component finite Fermi systems are discussed within the recently developed coordinate-space Hartree-Fock-Bogoliubov (HFB) code HFB-AX. This solver is capable of treating the salient features of weakly bound and extremely deformed systems. Two illustrative examples are presented: i) neutron-rich deformed Mg isotopes, and ii) spin-polarized atomic condensates in a strongly deformed harmonic trap.