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H. A. Weidenmueller

Publications and source records attributed to H. A. Weidenmueller.

At least 19 recordsLinked to original sources
arXiv2014

Doorway States in the Random-Phase Approximation

By coupling a doorway state to a see of random background states, we develop the theory of doorway states in the framework of the random-phase approximation (RPA). Because of the symmetry of the RPA equations, that theory is radically different from the standard description of doorway states in the shell model. We derive the Pastur equation in the limit of large matrix dimension and show that the results agree with those of matrix diagonalization in large spaces. The complexity of the Pastur equation does not allow for an analytical approach that would approximately describe the doorway state. Our numerical results display unexpected features: The coupling of the doorway state with states of opposite energy leads to strong mutual attraction.

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arXiv2014

Open Problems in Applying Random-Matrix Theory to Nuclear Reactions

Problems in applying random-matrix theory (RMT) to nuclear reactions arise in two domains. To justify the approach, statistical properties of isolated resonances observed experimentally must agree with RMT predictions. That agreement is less striking than would be desirable. In the implementation of the approach, the range of theoretically predicted observables is too narrow.

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arXiv2014

Effective Field Theory for Finite Systems with Spontaneously Broken Symmetry

We extend effective field theory to the case of spontaneous symmetry breaking in genuinely finite quantum systems such as small superfluid systems, molecules or atomic nuclei, and focus on deformed nuclei. In finite superfluids, symmetry arguments alone relate the spectra of systems with different particle numbers. For systems with non-spherical intrinsic ground states such as atomic nuclei or molecules, symmetry arguments alone yield the universal features of the low-lying excitations as vibrations that are the heads of rotational bands. The low-lying excitations in deformed nuclei differ from those in molecules because of symmetry properties caused by pairing.

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arXiv2013

Universal Quantum Graphs

For time-reversal invariant graphs we prove the Bohigas-Giannoni-Schmit conjecture in its most general form: For graphs that are mixing in the classical limit, all spectral correlation functions coincide with those of the Gaussian Orthogonal Ensemble of random matrices. For open graphs, we derive the analogous identities for all S matrix correlation functions.

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arXiv2013

Universal Chaotic Scattering on Quantum Graphs

We calculate the S-matrix correlation function for chaotic scattering on quantum graphs and show that it agrees with that of random--matrix theory (RMT). We also calculate all higher S-matrix correlation functions in the Ericson regime. These, too, agree with RMT results as far as the latter are known. We concjecture that our results give a universal description of chaotic scattering.

math-ph↗
arXiv2011

Chaos in fermionic many-body systems and the metal-insulator transition

We show that finite Fermi systems governed by a mean field and a few-body interaction generically possess spectral fluctuations of the Wigner-Dyson type and are, thus, chaotic. Our argument is based on an analogy to the metal-insulator transition. We construct a sparse random-matrix ensemble ScE that mimics that transition. Our claim then follows from the fact that the generic random-matrix ensemble modeling a fermionic interacting many-body system is much less sparse than ScE.

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arXiv2011

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.

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arXiv2010

Spreading Widths of Doorway States

As a function of energy E, the average strength function S(E) of a doorway state is commonly assumed to be Lorentzian in shape and characterized by two parameters, the peak energy E_0 and the spreading width Gamma. The simple picture is modified when the density of background states that couple to the doorway state changes significantly in an energy interval of size Gamma. For that case we derive an approximate analytical expression for S(E). We test our result successfully against numerical simulations. Our result may have important implications for shell--model calculations.

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arXiv2010

Photonuclear Reactions induced by Intense Short Laser Pulses

A measurement of the decay in time of nuclei excited by an intense short laser pulse of energy E(0) yields the Fourier transform of the autocorrelation function of the associated scattering matrix. We determine the optimal length (in time) of the pulse and evaluate the time-decay function using random-matrix theory. That function is shown to contain information not otherwise available. We approximate that function in a manner that is useful for the analysis of data. For E(0) below the threshold energy E(n) of the first neutron channel, the time-decay function is exponential in time t while it is the product of an exponential and a power in t for E(0) > E(n). The comparison of the measured decay functions in both energy domains yields an unambiguous and novel test of random-matrix theory in nuclei.

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arXiv2010

Quantum Chaotic Scattering in Microwave Resonators

In a frequency range where a microwave resonator simulates a chaotic quantum billiard, we have measured moduli and phases of reflection and transmission amplitudes in the regimes of both isolated and of weakly overlapping resonances and for resonators with and without time-reversal invariance. Statistical measures for S-matrix fluctuations were determined from the data and compared with extant and/or newly derived theoretical results obtained from the random-matrix approach to quantum chaotic scattering. The latter contained a small number of fit parameters. The large data sets taken made it possible to test the theoretical expressions with unprecedented accuracy. The theory is confirmed by both, a goodness-of-fit-test and the agreement of predicted values for those statistical measures that were not used for the fits, with the data.

