3,052 research outputs found
Fluctuations and Ergodicity of the Form Factor of Quantum Propagators and Random Unitary Matrices
We consider the spectral form factor of random unitary matrices as well as of
Floquet matrices of kicked tops. For a typical matrix the time dependence of
the form factor looks erratic; only after a local time average over a suitably
large time window does a systematic time dependence become manifest. For
matrices drawn from the circular unitary ensemble we prove ergodicity: In the
limits of large matrix dimension and large time window the local time average
has vanishingly small ensemble fluctuations and may be identified with the
ensemble average. By numerically diagonalizing Floquet matrices of kicked tops
with a globally chaotic classical limit we find the same ergodicity. As a
byproduct we find that the traces of random matrices from the circular
ensembles behave very much like independent Gaussian random numbers. Again,
Floquet matrices of chaotic tops share that universal behavior. It becomes
clear that the form factor of chaotic dynamical systems can be fully faithful
to random-matrix theory, not only in its locally time-averaged systematic time
dependence but also in its fluctuations.Comment: 12 pages, RevTEX, 4 figures in eps forma
Non Thermal Equilibrium States of Closed Bipartite Systems
We investigate a two-level system in resonant contact with a larger
environment. The environment typically is in a canonical state with a given
temperature initially. Depending on the precise spectral structure of the
environment and the type of coupling between both systems, the smaller part may
relax to a canonical state with the same temperature as the environment (i.e.
thermal relaxation) or to some other quasi equilibrium state (non thermal
relaxation). The type of the (quasi) equilibrium state can be related to the
distribution of certain properties of the energy eigenvectors of the total
system. We examine these distributions for several abstract and concrete (spin
environment) Hamiltonian systems, the significant aspect of these distributions
can be related to the relative strength of local and interaction parts of the
Hamiltonian.Comment: RevTeX, 8 pages, 13 figure
Multifractality and intermediate statistics in quantum maps
We study multifractal properties of wave functions for a one-parameter family
of quantum maps displaying the whole range of spectral statistics intermediate
between integrable and chaotic statistics. We perform extensive numerical
computations and provide analytical arguments showing that the generalized
fractal dimensions are directly related to the parameter of the underlying
classical map, and thus to other properties such as spectral statistics. Our
results could be relevant for Anderson and quantum Hall transitions, where wave
functions also show multifractality.Comment: 4 pages, 4 figure
Periodic-Orbit Theory of Level Correlations
We present a semiclassical explanation of the so-called
Bohigas-Giannoni-Schmit conjecture which asserts universality of spectral
fluctuations in chaotic dynamics. We work with a generating function whose
semiclassical limit is determined by quadruplets of sets of periodic orbits.
The asymptotic expansions of both the non-oscillatory and the oscillatory part
of the universal spectral correlator are obtained. Borel summation of the
series reproduces the exact correlator of random-matrix theory.Comment: 4 pages, 1 figure (+ web-only appendix with 2 pages, 1 figure
Classical versus Quantum Time Evolution of Densities at Limited Phase-Space Resolution
We study the interrelations between the classical (Frobenius-Perron) and the
quantum (Husimi) propagator for phase-space (quasi-)probability densities in a
Hamiltonian system displaying a mix of regular and chaotic behavior. We focus
on common resonances of these operators which we determine by blurring
phase-space resolution. We demonstrate that classical and quantum time
evolution look alike if observed with a resolution much coarser than a Planck
cell and explain how this similarity arises for the propagators as well as
their spectra. The indistinguishability of blurred quantum and classical
evolution implies that classical resonances can conveniently be determined from
quantum mechanics and in turn become effective for decay rates of quantum
correlations.Comment: 10 pages, 3 figure
Stringent Numerical Test of the Poisson Distribution for Finite Quantum Integrable Hamiltonians
Using a new class of exactly solvable models based on the pairing
interaction, we show that it is possible to construct integrable Hamiltonians
with a Wigner distribution of nearest neighbor level spacings. However, these
Hamiltonians involve many-body interactions and the addition of a small
integrable perturbation very quickly leads the system to a Poisson
distribution. Besides this exceptional cases, we show that the accumulated
distribution of an ensemble of random integrable two-body pairing hamiltonians
is in perfect agreement with the Poisson limit. These numerical results for
quantum integrable Hamiltonians provide a further empirical confirmation to the
work of the Berry and Tabor in the semiclassical limit.Comment: 5 pages, 4 figures, LaTeX (RevTeX 4) Content changed, References
added Accepted for publication in PR
Weak localization of the open kicked rotator
We present a numerical calculation of the weak localization peak in the
magnetoconductance for a stroboscopic model of a chaotic quantum dot. The
magnitude of the peak is close to the universal prediction of random-matrix
theory. The width depends on the classical dynamics, but this dependence can be
accounted for by a single parameter: the level curvature around zero magnetic
field of the closed system.Comment: 8 pages, 8 eps figure
Tracking quasi-classical chaos in ultracold boson gases
We study the dynamics of a ultra-cold boson gas in a lattice submitted to a
constant force. We track the route of the system towards chaos created by the
many-body-induced nonlinearity and show that relevant information can be
extracted from an experimentally accessible quantity, the gas mean position.
The threshold nonlinearity for the appearance of chaotic behavior is deduced
from KAM arguments and agrees with the value obtained by calculating the
associated Lyapunov exponent.Comment: 4 pages, revtex4, submitted to PR
Chaotic Quantum Decay in Driven Biased Optical Lattices
Quantum decay in an ac driven biased periodic potential modeling cold atoms
in optical lattices is studied for a symmetry broken driving. For the case of
fully chaotic classical dynamics the classical exponential decay is quantum
mechanically suppressed for a driving frequency \omega in resonance with the
Bloch frequency \omega_B, q\omega=r\omega_B with integers q and r.
Asymptotically an algebraic decay ~t^{-\gamma} is observed. For r=1 the
exponent \gamma agrees with as predicted by non-Hermitian random matrix
theory for q decay channels. The time dependence of the survival probability
can be well described by random matrix theory. The frequency dependence of the
survival probability shows pronounced resonance peaks with sub-Fourier
character.Comment: 7 pages, 5 figure
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