Chiral Symmetry Breaking and the Dirac Spectrum at Nonzero Chemical Potential

The relation between the spectral density of the QCD Dirac operator at nonzero baryon chemical potential and the chiral condensate is investigated. We use the analytical result for the eigenvalue density in the microscopic regime which shows oscillations with a period that scales as 1/V and an amplitude that diverges exponentially with the volume $V=L^4$. We find that the discontinuity of the chiral condensate is due to the whole oscillating region rather than to an accumulation of eigenvalues at the origin. These results also extend beyond the microscopic regime to chemical potentials $\mu \sim 1/L$.Comment: 4 pages, 1 figur

Statistics of eigenfunctions in open chaotic systems: a perturbative approach

We investigate the statistical properties of the complexness parameter which characterizes uniquely complexness (biorthogonality) of resonance eigenstates of open chaotic systems. Specifying to the regime of isolated resonances, we apply the random matrix theory to the effective Hamiltonian formalism and derive analytically the probability distribution of the complexness parameter for two statistical ensembles describing the systems invariant under time reversal. For those with rigid spectra, we consider a Hamiltonian characterized by a picket-fence spectrum without spectral fluctuations. Then, in the more realistic case of a Hamiltonian described by the Gaussian Orthogonal Ensemble, we reveal and discuss the r\^ole of spectral fluctuations

Distribution of Resonance Widths and Dynamics of Continuum Coupling

We analyze the statistics of resonance widths in a many-body Fermi system with open decay channels. Depending on the strength of continuum coupling, such a system reveals growing deviations from the standard chi-square (Porter-Thomas) width distribution. The deviations emerge from the process of increasing interaction of intrinsic states through common decay channels; in the limit of perfect coupling this process leads to the super-radiance phase transition. The width distribution depends also on the intrinsic dynamics (chaotic vs regular). The results presented here are important for understanding the recent experimental data concerning the width distribution for neutron resonances in nuclei.Comment: 5 pages, submitted to Phys. Rev. Let

Superconductor-proximity effect in chaotic and integrable billiards

We explore the effects of the proximity to a superconductor on the level density of a billiard for the two extreme cases that the classical motion in the billiard is chaotic or integrable. In zero magnetic field and for a uniform phase in the superconductor, a chaotic billiard has an excitation gap equal to the Thouless energy. In contrast, an integrable (rectangular or circular) billiard has a reduced density of states near the Fermi level, but no gap. We present numerical calculations for both cases in support of our analytical results. For the chaotic case, we calculate how the gap closes as a function of magnetic field or phase difference.Comment: 4 pages, RevTeX, 2 Encapsulated Postscript figures. To be published by Physica Scripta in the proceedings of the "17th Nordic Semiconductor Meeting", held in Trondheim, June 199

A study of nuclei of astrophysical interest in the continuum shell model

We present here the first application of realistic shell model (SM) including coupling between many-particle (quasi-)bound states and the continuum of one-particle scattering states to the spectroscopy of 8B and to the calculation of astrophysical factors in the reaction 7Be(p,gamma)8B.Comment: 9 pages incl. 3 figures, LaTeX with iopart class and epsf. Invited talk at the Int. Workshop on Physics with Radioactive Nuclear Beams, Jan. 12-17, 1998, Puri, India. Shortened version will be published in proceedings to apear as a separate J. Phys. G volum

Interfering Doorway States and Giant Resonances. II: Transition Strengths

The mixing of the doorway components of a giant resonance (GR) due to the interaction via common decay channels influences significantly the distribution of the multipole strength and the energy spectrum of the decay products of the GR. The concept of the partial widths of a GR becomes ambiguous when the mixing is strong. In this case, the partial widths determined in terms of the $K$- and $S$-matrices must be distinguished. The photoemission turns out to be most sensitive to the overlapping of the doorway states. At high excitation energies, the interference between the doorway states leads to a restructuring towards lower energies and apparent quenching of the dipole strength.Comment: 17 pages, LaTeX, 5 figures as JPEG, to appear in PRC (July 1997

Overtones of Isoscalar Giant Resonances in medium-heavy and heavy nuclei

A semi-microscopic approach based on both the continum-random-phase-approximation (CRPA) method and a phenomenological treatment of the spreading effect is extended and applied to describe the main properties (particle-hole strength distribution, energy-dependent transition density, partial direct-nucleon-decay branching ratios) of the isoscalar giant dipole, second monopole, and second quadrupole resonances. Abilities of the approach are checked by description of gross properties of the main-tone resonances. Calculation results obtained for the resonances in a few singly- and doubly-closed-shell nuclei are compared with available experimental data.Comment: 12 pages, 14 figures, submitted to Phys. Rev.

Fano interference and cross-section fluctuations in molecular photodissociation

We derive an expression for the total photodissociation cross section of a molecule incorporating both indirect processes that proceed through excited resonances, and direct processes. We show that this cross section exhibits generalized Beutler-Fano line shapes in the limit of isolated resonances. Assuming that the closed system can be modeled by random matrix theory, we derive the statistical properties of the photodissociation cross section and find that they are significantly affected by the direct processes. We identify a unique signature of the direct processes in the cross-section distribution in the limit of isolated resonances.Comment: 4 pages, 4 figure

Internal chaos in an open quantum system: From Ericson to conductance fluctuations

The model of an open Fermi-system is used for studying the interplay of intrinsic chaos and irreversible decay into open continuum channels. Two versions of the model are characterized by one-body chaos coming from disorder or by many-body chaos due to the inter-particle interactions. The continuum coupling is described by the effective non-Hermitian Hamiltonian. Our main interest is in specific correlations of cross sections for various channels in dependence on the coupling strength and degree of internal chaos. The results are generic and refer to common features of various mesoscopic objects including conductance fluctuations and resonance nuclear reactions.Comment: 10 pages, 5 figure

Observation of a Chiral State in a Microwave Cavity

A microwave experiment has been realized to measure the phase difference of the oscillating electric field at two points inside the cavity. The technique has been applied to a dissipative resonator which exhibits a singularity -- called exceptional point -- in its eigenvalue and eigenvector spectrum. At the singularity, two modes coalesce with a phase difference of $\pi/2 .$ We conclude that the state excited at the singularity has a definitiv chirality.Comment: RevTex 4, 5 figure