819 research outputs found
Semiclassical spin damping: Superradiance revisited
A well known description of superradiance from pointlike collections of many
atoms involves the dissipative motion of a large spin. The pertinent
``superradiance master equation'' allows for a formally exact solution which we
subject to a semiclassical evaluation. The clue is a saddle-point approximation
for an inverse Laplace transform. All previous approximate treatments,
disparate as they may appear, are encompassed in our systematic formulation. A
byproduct is a hitherto unknown rigorous relation between coherences and
probabilities. Our results allow for generalizations to spin dynamics with
chaos in the classical limit.Comment: 12 pages standard revtex; to be published in EPJ
Long-lived Quantum Coherence between Macroscopically Distinct States in Superradiance
The dephasing influence of a dissipative environment reduces linear
superpositions of macroscopically distinct quantum states (sometimes also
called Schr\"odinger cat states) usually almost immediately to a statistical
mixture. This process is called decoherence. Couplings to the environment with
a certain symmetry can lead to slow decoherence. In this Letter we show that
the collective coupling of a large number of two-level atoms to an
electromagnetic field mode in a cavity that leads to the phenomena of
superradiance has such a symmetry, at least approximately. We construct
superpositions of macroscopically distinct quantum states decohering only on a
classical time scale and propose an experiment in which the extraordinarily
slow decoherence should be observable.Comment: 4 pages of revte
Parametrization of spin-1 classical states
We give an explicit parametrization of the set of mixed quantum states and of
the set of mixed classical states for a spin--1. Classical states are defined
as states with a positive Glauber-Sudarshan P-function. They are at the same
time the separable symmetric states of two qubits. We explore the geometry of
this set, and show that its boundary consists of a two-parameter family of
ellipsoids. The boundary does not contain any facets, but includes
straight-lines corresponding to mixtures of pure classical states.Comment: 6 pages, 2 figure
Chaotic maps and flows: Exact Riemann-Siegel lookalike for spectral fluctuations
To treat the spectral statistics of quantum maps and flows that are fully
chaotic classically, we use the rigorous Riemann-Siegel lookalike available for
the spectral determinant of unitary time evolution operators . Concentrating
on dynamics without time reversal invariance we get the exact two-point
correlator of the spectral density for finite dimension of the matrix
representative of , as phenomenologically given by random matrix theory. In
the limit the correlator of the Gaussian unitary ensemble is
recovered. Previously conjectured cancellations of contributions of
pseudo-orbits with periods beyond half the Heisenberg time are shown to be
implied by the Riemann-Siegel lookalike
Periodic-orbit theory of universal level correlations in quantum chaos
Using Gutzwiller's semiclassical periodic-orbit theory we demonstrate
universal behaviour of the two-point correlator of the density of levels for
quantum systems whose classical limit is fully chaotic. We go beyond previous
work in establishing the full correlator such that its Fourier transform, the
spectral form factor, is determined for all times, below and above the
Heisenberg time. We cover dynamics with and without time reversal invariance
(from the orthogonal and unitary symmetry classes). A key step in our reasoning
is to sum the periodic-orbit expansion in terms of a matrix integral, like the
one known from the sigma model of random-matrix theory.Comment: 44 pages, 11 figures, changed title; final version published in New
J. Phys. + additional appendices B-F not included in the journal versio
Resonances of the Frobenius-Perron Operator for a Hamiltonian Map with a Mixed Phase Space
Resonances of the (Frobenius-Perron) evolution operator P for phase-space
densities have recently attracted considerable attention, in the context of
interrelations between classical and quantum dynamics. We determine these
resonances as well as eigenvalues of P for Hamiltonian systems with a mixed
phase space, by truncating P to finite size in a Hilbert space of phase-space
functions and then diagonalizing. The corresponding eigenfunctions are
localized on unstable manifolds of hyperbolic periodic orbits for resonances
and on islands of regular motion for eigenvalues. Using information drawn from
the eigenfunctions we reproduce the resonances found by diagonalization through
a variant of the cycle expansion of periodic-orbit theory and as rates of
correlation decay.Comment: 18 pages, 7 figure
Beyond the Heisenberg time: Semiclassical treatment of spectral correlations in chaotic systems with spin 1/2
The two-point correlation function of chaotic systems with spin 1/2 is
evaluated using periodic orbits. The spectral form factor for all times thus
becomes accessible. Equivalence with the predictions of random matrix theory
for the Gaussian symplectic ensemble is demonstrated. A duality between the
underlying generating functions of the orthogonal and symplectic symmetry
classes is semiclassically established
Universal spectral form factor for chaotic dynamics
We consider the semiclassical limit of the spectral form factor of
fully chaotic dynamics. Starting from the Gutzwiller type double sum over
classical periodic orbits we set out to recover the universal behavior
predicted by random-matrix theory, both for dynamics with and without time
reversal invariance. For times smaller than half the Heisenberg time
, we extend the previously known -expansion to
include the cubic term. Beyond confirming random-matrix behavior of individual
spectra, the virtue of that extension is that the ``diagrammatic rules'' come
in sight which determine the families of orbit pairs responsible for all orders
of the -expansion.Comment: 4 pages, 1 figur
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