131 research outputs found
Spectral Statistics of the Two-Body Random Ensemble Revisited
Using longer spectra we re-analyze spectral properties of the two-body random
ensemble studied thirty years ago. At the center of the spectra the old results
are largely confirmed, and we show that the non-ergodicity is essentially due
to the variance of the lowest moments of the spectra. The longer spectra allow
to test and reach the limits of validity of French's correction for the number
variance. At the edge of the spectra we discuss the problems of unfolding in
more detail. With a Gaussian unfolding of each spectrum the nearest neighbour
spacing distribution between ground state and first exited state is shown to be
stable. Using such an unfolding the distribution tends toward a semi-Poisson
distribution for longer spectra. For comparison with the nuclear table ensemble
we could use such unfolding obtaining similar results as in the early papers,
but an ensemble with realistic splitting gives reasonable results if we just
normalize the spacings in accordance with the procedure used for the data.Comment: 11 pages, 7 figure
Generalized seniority from random Hamiltonians
We investigate the generic pairing properties of shell-model many-body
Hamiltonians drawn from ensembles of random two-body matrix elements. Many
features of pairing that are commonly attributed to the interaction are in fact
seen in a large part of the ensemble space. Not only do the spectra show
evidence of pairing with favored J=0 ground states and an energy gap, but the
relationship between ground state wave functions of neighboring nuclei show
signatures of pairing as well. Matrix elements of pair creation/annihilation
operators between ground states tend to be strongly enhanced. Furthermore, the
same or similar pair operators connect several ground states along an isotopic
chain. This algebraic structure is reminiscent of the generalized seniority
model. Thus pairing may be encoded to a certain extent in the Fock space
connectivity of the interacting shell model even without specific features of
the interaction required.Comment: 10 pages, 7 figure
Spin relaxation in a complex environment
We report the study of a model of a two-level system interacting in a
non-diagonal way with a complex environment described by Gaussian orthogonal
random matrices (GORM). The effect of the interaction on the total spectrum and
its consequences on the dynamics of the two-level system are analyzed. We show
the existence of a critical value of the interaction, depending on the mean
level spacing of the environment, above which the dynamics is self-averaging
and closely obey a master equation for the time evolution of the observables of
the two-level system. Analytic results are also obtained in the strong coupling
regimes. We finally study the equilibrium values of the two-level system
population and show under which condition it thermalizes to the environment
temperature.Comment: 45 pages, 49 figure
Misleading signatures of quantum chaos
The main signature of chaos in a quantum system is provided by spectral
statistical analysis of the nearest neighbor spacing distribution and the
spectral rigidity given by . It is shown that some standard
unfolding procedures, like local unfolding and Gaussian broadening, lead to a
spurious increase of the spectral rigidity that spoils the
relationship with the regular or chaotic motion of the system. This effect can
also be misinterpreted as Berry's saturation.Comment: 4 pages, 5 figures, submitted to Physical Review
Spectral fluctuation properties of spherical nuclei
The spectral fluctuation properties of spherical nuclei are considered by use
of NNSD statistic. With employing a generalized Brody distribution included
Poisson, GOE and GUE limits and also MLE technique, the chaoticity parameters
are estimated for sequences prepared by all the available empirical data. The
ML-based estimated values and also KLD measures propose a non regular dynamic.
Also, spherical odd-mass nuclei in the mass region, exhibit a slight deviation
to the GUE spectral statistics rather than the GOE.Comment: 10 pages, 2 figure
The Impact of Isospin Breaking on the Distribution of Transition Probabilities
In the present paper we investigate the effect of symmetry breaking in the
statistical distributions of reduced transition amplitudes and reduced
transition probabilities. These quantities are easier to access experimentally
than the components of the eigenvectors and were measured by Adams et al. for
the electromagnetic transitions in ^{26}Al. We focus on isospin symmetry
breaking described by a matrix model where both, the Hamiltonian and the
electromagnetic operator, break the symmetry. The results show that for partial
isospin conservation, the statistical distribution of the reduced transition
probability can considerably deviate from the Porter-Thomas distribution.Comment: 16 pages, 8 figures, submitted to PR
Quantum master equation for a system influencing its environment
A perturbative quantum master equation is derived for a system interacting
with its environment, which is more general than the ones derived before. Our
master equation takes into account the effect of the energy exchanges between
the system and the environment and the conservation of energy in a finite total
system. This master quantum describes relaxation mechanisms in isolated
nanoscopic quantum systems. In its most general form, this equation is
non-Markovian and a Markovian version of it rules the long-time relaxation. We
show that our equation reduces to the Redfield equation in the limit where the
energy of the system does not affect the density of state of its environment.
This master equation and the Redfield one are applied to a spin-environment
model defined in terms of random matrices and compared with the solutions of
the exact von Neumann equation. The comparison proves the necessity to allow
energy exchange between the subsystem and the environment in order to correctly
describe the relaxation in isolated nanoscopic total system.Comment: 39 pages, 10 figure
Quantum Chaos Versus Classical Chaos: Why is Quantum Chaos Weaker?
We discuss the questions: How to compare quantitatively classical chaos with
quantum chaos? Which one is stronger? What are the underlying physical reasons
Nonergodic Behavior of Interacting Bosons in Harmonic Traps
We study the time evolution of a system of interacting bosons in a harmonic
trap. In the low-energy regime, the quantum system is not ergodic and displays
rather large fluctuations of the ground state occupation number. In the high
energy regime of classical physics we find nonergodic behavior for modest
numbers of trapped particles. We give two conditions that assure the ergodic
behavior of the quantum system even below the condensation temperature.Comment: 11 pages, 3 PS-figures, uses psfig.st
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