arXiv subjects
Publications and source records attributed to Hans A. Weidenmueller.
Recent data on neutron resonance widths indicate disagreement with the Porter-Thomas distribution (PTD). I discuss the theoretical arguments for the PTD, possible theoretical modifications, and I summarize the experimantal evidence.
We derive Fourier's law for a completely coherent quasi one--dimensional chaotic quantum system coupled locally to two heat baths at different temperatures. We solve the master equation to first order in the temperature difference. We show that the heat conductance can be expressed as a thermodynamic equilibrium coefficient taken at some intermediate temperature. We use that expression to show that for temperatures large compared to the mean level spacing of the system, the heat conductance is inversely proportional to the level density and, thus, inversely proportional to the length of the system.
A zeptosecond multi--MeV laser pulse may either excite a "plasma" of strongly interacting nucleons or a collective mode. We derive the conditions on laser energy and photon number such that either of these scenarios is realized. We use the nuclear Giant Dipole Resonance as a representative example, and a random--matrix description of the fine--structure states and perturbation theory as tools.
For nuclei near a maximum of the neutron strength function, the secular dependence on energy E of s-wave partial neutron widths differs from the canonical form given by the square root of E. We derive the universal form of that dependence and show that it is expected to significantly influence the analysis of neutron resonance data.
We propose a controlled experiment to clarify the physical mechanism causing phase lapses of the amplitude for electron transmission through nanoscale devices. Such lapses are generically observed in valleys between adjacent Coulomb--blockade peaks. The experiment involves two quantum dots embedded in the same arm of an Aharonov--Bohm interferometer. It offers a decisive test of "population switching", one of the leading contenders for an explanation of the phenomenon.
We show that parametric level correlations in random-matrix theories are closely related to a breaking of the symmetry between the advanced and the retarded Green's functions. The form of the parametric level correlation function is the same as for the disordered case considered earlier by Simons and Altshuler and is given by the graded trace of the commutator of the saddle--point solution with the particular matrix that describes the symmetry breaking in the actual case of interest. The strength factor differs from the case of disorder. It is determined solely by the Goldstone mode. It is essentially given by the number of levels that are strongly mixed as the external parameter changes. The factor can easily be estimated in applications.
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.
Two electrons move in a quasi one--dimensional wire under the influence of a short--range interaction. We restrict Hilbert space to those states where the two electrons are close to each other. Using supersymmetry, we present a complete analytical solution to this problem. The two--body interaction affects the density of states and, thereby, the localization length. We derive a criterion for the onset of changes of the localization length due to the two--body interaction.
In two recent papers, O. Entin-Wohlman et al. studied the question: ``Which physical information is carried by the transmission phase through a quantum dot?'' In the present paper, this question is answered for an islolated Coulomb-blockade resonance and within a theoretical model which is more closely patterned after the geometry of the actual experiment by Schuster et al. than is the model of O. Entin-Wohlman et al. We conclude that whenever the number of leads coupled to the Aharanov-Bohm interferometer is larger than two, and the total number of channels is sufficiently large, the transmission phase does reflect the Breit-Wigner behavior of the resonance phase shift.
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 $k << m << l$.
Using a novel approach, we investigate the shape of the average spectrum and the spectral fluctuations of the $k$-body embedded unitary ensemble in the limit of large matrix dimension. We identify the transition point between semicircle and Gaussian shape. The transition also affects the spectral fluctuations which deviate from Wigner-Dyson form and become Poissonian in the limit $k << m << l$. Here $m$ is the number of Fermions and $l$ the number of degenerate single-particle states.
Many models for chaotic systems consist of joining two integrable systems with incompatible constants of motion. The quantum counterparts of such models have a propagator which factorizes into two integrable parts. Each part can be diagonalized. The two eigenvector bases are related by an orthogonal (or unitary) transformation. We construct a random matrix ensemble that mimics this situation and consists of a product of a diagonal, an orthogonal, another diagonal and the transposed orthogonal matrix. The diagonal phases are chosen at random and the orthogonal matrix from Haar's measure. We derive asymptotic results (dimension N -> \infty) using Wick contractions. A new approximation for the group integration yields the next order in 1/N. We obtain a finite correction to the circular orthogonal ensemble, important in the long-range part of spectral correlations.
We use random-matrix theory and supersymmetry techniques to work out the two-point correlation function between states in a hierarchical model which employs Feshbach's chaining hypothesis: Classes of many-body states are introduced. Only states within the same or neighboring classes are coupled. We assume that the density of states per class grows monotonically with class index. The problem is mapped onto a one-dimensional non-linear sigma model. In the limit of a large number of states in each class we derive the critical exponent for the growth of the level density with class index for which delocalization sets in. From a realistic modelling of the class-dependence of the level density, we conclude that the model does not predict Fock-space localization in nuclei.
Motivated by an experiment by Sivan et al. (Europhys. Lett. 25, 605 (1994)) and by subsequent theoretical work on localization in Fock space, we study numerically a hierarchical model for a finite many-body system of Fermions moving in a disordered potential and coupled by a two-body interaction. We focus attention on the low-lying states close to the Fermi energy. Both the spreading width and the participation number depend smoothly on excitation energy. This behavior is in keeping with naive expectations and does not display Anderson localization. We show that the model reproduces essential features of the experiment by Sivan et al.
Are Markovian master equations for quantum Brownian motion independent of model assumptions used in the derivation and, thus, universal? With the aim of answering this question, we use a random band-matrix model for the system-bath interaction to derive Markovian master equations for the time evolution of one-dimensional quantum systems weakly coupled to a heat bath. We study in detail two simple systems, the harmonic oscillator and the two-level system. Our results are in complete agreement with those of earlier models, like the Caldeira-Legget model and, in the large-band limit, with the Agarwal equations (both with and without rotating-wave approximation). This proves the universality of these master equations.
We investigate the Coulomb blockade resonances and the phase of the transmission amplitude of a deformed ballistic quantum dot weakly coupled to leads. We show that preferred single--particle levels exist which stay close to the Fermi energy for a wide range of values of the gate voltage. These states give rise to sequences of Coulomb blockade resonances with correlated peak heights and transmission phases. The correlation of the peak heights becomes stronger with increasing temperature. The phase of the transmission amplitude shows lapses by $π$ between the resonances. Implications for recent experiments on ballistic quantum dots are discussed.
We review the development of random-matrix theory (RMT) during the last decade. We emphasize both the theoretical aspects, and the application of the theory to a number of fields. These comprise chaotic and disordered systems, the localization problem, many-body quantum systems, the Calogero-Sutherland model, chiral symmetry breaking in QCD, and quantum gravity in two dimensions. The review is preceded by a brief historical survey of the developments of RMT and of localization theory since their inception. We emphasize the concepts common to the above-mentioned fields as well as the great diversity of RMT. In view of the universality of RMT, we suggest that the current development signals the emergence of a new "statistical mechanics": Stochasticity and general symmetry requirements lead to universal laws not based on dynamical principles.