24 research outputs found
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.Comment: 10 page
Random Matrices and Chaos in Nuclear Spectra
We speak of chaos in quantum systems if the statistical properties of the
eigenvalue spectrum coincide with predictions of random-matrix theory. Chaos is
a typical feature of atomic nuclei and other self-bound Fermi systems. How can
the existence of chaos be reconciled with the known dynamical features of
spherical nuclei? Such nuclei are described by the shell model (a mean-field
theory) plus a residual interaction. We approach the question by using a
statistical approach (the two-body random ensemble): The matrix elements of the
residual interaction are taken to be random variables. We show that chaos is a
generic feature of the ensemble and display some of its properties, emphasizing
those which differ from standard random-matrix theory. In particular, we
display the existence of correlations among spectra carrying different quantum
numbers. These are subject to experimental verification.Comment: 17 pages, 20 figures, colloquium article, submitted to Reviews of
Modern Physic
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.Comment: 9 pages; considerably expanded presentation; example of emergent U(1)
breaking adde
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.Comment: 4 page
Disordered mesoscopic systems with interactions: induced two-body ensembles and the Hartree-Fock approach
We introduce a generic approach to study interaction effects in diffusive or
chaotic quantum dots in the Coulomb blockade regime. The randomness of the
single-particle wave functions induces randomness in the two-body interaction
matrix elements. We classify the possible induced two-body ensembles, both in
the presence and absence of spin degrees of freedom. The ensembles depend on
the underlying space-time symmetries as well as on features of the two-body
interaction. Confining ourselves to spinless electrons, we then use the
Hartree-Fock (HF) approximation to calculate HF single-particle energies and HF
wave functions for many realizations of the ensemble. We study the statistical
properties of the resulting one-body HF ensemble for a fixed number of
electrons. In particular, we determine the statistics of the interaction matrix
elements in the HF basis, of the HF single-particle energies (including the HF
gap between the last occupied and the first empty HF level), and of the HF
single-particle wave functions. We also study the addition of electrons, and in
particular the distribution of the distance between successive conductance
peaks and of the conductance peak heights.Comment: 25 pages, 16 figure
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.Comment: 13 pages, 7 figure
Interaction of Regular and Chaotic States
Modelling the chaotic states in terms of the Gaussian Orthogonal Ensemble of
random matrices (GOE), we investigate the interaction of the GOE with regular
bound states. The eigenvalues of the latter may or may not be embedded in the
GOE spectrum. We derive a generalized form of the Pastur equation for the
average Green's function. We use that equation to study the average and the
variance of the shift of the regular states, their spreading width, and the
deformation of the GOE spectrum non-perturbatively. We compare our results with
various perturbative approaches.Comment: 26 pages, 9 figure
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.Comment: 50 pages, 26 figure