Universal behaviour of ideal and interacting quantum gases in two dimensions

I discuss ideal and interacting quantum gases obeying general fractional exclusion statistics. For systems with constant density of single-particle states, described in the mean field approximation, the entropy depends neither on the microscopic exclusion statistics, nor on the interaction. Such systems are called {\em thermodynamically equivalent} and I show that the microscopic reason for this equivalence is a one-to-one correspondence between the excited states of these systems. This provides a method, different from the bosonisation technique, to transform between systems of different exclusion statistics. In the last section the macroscopic aspects of this method are discussed. In Appendix A I calculate the fluctuation of the ground state population of a condensed Bose gas in grandcanonical ensemble and mean field approximation, while in Appendix B I show a situation where although the system exhibits fractional exclusion properties on microscopic energy intervals, a rigorous calculation of the population of single particle states reveals a condensation phenomenon. This also implies a malfunction of the usual and simplified calculation technique of the most probable statistical distributions.Comment: About 14 journal pages, with 1 figure. Changes: Body of paper: same content, with slight rephrasing. Apendices are new. In the original submission I just mentioned the condensation, which is now detailed in Appendix B. They were intended for a separate paper. Reason for changes: rejection from Phys. Rev. Lett., resubmission to J. Phys. A: Math. Ge

On the difference between proton and neutron spin-orbit splittings in nuclei

The latest experimental data on nuclei at $^{132}$Sn permit us for the first time to determine the spin-orbit splittings of neutrons and protons in identical orbits in this neutron-rich doubly-magic region and compare the case to that of $^{208}$Pb. Using the new results, which are now consistent for the two neutron-rich doubly magic regions, a theoretical analysis defines the isotopic dependence of the mean field spin-orbit potential and leads to a simple explicit expression for the difference between the spin-orbit splittings of neutrons and protons. The isotopic dependence is explained in the framework of different theoretical approaches.Comment: 8 pages, revte

On the isospin dependence of the mean spin-orbit field in nuclei

By the use of the latest experimental data on the spectra of $^{133}$Sb and $^{131}$Sn and on the analysis of properties of other odd nuclei adjacent to doubly magic closed shells the isospin dependence of a mean spin-orbit potential is defined. Such a dependence received the explanation in the framework of different theoretical approaches.Comment: 52 pages, Revtex, no figure

Classical antiferromagnet on a hyperkagome lattice

Motivated by recent experiments on Na_4Ir_3O_8 [Y. Okamoto, M. Nohara, H. Aruga-Katori, and H. Takagi, arXiv:0705.2821 (unpublished)], we study the classical antiferromagnet on a frustrated three-dimensional lattice obtained by selectively removing one of four sites in each tetrahedron of the pyrochlore lattice. This ``hyperkagome'' lattice consists of corner-sharing triangles. We present the results of large-N mean field theory and Monte Carlo computations on O(N) classical spin models. It is found that the classical ground states are highly degenerate. Nonetheless a nematic order emerges at low temperatures in the Heisenberg model (N=3) via ``order by disorder'', representing the dominance of coplanar spin configurations. Implications for ongoing experiments are discussed.Comment: 4 pages, 6 figures, published versio

An embedding potential definition of channel functions

We show that the imaginary part of the embedding potential, a generalised logarithmic derivative, defined over the interface between an electrical lead and some conductor, has orthogonal eigenfunctions which define conduction channels into and out of the lead. In the case of an infinitely extended interface we establish the relationship between these eigenfunctions and the Bloch states evaluated over the interface. Using the new channel functions, a well-known result for the total transmission through the conductor system is simply derived.Comment: 14 pages, 2 figure

Inverse problems for Schrodinger equations with Yang-Mills potentials in domains with obstacles and the Aharonov-Bohm effect

We study the inverse boundary value problems for the Schr\"{o}dinger equations with Yang-Mills potentials in a bounded domain $\Omega_0\subset\R^n$ containing finite number of smooth obstacles $\Omega_j,1\leq j \leq r$. We prove that the Dirichlet-to-Neumann operator on $\partial\Omega_0$ determines the gauge equivalence class of the Yang-Mills potentials. We also prove that the metric tensor can be recovered up to a diffeomorphism that is identity on $\partial\Omega_0$.Comment: 15 page

Relativistic Nuclear Energy Density Functionals: adjusting parameters to binding energies

We study a particular class of relativistic nuclear energy density functionals in which only nucleon degrees of freedom are explicitly used in the construction of effective interaction terms. Short-distance (high-momentum) correlations, as well as intermediate and long-range dynamics, are encoded in the medium (nucleon density) dependence of the strength functionals of an effective interaction Lagrangian. Guided by the density dependence of microscopic nucleon self-energies in nuclear matter, a phenomenological ansatz for the density-dependent coupling functionals is accurately determined in self-consistent mean-field calculations of binding energies of a large set of axially deformed nuclei. The relationship between the nuclear matter volume, surface and symmetry energies, and the corresponding predictions for nuclear masses is analyzed in detail. The resulting best-fit parametrization of the nuclear energy density functional is further tested in calculations of properties of spherical and deformed medium-heavy and heavy nuclei, including binding energies, charge radii, deformation parameters, neutron skin thickness, and excitation energies of giant multipole resonances.Comment: 53 pages, 23 figures, accepted for publication in Physical Review

A new approach to hyperbolic inverse problems II (Global step)

We study the inverse problem for the second order self-adjoint hyperbolic equation with the boundary data given on a part of the boundary. This paper is the continuation of the author's paper [E]. In [E] we presented the crucial local step of the proof. In this paper we prove the global step. Our method is a modification of the BC-method with some new ideas. In particular, the way of the determination of the metric is new.Comment: 21 pages, 2 figure