165 research outputs found
A Simple Mode on a Highly Excited Background: Collective Strength and Damping in the Continuum
Simple states, such as isobaric analog states or giant resonances, embedded
into continuum are typical for mesoscopic many-body quantum systems. Due to the
coupling to compound states in the same energy range, a simple mode acquires a
damping width ("internal" dynamics). When studied experimentally with the aid
of various reactions, such states reveal enhanced cross sections in specific
channels at corresponding resonance energies ("external" dynamics which include
direct decay of a simple mode and decays of intrinsic compound states through
their own channels). We consider the interplay between internal and external
dynamics using a general formalism of the effective nonhermitian hamiltonian
and looking at the situation both from "inside" (strength functions and
spreading widths) and from "outside" (S-matrix, cross sections and delay
times). The restoration of isospin purity and disappearance of the collective
strength of giant resonances at high excitation energy are discussed as
important particular manifestations of this complex interplay.Comment: 23 pages, LaTeX, 5 ps-figures included, to appear in PRC (Jule 1997
Internal chaos in an open quantum system: From Ericson to conductance fluctuations
The model of an open Fermi-system is used for studying the interplay of
intrinsic chaos and irreversible decay into open continuum channels. Two
versions of the model are characterized by one-body chaos coming from disorder
or by many-body chaos due to the inter-particle interactions. The continuum
coupling is described by the effective non-Hermitian Hamiltonian. Our main
interest is in specific correlations of cross sections for various channels in
dependence on the coupling strength and degree of internal chaos. The results
are generic and refer to common features of various mesoscopic objects
including conductance fluctuations and resonance nuclear reactions.Comment: 10 pages, 5 figure
Open system of interacting fermions: Statistical properties of cross sections and fluctuations
Statistical properties of cross sections are studied for an open system of
interacting fermions. The description is based on the effective non-Hermitian
Hamiltonian that accounts for the existence of open decay channels preserving
the unitarity of the scattering matrix. The intrinsic interaction is modelled
by the two-body random ensemble of variable strength. In particular, the
crossover region from isolated to overlapping resonances accompanied by the
effect of the width redistribution creating super-radiant and trapped states is
studied in detail. The important observables, such as average cross section,
its fluctuations, autocorrelation functions of the cross section and scattering
matrix, are very sensitive to the coupling of the intrinsic states to the
continuum around the crossover. A detailed comparison is made of our results
with standard predictions of statistical theory of cross sections, such as the
Hauser-Feshbach formula for the average cross section and Ericson theory of
fluctuations and correlations of cross sections. Strong deviations are found in
the crossover region, along with the dependence on intrinsic interactions and
degree of chaos inside the system.Comment: 13 pages, 11 figure
Transition from isolated to overlapping resonances in the open system of interacting fermions
We study the statistical properties of resonance widths and spacings in an
open system of interacting fermions at the transition between isolated and
overlapping resonances, where a radical change in the width distribution
occurs. Our main interest is to reveal how this transition is influenced by the
onset of chaos in the internal dynamics as the strength of random two-body
interaction between the particles increases. We have found that in the region
of overlapped resonances, the fluctuations of the widths (rather than their
mean values) are strongly affected by the onset of an internal chaos. The
results may be applied to the analysis of neutron cross sections, as well as in
the physics of mesoscopic devices with strongly interacting electrons.Comment: 4 pages, 5 figures, corrected version, figures are replace
Quantum Chaos and Thermalization in Isolated Systems of Interacting Particles
This review is devoted to the problem of thermalization in a small isolated
conglomerate of interacting constituents. A variety of physically important
systems of intensive current interest belong to this category: complex atoms,
molecules (including biological molecules), nuclei, small devices of condensed
matter and quantum optics on nano- and micro-scale, cold atoms in optical
lattices, ion traps. Physical implementations of quantum computers, where there
are many interacting qubits, also fall into this group. Statistical
regularities come into play through inter-particle interactions, which have two
fundamental components: mean field, that along with external conditions, forms
the regular component of the dynamics, and residual interactions responsible
for the complex structure of the actual stationary states. At sufficiently high
level density, the stationary states become exceedingly complicated
superpositions of simple quasiparticle excitations. At this stage, regularities
typical of quantum chaos emerge and bring in signatures of thermalization. We
describe all the stages and the results of the processes leading to
thermalization, using analytical and massive numerical examples for realistic
atomic, nuclear, and spin systems, as well as for models with random
parameters. The structure of stationary states, strength functions of simple
configurations, and concepts of entropy and temperature in application to
isolated mesoscopic systems are discussed in detail. We conclude with a
schematic discussion of the time evolution of such systems to equilibrium.Comment: 69 pages, 31 figure
Schiff Theorem Revisited
We carefully rederive the Schiff theorem and prove that the usual expression
of the Schiff moment operator is correct and should be applied for calculations
of atomic electric dipole moments. The recently discussed corrections to the
definition of the Schiff moment are absent.Comment: 6 page
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