A semiclassical approximation for matrix elements involving non-orthogonal bound states

We analyse the phase diagram of a lattice gas model with both condenseation and order-disorder phase transitions, when the system is confined between two walls. The gas-liquid transition is shifted into the, so called, capillary condensation. The crystallization, both from the gas and from the liquid, is also shifted from the bulk values, but the ordered structure is frustrated or enhanced depending on its commensuration with the walls separation, H. This produces a strong oscillatory dependence of the phase diagram with H.     

Is Hawking temperature modified by the quantum tunneling beyond semiclassical approximation

Hawking temperature of a static and spherically symmetric black hole beyond semiclassical approximation is studied. The calculations show us that different definition of the particle’s energy gives different Hawking temperature. However, we argue that the result obtained using the standard definition of the particle energy is reasonable because it keeps the validity of the first law of the thermodynamics, i.e., both the Hawking temperature and entropy are not modified by the quantum tunneling beyond semiclassical approximation. The result shows us that any hypothetical (^h/_2p){\hbar} corrections to the tunneling rate are to be interpreted not as quantum corrections to the Hawking temperature but as fluctuations about a thermal background.     

A semiclassical approach to the ground state and density oscillations of quantum dots

A semiclassical Thomas–Fermi method, including a Weizsäcker gradient term, is implemented to describe ground states of two-dimensional nanostructures of arbitrary shape. Time-dependent density oscillations are addressed in the same spirit using the corresponding semiclassical time-dependent equations. The validity of the approximations is tested, both for ground state and density oscillations, compared with the available microscopic Kohn–Sham solutions.     

Neutrons in the classically forbidden region in neutron-rich nucleus 68Ca

Neutrons tunneling to the classically forbidden (CF) region in the neutron-rich nucleus 68Ca are invest-igated in the Skyrme Hartree-Fock (HF) and Hartree-Fock-...     

A density matrix approach to the Goldanskii-Karyagin effect

A density matrix formalism has been introduced to describe the perturbation of the Mössbauer line intensities caused by the anisotropic recoilless fraction in random absorbers. General properties of the matrix elements are discussed and relationships between thermal tensors and density matrices are investigated with the attention focused on the possibility to extract as much information about the thermal tensors as possible from the observed line intensities. It is shown, that quartic (anharmonic) anisotropy may be observable in quadrupolarly dominated transitions under favourable conditions.     

A simple approximation for the nuclear density matrix

We propose a new approximation for the nuclear density matrix based on the Density Matrix Expansion (DME) of Negele and Vautherin. When applied to a number of simple problems it gives better results than the Slater and the truncated DME approximations.     

Random matrix theory and equilibrium statistics for the quasienergies of classically chaotic systems

We calculate thek-level correlation function for the eigenphases of theN-dimensional Floquet operator of kicked dynamics whose classical counterpart is chaotic in the limitN by applying standard equilibrium statistical mechanics to a fictitiousN-particle system which is constructed from the eigenvalue equation of the Floquet operator and show that they become equal to those of random matrices from the circular ensemble associated with the appropriate universality class.     

Validity of the semiclassical kinetic energy density functional for deformed nuclear shapes

We investigate the semiclassical kinetic energy density functionalτ[ρ] for deformed nuclear shapes. Using Strutinsky-averaged quantities as reference, we demonstrate that the functionalτ[ρ] is able to reproduce the averaged kinetic energies very accurately, even at very large deformations.     

A semiclassical theory of the laser

The kinetic equation for the density matrix is used to study the response of a laser system to a monochromatic electromagnetic standing wave. Steady-state laser operation is studied through joint solution of Maxwell's equations and the equations for the density matrix. Allowances are made for nonuniformities in the radiating medium modulated by the field and for the motion of the radiating particles. Steady-state operating conditions and oscillation thresholds for gas and solid-state lasers are compared.     

A simple Gaussian approximation for the one-body density matrix

A simple form of the nonlocal one-body density matrix ϱ(r, r′) is proposed whose parameters are determined by imposing the correct local semiclassical kinetic energy density and the projector character of ϱ in an integrated form. The validity of this approach is assessed for physical quantities sensitive to the nonlocal nature of the density matrix such as the momentum distribution in the nucleus, the exchange energies of the Gogny and the Coulomb force and the two-body center-of-mass correction for various nuclei,     

A scattering matrix approach to quantum pumping: beyond the small-AC-driving-amplitude limit

In the adiabatic and weak-modulation quantum pump, net electron flow is driven from one reservoir to another by absorbing or emitting an energy quantum hω from or to the reservoirs. This paper considers high-order dependence of the scattering matrix on the time. Non-sinusoidal behaviour of strong pumping is revealed. The relation between the pumped current and the ac driving amplitude varies from power of 2, 1 to 1/2 when stronger modulation is exerted. Open experimental observation can be interpreted by multi-energy-quantum-related processes.     

Quantum corrections to the semiclassical level density of the circular disk in homogeneous magnetic fields

In the semiclassical trace formula for the level density of a circular disk in homogeneous magnetic fields, quantum corrections to the Maslov phase have been shown to be important in strong fields. In this article further quantum corrections are considered, namely, grazing corrections which are relevant for whispering-gallery orbits, and a uniform approximation to the bifurcation points in strong fields is applied. Both corrections are shown to have a surprisingly small effect on the semiclassical level density. Implementing those corrections requires a technique different from the common Gaussian smoothing in the numerical evaluation of the trace formula. The appropriate generalization is presented. 1997 Elsevier Science B.V. All rights reserved.     

A direct determination of the density matrix in a nuclear system

We introduce an iterative steepest descent approach to determine directly the best one-body density matrix which minimizes the total energy of a nuclear system in the Hartree-Fock approximation, without solving the HF equations. An application is shown to the ²⁰Ne deformed nucleus with a Skyrme interaction. The possibility to introduce external shape constraints to describe general form of deformations is discussed.