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arXiv2010

Random Matrices and Chaos in Nuclear Physics: Nuclear Reactions

The application of random-matrix theory (RMT) to compound-nucleus (CN) reactions is reviewed. An introduction into the basic concepts of nuclear scattering theory is followed by a survey of phenomenological approaches to CN scattering. The implementation of a random-matrix approach into scattering theory leads to a statistical theory of CN reactions. Since RMT applies generically to chaotic quantum systems, that theory is, at the same time, a generic theory of quantum chaotic scattering. It uses a minimum of input parameters (average S-matrix and mean level spacing of the CN). Predictions of the theory are derived with the help of field-theoretical methods adapted from condensed-matter physics and compared with those of phenomenological approaches. Thorough tests of the theory are reviewed, as are applications in nuclear physics, with special attention given to violation of symmetries (isospin, parity) and time-reversal invariance.

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arXiv2009

Cross-Section Fluctuations in Chaotic Scattering

For the theoretical prediction of cross-section fluctuations in chaotic scattering, the cross-section autocorrelation function is needed. That function is not known analytically. Using experimental data and numerical simulations, we show that an analytical approximation to the cross-section autocorrelation function can be obtained with the help of expressions first derived by Davis and Boose. Given the values of the average S-matrix elements and the mean level density of the scattering system, one can then reliably predict cross-section fluctuations.

nlin.CD↗
arXiv2009

Induced Violation of Time-Reversal Invariance in the Regime of Weakly Overlapping Resonances

We measure the complex scattering amplitudes of a flat microwave cavity (a "chaotic billiard"). Time-reversal T-invariance is partially broken by a magnetized ferrite placed within the cavity. We extend the random-matrix approach to T-violation in scattering, fit some of the properties of the scattering amplitudes, and then successfully predict others. Our work constitutes the most precise test of the theoretical approach to T-violation within the framework of random-matrix theory so far available.

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arXiv2009

Spectral fluctuation properties of constrained unitary ensembles of Gaussian-distributed random matrices

We investigate the spectral fluctuation properties of constrained ensembles of random matrices (defined by the condition that a number N(Q) of matrix elements vanish identically; that condition is imposed in unitarily invariant form) in the limit of large matrix dimension. We show that as long as N(Q) is smaller than a critical value (at which the quadratic level repulsion of the Gaussian unitary ensemble of random matrices may be destroyed) all spectral fluctuation measures have the same form as for the Gaussian unitary ensemble.

math-ph↗
arXiv2008

Random-Matrix Approach to RPA equations. I

We study the RPA equations in their most general form by taking the matrix elements appearing in the RPA equations as random. This yields either a unitarily or an orthogonally invariant random-matrix model which is not of the Cartan type. The average spectrum of the model is studied with the help of a generalized Pastur equation. Two independent parameters govern the behaviour of the system: The strength $α^2$ of the coupling between positive- and negative-energy states and the distance between the origin and the centers of the two semicircles that describe the average spectrum for $α^2 = 0$, the latter measured in units of the equal radii of the two semicircles. With increasing $α^2$, positive- and negative-energy states become mixed and ever more of the spectral strength of the positive-energy states is transferred to those at negative energy, and vice versa. The two semicircles are deformed and pulled toward each other. As they begin to overlap, the RPA equations yield non--real eigenvalues: The system becomes unstable. We determine analytically the critical value of the strength for the instability to occur. Several features of the model are illustrated numerically.

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arXiv2008

Chaotic Scattering in the Regime of Weakly Overlapping Resonances

We measure the transmission and reflection amplitudes of microwaves in a resonator coupled to two antennas at room temperature in the regime of weakly overlapping resonances and in a frequency range of 3 to 16 GHz. Below 10.1 GHz the resonator simulates a chaotic quantum system. The distribution of the elements of the scattering matrix S is not Gaussian. The Fourier coefficients of S are used for a best fit of the autocorrelation function if S to a theoretical expression based on random--matrix theory. We find very good agreement below but not above 10.1 GHz.

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arXiv2008

Abundance of Ground States with Positive Parity

We investigate analytically and numerically a random-matrix model for m fermions occupying l1 single-particle states with positive parity and l2 single-particle states with negative parity and interacting through random two-body forces that conserve parity. The single-particle states are completely degenerate and carry no further quantum numbers. We compare spectra of many-body states with positive and with negative parity. We show that in the dilute limit, ground states with positive and with negative parity occur with equal probability. Differences in the ground-state probabilities are, thus, a finite-size effect and are mainly due to different dimensions of the Hilbert spaces of either parity.

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