1,980 research outputs found
Quantum Versus Classical Decay Laws in Open Chaotic Systems
We study analytically the time evolution in decaying chaotic systems and
discuss in detail the hierarchy of characteristic time scales that appeared in
the quasiclassical region. There exist two quantum time scales: the Heisenberg
time t_H and the time t_q=t_H/\sqrt{\kappa T} (with \kappa >> 1 and T being the
degree of resonance overlapping and the transmission coefficient respectively)
associated with the decay. If t_q < t_H the quantum deviation from the
classical decay law starts at the time t_q and are due to the openness of the
system. Under the opposite condition quantum effects in intrinsic evolution
begin to influence the decay at the time t_H. In this case we establish the
connection between quantities which describe the time evolution in an open
system and their closed counterparts.Comment: 3 pages, REVTeX, no figures, replaced with the published version
(misprints corrected, references updated
Statistics of resonance width shifts as a signature of eigenfunction non-orthogonality
We consider an open (scattering) quantum system under the action of a
perturbation of its closed counterpart. It is demonstrated that the resulting
shift of resonance widths is a sensitive indicator of the non-orthogonality of
resonance wavefunctions, being zero only if those were orthogonal. Focusing
further on chaotic systems, we employ random matrix theory to introduce a new
type of parametric statistics in open systems, and derive the distribution of
the resonance width shifts in the regime of weak coupling to the continuum.Comment: 4 pages, 1 figure (published version with minor changes
Statistics of eigenfunctions in open chaotic systems: a perturbative approach
We investigate the statistical properties of the complexness parameter which
characterizes uniquely complexness (biorthogonality) of resonance eigenstates
of open chaotic systems. Specifying to the regime of isolated resonances, we
apply the random matrix theory to the effective Hamiltonian formalism and
derive analytically the probability distribution of the complexness parameter
for two statistical ensembles describing the systems invariant under time
reversal. For those with rigid spectra, we consider a Hamiltonian characterized
by a picket-fence spectrum without spectral fluctuations. Then, in the more
realistic case of a Hamiltonian described by the Gaussian Orthogonal Ensemble,
we reveal and discuss the r\^ole of spectral fluctuations
Analytic continuation as a bridge between continuum and bound states
The problem of obtaining characteristics of bound nuclear states from continuum states data is discussed. It is shown that the ambiguities due to the existence of phase-equivalent potentials can be resolved by using the analytic properties of scattering amplitudes. The methods of determination of asymptotic normalization coefficients and vertex constants are considered. The asymptotic normalization coefficients for 6Li in the α + d channel are found by analytic continuation of the two-channel effective range expansion. The account of inelastic channels within the effective range approach is discussed
Distribution of reflection eigenvalues in many-channel chaotic cavities with absorption
The reflection matrix R=S^{\dagger}S, with S being the scattering matrix,
differs from the unit one, when absorption is finite. Using the random matrix
approach, we calculate analytically the distribution function of its
eigenvalues in the limit of a large number of propagating modes in the leads
attached to a chaotic cavity. The obtained result is independent on the
presence of time-reversal symmetry in the system, being valid at finite
absorption and arbitrary openness of the system. The particular cases of
perfectly and weakly open cavities are considered in detail. An application of
our results to the problem of thermal emission from random media is briefly
discussed.Comment: 4 pages, 2 figures; (Ref.[5b] added, appropriate modification in
text
Normal form for travelling kinks in discrete Klein-Gordon lattices
We study travelling kinks in the spatial discretizations of the nonlinear
Klein--Gordon equation, which include the discrete lattice and the
discrete sine--Gordon lattice. The differential advance-delay equation for
travelling kinks is reduced to the normal form, a scalar fourth-order
differential equation, near the quadruple zero eigenvalue. We show numerically
non-existence of monotonic kinks (heteroclinic orbits between adjacent
equilibrium points) in the fourth-order equation. Making generic assumptions on
the reduced fourth-order equation, we prove the persistence of bounded
solutions (heteroclinic connections between periodic solutions near adjacent
equilibrium points) in the full differential advanced-delay equation with the
technique of center manifold reduction. Existence and persistence of multiple
kinks in the discrete sine--Gordon equation are discussed in connection to
recent numerical results of \cite{ACR03} and results of our normal form
analysis
Efficient semiclassical approach for time delays
The Wigner time delay, defined by the energy derivative of the total scattering phase shift, is an important spectral measure of an open quantum system characterizing the duration of the scattering event. It is proportional to the trace of the Wigner-Smith matrix Q that also encodes other time-delay characteristics. For chaotic cavities, these quantities exhibit universal fluctuations that are commonly described within random matrix theory. Here, we develop a new semiclassical approach to the time-delay matrix which is formulated in terms of the classical trajectories that connect the exterior and interior regions of the system. This approach is superior to previous treatments because it avoids the energy derivative. We demonstrate the method's efficiency by going beyond previous work in establishing the universality of time-delay statistics for chaotic cavities with perfectly connected leads. In particular, the moment generating function of the proper time-delays (eigenvalues of Q) is found semiclassically for the first five orders in the inverse number of scattering channels for systems with and without time-reversal symmetry. We also show the equivalence of random matrix and semiclassical results for the second moments and for the variance of the Wigner time delay at any channel number.https://arxiv.org/abs/1409.1532v
Delay times and reflection in chaotic cavities with absorption
Absorption yields an additional exponential decay in open quantum systems
which can be described by shifting the (scattering) energy E along the
imaginary axis, E+i\hbar/2\tau_{a}. Using the random matrix approach, we
calculate analytically the distribution of proper delay times (eigenvalues of
the time-delay matrix) in chaotic systems with broken time-reversal symmetry
that is valid for an arbitrary number of generally nonequivalent channels and
an arbitrary absorption rate 1/\tau_{a}. The relation between the average delay
time and the ``norm-leakage'' decay function is found. Fluctuations above the
average at large values of delay times are strongly suppressed by absorption.
The relation of the time-delay matrix to the reflection matrix S^{\dagger}S is
established at arbitrary absorption that gives us the distribution of
reflection eigenvalues. The particular case of single-channel scattering is
explicitly considered in detail.Comment: 5 pages, 3 figures; final version to appear in PRE (relation to
reflection extended, new material with Fig.3 added, experiment
cond-mat/0305090 discussed
- …