73 research outputs found
Nearest-Neighbor Distributions and Tunneling Splittings in Interacting Many-Body Two-Level Boson Systems
We study the nearest-neighbor distributions of the -body embedded
ensembles of random matrices for bosons distributed over two-degenerate
single-particle states. This ensemble, as a function of , displays a
transition from harmonic oscillator behavior () to random matrix type
behavior (). We show that a large and robust quasi-degeneracy is present
for a wide interval of values of when the ensemble is time-reversal
invariant. These quasi-degenerate levels are Shnirelman doublets which appear
due to the integrability and time-reversal invariance of the underlying
classical systems. We present results related to the frequency in the spectrum
of these degenerate levels in terms of , and discuss the statistical
properties of the splittings of these doublets.Comment: 13 pages (double column), 7 figures some in color. The movies can be
obtained at http://link.aps.org/supplemental/10.1103/PhysRevE.81.03621
Fidelity decay in interacting two-level boson systems: Freezing and revivals
We study the fidelity decay in the -body embedded ensembles of random
matrices for bosons distributed in two single-particle states, considering the
reference or unperturbed Hamiltonian as the one-body terms and the diagonal
part of the -body embedded ensemble of random matrices, and the perturbation
as the residual off-diagonal part of the interaction. We calculate the
ensemble-averaged fidelity with respect to an initial random state within
linear response theory to second order on the perturbation strength, and
demonstrate that it displays the freeze of the fidelity. During the freeze, the
average fidelity exhibits periodic revivals at integer values of the Heisenberg
time . By selecting specific -body terms of the residual interaction,
we find that the periodicity of the revivals during the freeze of fidelity is
an integer fraction of , thus relating the period of the revivals with the
range of the interaction of the perturbing terms. Numerical calculations
confirm the analytical results
Scar Intensity Statistics in the Position Representation
We obtain general predictions for the distribution of wave function
intensities in position space on the periodic orbits of chaotic ballistic
systems. The expressions depend on effective system size N, instability
exponent lambda of the periodic orbit, and proximity to a focal point of the
orbit. Limiting expressions are obtained that include the asymptotic
probability distribution of rare high-intensity events and a perturbative
formula valid in the limit of weak scarring. For finite system sizes, a single
scaling variable lambda N describes deviations from the semiclassical N ->
infinity limit.Comment: To appear in Phys. Rev. E, 10 pages, including 4 figure
Alternatives to Eigenstate Thermalization
An isolated quantum many-body system in an initial pure state will come to
thermal equilibrium if it satisfies the eigenstate thermalization hypothesis
(ETH). We consider alternatives to ETH that have been proposed. We first show
that von Neumann's quantum ergodic theorem relies on an assumption that is
essentially equivalent to ETH. We also investigate whether, following a sudden
quench, special classes of pure states can lead to thermal behavior in systems
that do not obey ETH, namely, integrable systems. We find examples of this, but
only for initial states that obeyed ETH before the quench.Comment: 5 pages, 3 figures, as publishe
Young Measures Generated by Ideal Incompressible Fluid Flows
In their seminal paper "Oscillations and concentrations in weak solutions of
the incompressible fluid equations", R. DiPerna and A. Majda introduced the
notion of measure-valued solution for the incompressible Euler equations in
order to capture complex phenomena present in limits of approximate solutions,
such as persistence of oscillation and development of concentrations.
Furthermore, they gave several explicit examples exhibiting such phenomena. In
this paper we show that any measure-valued solution can be generated by a
sequence of exact weak solutions. In particular this gives rise to a very
large, arguably too large, set of weak solutions of the incompressible Euler
equations.Comment: 35 pages. Final revised version. To appear in Arch. Ration. Mech.
Ana
Semiclassical structure of chaotic resonance eigenfunctions
We study the resonance (or Gamow) eigenstates of open chaotic systems in the
semiclassical limit, distinguishing between left and right eigenstates of the
non-unitary quantum propagator, and also between short-lived and long-lived
states. The long-lived left (right) eigenstates are shown to concentrate as
on the forward (backward) trapped set of the classical dynamics.
The limit of a sequence of eigenstates is found
to exhibit a remarkably rich structure in phase space that depends on the
corresponding limiting decay rate. These results are illustrated for the open
baker map, for which the probability density in position space is observed to
have self-similarity properties.Comment: 4 pages, 4 figures; some minor corrections, some changes in
presentatio
Generalized Berry Conjecture and mode correlations in chaotic plates
We consider a modification of the Berry Conjecture for eigenmode statistics
in wave-bearing systems. The eigenmode correlator is conjectured to be
proportional to the imaginary part of the Green's function. The generalization
is applicable not only to scalar waves in the interior of homogeneous isotropic
systems where the correlator is a Bessel function, but to arbitrary points of
heterogeneous systems as well. In view of recent experimental measurements,
expressions for the intensity correlator in chaotic plates are derived.Comment: 5 pages, 1 figur
On the Convergence to Ergodic Behaviour of Quantum Wave Functions
We study the decrease of fluctuations of diagonal matrix elements of
observables and of Husimi densities of quantum mechanical wave functions around
their mean value upon approaching the semi-classical regime (). The model studied is a spin (SU(2)) one in a classically strongly chaotic
regime. We show that the fluctuations are Gaussian distributed, with a width
decreasing as the square root of Planck's constant. This is
consistent with Random Matrix Theory (RMT) predictions, and previous studies on
these fluctuations. We further study the width of the probability distribution
of -dependent fluctuations and compare it to the Gaussian Orthogonal
Ensemble (GOE) of RMT.Comment: 13 pages Latex, 5 figure
Quantum ergodicity on graphs
We investigate the equidistribution of the eigenfunctions on quantum graphs
in the high-energy limit. Our main result is an estimate of the deviations from
equidistribution for large well-connected graphs. We use an exact
field-theoretic expression in terms of a variant of the supersymmetric
nonlinear sigma-model. Our estimate is based on a saddle-point analysis of this
expression and leads to a criterion for when equidistribution emerges
asymptotically in the limit of large graphs. Our theory predicts a rate of
convergence that is a significant refinement of previous estimates,
long-assumed to be valid for quantum chaotic systems, agreeing with them in
some situations but not all. We discuss specific examples for which the theory
is tested numerically.Comment: 4 pages, 1 figur
Deviations from Berry--Robnik Distribution Caused by Spectral Accumulation
By extending the Berry--Robnik approach for the nearly integrable quantum
systems,\cite{[1]} we propose one possible scenario of the energy level spacing
distribution that deviates from the Berry--Robnik distribution. The result
described in this paper implies that deviations from the Berry--Robnik
distribution would arise when energy level components show strong accumulation,
and otherwise, the level spacing distribution agrees with the Berry--Robnik
distribution.Comment: 4 page
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