arXiv subjects
Publications and source records attributed to Aurel Bulgac.
The inner crust of neutron stars consists of nuclei of various shapes immersed in a neutron gas and stabilized by the Coulomb interaction in the form of a crystal lattice. The scattering of neutrons on nuclear inhomegeneities leads to the quantum correction to the total energy of the system. This correction resembles the Casimir energy and turns out to have a large influence on the structure of the crust.
We introduce a natural and simple to implement renormalization scheme of the Hartree-Fock-Bogoliubov (HFB) equations for the case of zero range pairing interaction. This renormalization scheme proves to be equivalent to a simple energy cut-off with a position or density dependent running coupling constant. Subsequently, we present self-consistent HFB calculations with a full consideration of the continuum of long chains of spherical tin and lead nuclei (essentially from one drip line to another) using the SLy5 interaction. In the pairing channel we use a zero range interaction, treated by means of this new regularization scheme.
We introduce a natural and simple to implement renormalization scheme of the Hartree-Fock-Bogoliubov (HFB) equations for the case of zero range pairing interaction. This renormalization scheme proves to be equivalent to a simple energy cut-off with a position dependent running coupling constant.
Using ensembles of two, three and four spheres immersed in a fermionic background we evaluate the (integrated) density of states and the Casimir energy. We thus infer that for sufficiently smooth objects, whose various geometric characteristic lengths are larger then the Fermi wave length one can use the simplest semiclassical approximation (the contribution due shortest periodic orbits only) to evaluate the Casimir energy. We also show that the Casimir energy for several objects can be represented fairly accurately as a sum of pairwise Casimir interactions between pairs of objects.
Some general features of the spectrum of the Hartree-Fock-Bogoliubov equations are examined. Special attention is paid to the asymptotic behavior of the single quasiparticle wave functions (s.qp.w.fs.), matter density distribution and density of the pair condensate. It is shown that due to the coupling between hole and particle states,the deeply bound hole states acquire a width and have to be treated as continuum states. The proper normalization of the s.qp.w.fs. is discussed.
We analyze the character of the shell effects/Casimir energy in inhomogeneous fermion systems. We estimate magnitude of the shell effects and discuss their dependence on a number of physical parameters (geometry, fermion density, temperature).
We briefly review the significance of quantum corrections in the total energy of systems with voids: bubble nuclei, atomic clusters and the inhomogeneous phase of neutron stars.
Homogeneous neutron matter at subnuclear densities becomes unstable towards the formation of inhomogeneities. Depending on the average value of the neutron density one can observe the appearance of either bubbles, rods, tubes or plates embeded in a neutron gas. We estimate the quantum corrections to the ground state energy (which could be termed either shell correction or Casimir energy) of such phases of neutron matter. The calculations are performed by evaluating the contribution of the shortest periodic orbits in the Gutzwiller trace formula for the density of states. The magnitude of the quantum corrections to the ground state energy of neutron matter are of the same order as the energy differences between various phases.
We present a microscopic approach to quantum dissipation and sketch the derivation of the kinetic equation describing the evolution of a simple quantum system in interaction with a complex quantum system. A typical quantum complex system is modeled by means of parametric banded random matrices coupled to the subsystem of interest. We do not assume the weak coupling limit and allow for an independent dynamics of the ``reservoir''. We discuss the reasons for having a new theoretical approach and the new elements introduced by us. The present approach incorporates known limits and previous results, but at the same time includes new cases, previously never derived on a microscopic level. We briefly discuss the kinetic equation and its solution for a particle in the absence of an external field.
Stochastic processes are shown to emerge from the time evolution of complex quantum systems. Using parametric, banded random matrix ensembles to describe a quantum chaotic environment, we show that the dynamical evolution of a particle coupled to such environments displays a variety of stochastic behaviors, ranging from turbulent diffusion to Lévy processes and Brownian motion. Dissipation and diffusion emerge naturally in the stochastic interpretation of the dynamics. This approach provides a derivation of a fractional kinetic theory in the classical limit and leads to classical Lévy dynamics.
The positioning of a bubble inside a many fermion system does not affect the volume, surface or curvature terms in the liquid drop expansion of the total energy. Besides possible Coulomb effects, the only other contribution to the ground state energy of such a system arises from shell effects. We show that the potential energy surface is a rather shallow function of the displacement of the bubble from the center and in most cases the preferential position of a bubble is off center. Systems with bubbles are expected to have bands of extremely low lying collective states, corresponding to various bubble displacements.
A theoretically consistent approach to the calculation of the Coulomb correlation corrections to the single--particle energies is presented. New contributions to the single--particle energies previously overlooked in the literature are now identified and taken into account. We show that the interplay between the Coulomb interaction and the strong interaction, which is enhanced in the nuclear surface, leads to an upward shift of the proton single--particle levels. This shift affects the position of the calculated proton drip line, a shift towards decreasing $Z$. We describe briefly a similar mechanism which is at work for neutron levels. The same mechanism is responsible for significant corrections to the mass difference of the mirror nuclei (Nolen--Schiffer anomaly) and to the effective proton mass.
A new algorithm for determining the eigenstates of n-dimensional billiards is presented. It is based on the application of the Cauchy theorem for the determination of the null space of the boundary overlap matrix. The method is free from the limitations associated with the shape of the billiard and could be applied even for nonconvex geometries where other algorithms face difficulties. Moreover it does not suffer from the existence of eigenvalue degeneracies which is another serious shortcoming of many methods. In the paper we apply the algorithm to a few simple cases where the analytical solutions exist. Numerical solutions have been investigated for the case of annular billiard.
Exotic stochastic processes are shown to emerge in the quantum evolution of complex systems. Using influence function techniques, we consider the dynamics of a system coupled to a chaotic subsystem described through random matrix theory. We find that the reduced density matrix can display dynamics given by Lévy stable laws. The classical limit of these dynamics can be related to fractional kinetic equations. In particular we derive a fractional extension of Kramers equation.
The positioning of one or more bubbles inside a many fermion or boson system, does not affect the volume, surface or curvature terms in the liquid drop expansion of the total energy. If Coulomb effects are irrelevant, the only contribution to the ground state energy of a system with one or more voids arises from quantum effects, which is similar to the Casimir effect in vacuum or in critical phenomena. We discuss the characteristics of such systems, the interplay among various effects, such as shell corrections and chaotic behavior, and briefly mention the role of the temperature and pairing.
We present a theory for the dynamical evolution of a quantum system coupled to a complex many-body intrinsic system/environment. By modelling the intrinsic many-body system with parametric random matrices, we study the types of effective stochastic models which emerge from random matrix theory. Using the Feynman-Vernon path integral formalism, we derive the influence functional and obtain either analytical or numerical solutions for the time evolution of the entire quantum system. We discuss thoroughly the structure of the solutions for some representative cases and make connections to well known limiting results, particularly to Brownian motion, Kramers classical limit and the Caldeira-Leggett approach.
We study a quantum particle propagating through a ``quantum mechanically chaotic'' background, described by parametric random matrices with only short range spatial correlations. The particle is found to exhibit turbulent-like diffusion under very general situations, without the apriori introduction of power law noise or scaling in the background properties.
A new method to obtain a local parameterization for the exchange term in the many--body electronic problem is presented. The approach amounts to the introduction of a coordinate dependent electron effective mass. Numerical results for metallic clusters in the jellium model are compared with other standard methods.