17,323 research outputs found
Physical properties of the Schur complement of local covariance matrices
General properties of global covariance matrices representing bipartite
Gaussian states can be decomposed into properties of local covariance matrices
and their Schur complements. We demonstrate that given a bipartite Gaussian
state described by a covariance matrix \textbf{V}, the
Schur complement of a local covariance submatrix of it can be
interpreted as a new covariance matrix representing a Gaussian operator of
party 1 conditioned to local parity measurements on party 2. The connection
with a partial parity measurement over a bipartite quantum state and the
determination of the reduced Wigner function is given and an operational
process of parity measurement is developed. Generalization of this procedure to
a -partite Gaussian state is given and it is demonstrated that the
system state conditioned to a partial parity projection is given by a
covariance matrix such as its block elements are Schur complements
of special local matrices.Comment: 10 pages. Replaced with final published versio
Uniform approximation for the overlap caustic of a quantum state with its translations
The semiclassical Wigner function for a Bohr-quantized energy eigenstate is
known to have a caustic along the corresponding classical closed phase space
curve in the case of a single degree of freedom. Its Fourier transform, the
semiclassical chord function, also has a caustic along the conjugate curve
defined as the locus of diameters, i.e. the maximal chords of the original
curve. If the latter is convex, so is its conjugate, resulting in a simple fold
caustic. The uniform approximation through this caustic, that is here derived,
describes the transition undergone by the overlap of the state with its
translation, from an oscillatory regime for small chords, to evanescent
overlaps, rising to a maximum near the caustic. The diameter-caustic for the
Wigner function is also treated.Comment: 14 pages, 9 figure
Universal quantum signature of mixed dynamics in antidot lattices
We investigate phase coherent ballistic transport through antidot lattices in
the generic case where the classical phase space has both regular and chaotic
components. It is shown that the conductivity fluctuations have a non-Gaussian
distribution, and that their moments have a power-law dependence on a
semiclassical parameter, with fractional exponents. These exponents are
obtained from bifurcating periodic orbits in the semiclassical approximation.
They are universal in situations where sufficiently long orbits contribute.Comment: 7 page
Semiclassical Evolution of Dissipative Markovian Systems
A semiclassical approximation for an evolving density operator, driven by a
"closed" hamiltonian operator and "open" markovian Lindblad operators, is
obtained. The theory is based on the chord function, i.e. the Fourier transform
of the Wigner function. It reduces to an exact solution of the Lindblad master
equation if the hamiltonian operator is a quadratic function and the Lindblad
operators are linear functions of positions and momenta.
Initially, the semiclassical formulae for the case of hermitian Lindblad
operators are reinterpreted in terms of a (real) double phase space, generated
by an appropriate classical double Hamiltonian. An extra "open" term is added
to the double Hamiltonian by the non-hermitian part of the Lindblad operators
in the general case of dissipative markovian evolution. The particular case of
generic hamiltonian operators, but linear dissipative Lindblad operators, is
studied in more detail. A Liouville-type equivariance still holds for the
corresponding classical evolution in double phase, but the centre subspace,
which supports the Wigner function, is compressed, along with expansion of its
conjugate subspace, which supports the chord function.
Decoherence narrows the relevant region of double phase space to the
neighborhood of a caustic for both the Wigner function and the chord function.
This difficulty is avoided by a propagator in a mixed representation, so that a
further "small-chord" approximation leads to a simple generalization of the
quadratic theory for evolving Wigner functions.Comment: 33 pages - accepted to J. Phys.
Alternate islands of multiple isochronous chains in wave-particle interactions
We analyze the dynamics of a relativistic particle moving in a uniform
magnetic field and perturbed by a standing electrostatic wave. We show that a
pulsed wave produces an infinite number of perturbative terms with the same
winding number, which may generate islands in the same region of phase space.
As a consequence, the number of isochronous island chains varies as a function
of the wave parameters. We observe that in all the resonances, the number of
chains is related to the amplitude of the various resonant terms. We determine
analytically the position of the periodic points and the number of island
chains as a function of the wave number and wave period. Such information is
very important when one is concerned with regular particle acceleration, since
it is necessary to adjust the initial conditions of the particle to obtain the
maximum acceleration.Comment: Submitte
Quantization of multidimensional cat maps
In this work we study cat maps with many degrees of freedom. Classical cat
maps are classified using the Cayley parametrization of symplectic matrices and
the closely associated center and chord generating functions. Particular
attention is dedicated to loxodromic behavior, which is a new feature of
two-dimensional maps. The maps are then quantized using a recently developed
Weyl representation on the torus and the general condition on the Floquet
angles is derived for a particular map to be quantizable. The semiclassical
approximation is exact, regardless of the dimensionality or of the nature of
the fixed points.Comment: 33 pages, latex, 6 figures, Submitted to Nonlinearit
Periodic orbit bifurcations and scattering time delay fluctuations
We study fluctuations of the Wigner time delay for open (scattering) systems
which exhibit mixed dynamics in the classical limit. It is shown that in the
semiclassical limit the time delay fluctuations have a distribution that
differs markedly from those which describe fully chaotic (or strongly
disordered) systems: their moments have a power law dependence on a
semiclassical parameter, with exponents that are rational fractions. These
exponents are obtained from bifurcating periodic orbits trapped in the system.
They are universal in situations where sufficiently long orbits contribute. We
illustrate the influence of bifurcations on the time delay numerically using an
open quantum map.Comment: 9 pages, 3 figures, contribution to QMC200
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