1,656 research outputs found
Single qubit decoherence under a separable coupling to a random matrix environment
This paper describes the dynamics of a quantum two-level system (qubit) under
the influence of an environment modeled by an ensemble of random matrices. In
distinction to earlier work, we consider here separable couplings and focus on
a regime where the decoherence time is of the same order of magnitude than the
environmental Heisenberg time. We derive an analytical expression in the linear
response approximation, and study its accuracy by comparison with numerical
simulations. We discuss a series of unusual properties, such as purity
oscillations, strong signatures of spectral correlations (in the environment
Hamiltonian), memory effects and symmetry breaking equilibrium states.Comment: 13 pages, 7 figure
Scattering approach to fidelity decay in closed systems and parametric level correlations
This paper is based on recent work which provided an exact analytical
description of scattering fidelity experiments with a microwave cavity under
the variation of an antenna coupling [K\"ober et al., Phys. Rev. E 82, 036207
(2010)]. It is shown that this description can also be used to predict the
decay of the fidelity amplitude for arbitrary Hermitian perturbations of a
closed system. Two applications are presented: First, the known result for
global perturbations is re-derived, and second, the exact analytical expression
for the perturbation due to a moving S-wave scatterer is worked out. The latter
is compared to measured data from microwave experiments, which have been
reported some time ago. Finally, we generalize an important relation between
fidelity decay and parametric level correlations to arbitrary perturbations.Comment: 20 pages, 2 figures, research article, (v2: stylistic changes, ref.
added
Integrals of monomials over the orthogonal group
A recursion formula is derived which allows to evaluate invariant integrals
over the orthogonal group O(N), where the integrand is an arbitrary finite
monomial in the matrix elements of the group. The value of such an integral is
expressible as a finite sum of partial fractions in . The recursion formula
largely extends presently available integration formulas for the orthogonal
group.Comment: 9 pages, no figure
A trivial observation on time reversal in random matrix theory
It is commonly thought that a state-dependent quantity, after being averaged
over a classical ensemble of random Hamiltonians, will always become
independent of the state. We point out that this is in general incorrect: if
the ensemble of Hamiltonians is time reversal invariant, and the quantity
involves the state in higher than bilinear order, then we show that the
quantity is only a constant over the orbits of the invariance group on the
Hilbert space. Examples include fidelity and decoherence in appropriate models.Comment: 7 pages 3 figure
Fidelity amplitude of the scattering matrix in microwave cavities
The concept of fidelity decay is discussed from the point of view of the
scattering matrix, and the scattering fidelity is introduced as the parametric
cross-correlation of a given S-matrix element, taken in the time domain,
normalized by the corresponding autocorrelation function. We show that for
chaotic systems, this quantity represents the usual fidelity amplitude, if
appropriate ensemble and/or energy averages are taken. We present a microwave
experiment where the scattering fidelity is measured for an ensemble of chaotic
systems. The results are in excellent agreement with random matrix theory for
the standard fidelity amplitude. The only parameter, namely the perturbation
strength could be determined independently from level dynamics of the system,
thus providing a parameter free agreement between theory and experiment
Scattering fidelity in elastodynamics
The recent introduction of the concept of scattering fidelity, causes us to
revisit the experiment by Lobkis and Weaver [Phys. Rev. Lett. 90, 254302
(2003)]. There, the ``distortion'' of the coda of an acoustic signal is
measured under temperature changes. This quantity is in fact the negative
logarithm of scattering fidelity. We re-analyse their experimental data for two
samples, and we find good agreement with random matrix predictions for the
standard fidelity. Usually, one may expect such an agreement for chaotic
systems only. While the first sample, may indeed be assumed chaotic, for the
second sample, a perfect cuboid, such an agreement is more surprising. For the
first sample, the random matrix analysis yields a perturbation strength
compatible with semiclassical predictions. For the cuboid the measured
perturbation strength is much larger than expected, but with the fitted values
for this strength, the experimental data are well reproduced.Comment: 4 page
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