2,303 research outputs found
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
Characterization of complex quantum dynamics with a scalable NMR information processor
We present experimental results on the measurement of fidelity decay under
contrasting system dynamics using a nuclear magnetic resonance quantum
information processor. The measurements were performed by implementing a
scalable circuit in the model of deterministic quantum computation with only
one quantum bit. The results show measurable differences between regular and
complex behaviour and for complex dynamics are faithful to the expected
theoretical decay rate. Moreover, we illustrate how the experimental method can
be seen as an efficient way for either extracting coarse-grained information
about the dynamics of a large system, or measuring the decoherence rate from
engineered environments.Comment: 4pages, 3 figures, revtex4, updated with version closer to that
publishe
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
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
Fidelity recovery in chaotic systems and the Debye-Waller factor
Using supersymmetry calculations and random matrix simulations, we studied
the decay of the average of the fidelity amplitude f_epsilon(tau)=<psi(0)|
exp(2 pi i H_epsilon tau) exp(-2 pi i H_0 tau) |psi(0)>, where H_epsilon
differs from H_0 by a slight perturbation characterized by the parameter
epsilon. For strong perturbations a recovery of f_epsilon(tau) at the
Heisenberg time tau=1 is found. It is most pronounced for the Gaussian
symplectic ensemble, and least for the Gaussian orthogonal one. Using Dyson's
Brownian motion model for an eigenvalue crystal, the recovery is interpreted in
terms of a spectral analogue of the Debye-Waller factor known from solid state
physics, describing the decrease of X-ray and neutron diffraction peaks with
temperature due to lattice vibrations.Comment: revised version (major changes), 4 pages, 4 figure
Finite-difference distributions for the Ginibre ensemble
The Ginibre ensemble of complex random matrices is studied. The complex
valued random variable of second difference of complex energy levels is
defined. For the N=3 dimensional ensemble are calculated distributions of
second difference, of real and imaginary parts of second difference, as well as
of its radius and of its argument (angle). For the generic N-dimensional
Ginibre ensemble an exact analytical formula for second difference's
distribution is derived. The comparison with real valued random variable of
second difference of adjacent real valued energy levels for Gaussian
orthogonal, unitary, and symplectic, ensemble of random matrices as well as for
Poisson ensemble is provided.Comment: 8 pages, a number of small changes in the tex
Universality of Decoherence
We consider environment induced decoherence of quantum superpositions to
mixtures in the limit in which that process is much faster than any competing
one generated by the Hamiltonian of the isolated system. While
the golden rule then does not apply we can discard . By allowing
for simultaneous couplings to different reservoirs, we reveal decoherence as a
universal short-time phenomenon independent of the character of the system as
well as the bath and of the basis the superimposed states are taken from. We
discuss consequences for the classical behavior of the macroworld and quantum
measurement: For the decoherence of superpositions of macroscopically distinct
states the system Hamiltonian is always negligible.Comment: 4 revtex pages, no figure
Splitting of Andreev levels in a Josephson junction by spin-orbit coupling
We consider the effect of spin-orbit coupling on the energy levels of a
single-channel Josephson junction below the superconducting gap. We investigate
quantitatively the level splitting arising from the combined effect of
spin-orbit coupling and the time-reversal symmetry breaking by the phase
difference between the superconductors. Using the scattering matrix approach we
establish a simple connection between the quantum mechanical time delay matrix
and the effective Hamiltonian for the level splitting. As an application we
calculate the distribution of level splittings for an ensemble of chaotic
Josephson junctions. The distribution falls off as a power law for large
splittings, unlike the exponentially decaying splitting distribution given by
the Wigner surmise -- which applies for normal chaotic quantum dots with
spin-orbit coupling in the case that the time-reversal symmetry breaking is due
to a magnetic field.Comment: 6 pages, 3 figure
Scattering of quantum wave packets by shallow potential islands: a quantum lens
We consider the problem of quantum scattering of a localized wave packet by a weak Gaussian potential in two spatial dimensions. We show that, under certain conditions, this problem bears close analogy with that of focusing (or defocusing) of light rays by a thin optical lens: Quantum interference between straight paths yields the same lens equation as for refracted rays in classical optics
The effect of short ray trajectories on the scattering statistics of wave chaotic systems
In many situations, the statistical properties of wave systems with chaotic
classical limits are well-described by random matrix theory. However,
applications of random matrix theory to scattering problems require
introduction of system specific information into the statistical model, such as
the introduction of the average scattering matrix in the Poisson kernel. Here
it is shown that the average impedance matrix, which also characterizes the
system-specific properties, can be expressed in terms of classical trajectories
that travel between ports and thus can be calculated semiclassically.
Theoretical results are compared with numerical solutions for a model
wave-chaotic system
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