Chaotic Scattering with Resonance Enhancement

The passage of light or of electrons through a disordered medium is modified in the presence of resonances. We describe a simple model for this problem, and present first results.Comment: 13 pages, 2 figures, REVTEX. To appear in Nucl. Phys. A (1996

Persistent currents in n-fold twisted Moebius strips

We investigate the influence of the topology on generic features of the persistent current in n-fold twisted Moebius strips formed of quasi one--dimensional mesoscopic rings, both for free electrons and in the weakly disordered regime. We find that there is no generic difference between the persistent current for untwisted rings and for Moebius strips with an arbitrary number of twists.Comment: 7 pages, 2 figure

Statistical fluctuations of ground-state energies and binding energies in nuclei

The statistical fluctuations of the ground-state energy and of the binding energy of nuclei are investigated using both perturbation theory and supersymmetry. The fluctuations are induced by the experimentally observed stochastic behavior of levels in the vicinity of neutron threshold. The results are compared with a recent analysis of binding-energy fluctuations by Bohigas and Leboeuf, and with theoretical work by Feshbach et al.Comment: 8 pages, 2 figure

Asymptotic Expansion for the Magnetoconductance Autocorrelation Function

We complement a recent calculation (P.B. Gossiaux and the present authors, Ann. Phys. (N.Y.) in press) of the autocorrelation function of the conductance versus magnetic field strength for ballistic electron transport through microstructures with the shape of a classically chaotic billiard coupled to ideal leads. The function depends on the total number M of channels and the parameter t which measures the difference in magnetic field strengths. We determine the leading terms in an asymptotic expansion for large t at fixed M, and for large M at fixed t/M. We compare our results and the ones obtained in the previous paper with the squared Lorentzian suggested by semiclassical theory.Comment: submitted to Annals of Physics (N.Y.

Origin of chaos in the spherical nuclear shell model: role of symmetries

To elucidate the mechanism by which chaos is generated in the shell model, we compare three random-matrix ensembles: the Gaussian orthogonal ensemble, French's two-body embedded ensemble, and the two-body random ensemble (TBRE) of the shell model. Of these, the last two take account of the two-body nature of the residual interaction, and only the last, of the existence of conserved quantum numbers like spin, isospin, and parity. While the number of independent random variables decreases drastically as we follow this sequence, the complexity of the (fixed) matrices which support the random variables, increases even more. In that sense we can say that in the TBRE, chaos is largely due to the existence of (an incomplete set of) symmetries.Comment: 21 pages, 3 ps-figures. Revised version to appear in Nucl. Phys. A. New text and figures adde

Spectral Properties of the k-Body Embedded Gaussian Ensembles of Random Matrices

We consider $m$ spinless Fermions in $l > m$ degenerate single-particle levels interacting via a $k$-body random interaction with Gaussian probability distribution and $k <= m$ in the limit $l$ to infinity (the embedded $k$-body random ensembles). We address the cases of orthogonal and unitary symmetry. We derive a novel eigenvalue expansion for the second moment of the Hilbert-space matrix elements of these ensembles. Using properties of the expansion and the supersymmetry technique, we show that for $2k > m$, the average spectrum has the shape of a semicircle, and the spectral fluctuations are of Wigner-Dyson type. Using a generalization of the binary correlation approximation, we show that for $k << m << l$, the spectral fluctuations are Poissonian. This is consistent with the case $k = 1$ which can be solved explicitly. We construct limiting ensembles which are either fully integrable or fully chaotic and show that the $k$-body random ensembles lie between these two extremes. Combining all these results we find that the spectral correlations for the embedded ensembles gradually change from Wigner-Dyson for $2k > m$ to Poissonian for $k << m << l$.Comment: 44 pages, 3 postscript figures, revised version including a new proof of one of our main claim

Crossing of two Coulomb-Blockade Resonances

We investigate theoretically the transport of non--interacting electrons through an Aharanov--Bohm (AB) interferometer with two quantum dots (QD) embedded into its arms. In the Coulomb-blockade regime, transport through each QD proceeds via a single resonance. The resonances are coupled through the arms of the AB device but may also be coupled directly. In the framework of the Landauer--Buttiker approach, we present expressions for the scattering matrix which depend explicitly on the energies of the two resonances and on the AB phase. We pay particular attention to the crossing of the two resonances.Comment: 15 pages, 1 figur

Correlation Widths in Quantum--Chaotic Scattering

An important parameter to characterize the scattering matrix S for quantum-chaotic scattering is the width Gamma_{corr} of the S-matrix autocorrelation function. We show that the "Weisskopf estimate" d/(2pi) sum_c T_c (where d is the mean resonance spacing, T_c with 0 <= T_c <= 1 the "transmission coefficient" in channel c and where the sum runs over all channels) provides a very good approximation to Gamma_{corr} even when the number of channels is small. That same conclusion applies also to the cross-section correlation function

The chiral phase transition in a random matrix model with molecular correlations

The chiral phase transition of QCD is analyzed in a model combining random matrix elements of the Dirac operator with specially chosen non-random ones. The special form of the latter is motivated by the assumption that the fermionic quasi-zero modes associated with instanton and anti-instanton configurations determine the chiral properties of QCD. Our results show that the degree of correlation between these modes plays the decisive role. To reduce the value of the chiral condensate by more than a factor of 2 about 95 percent of the instantons and anti-instantons must form so-called molecules. This conclusion agrees with numerical results of the Stony Brook group.Comment: published version (minor changes in text and one additional reference, one misprint in published version corrected); 12 pages including 1 figure, LaTeX with elsart.sty and psfig.st

Spectral Properties of the k-Body Embedded Gaussian Ensembles of Random Matrices for Bosons

We consider $m$ spinless Bosons distributed over $l$ degenerate single-particle states and interacting through a $k$-body random interaction with Gaussian probability distribution (the Bosonic embedded $k$-body ensembles). We address the cases of orthogonal and unitary symmetry in the limit of infinite matrix dimension, attained either as $l \to \infty$ or as $m \to \infty$. We derive an eigenvalue expansion for the second moment of the many-body matrix elements of these ensembles. Using properties of this expansion, the supersymmetry technique, and the binary correlation method, we show that in the limit $l \to \infty$ the ensembles have nearly the same spectral properties as the corresponding Fermionic embedded ensembles. Novel features specific for Bosons arise in the dense limit defined as $m \to \infty$ with both $k$ and $l$ fixed. Here we show that the ensemble is not ergodic, and that the spectral fluctuations are not of Wigner-Dyson type. We present numerical results for the dense limit using both ensemble unfolding and spectral unfolding. These differ strongly, demonstrating the lack of ergodicity of the ensemble. Spectral unfolding shows a strong tendency towards picket-fence type spectra. Certain eigenfunctions of individual realizations of the ensemble display Fock-space localization.Comment: Minor corrections; figure 5 slightly modified (30 pages, 6 figs