1,774 research outputs found

### Semiclassical Green Function in Mixed Spaces

A explicit formula on semiclassical Green functions in mixed position and
momentum spaces is given, which is based on Maslov's multi-dimensional
semiclassical theory. The general formula includes both coordinate and momentum
representations of Green functions as two special cases of the form.Comment: 8 pages, typeset by Scientific Wor

### Semiclassical approach to Bose-Einstein condensates in a triple well potential

We present a new approach for the analysis of Bose-Einstein condensates in a
few mode approximation. This method has already been used to successfully
analyze the vibrational modes in various molecular systems and offers a new
perspective on the dynamics in many particle bosonic systems. We discuss a
system consisting of a Bose-Einstein condensate in a triple well potential.
Such systems correspond to classical Hamiltonian systems with three degrees of
freedom. The semiclassical approach allows a simple visualization of the
eigenstates of the quantum system referring to the underlying classical
dynamics. From this classification we can read off the dynamical properties of
the eigenstates such as particle exchange between the wells and entanglement
without further calculations. In addition, this approach offers new insights
into the validity of the mean-field description of the many particle system by
the Gross-Pitaevskii equation, since we make use of exactly this correspondence
in our semiclassical analysis. We choose a three mode system in order to
visualize it easily and, moreover, to have a sufficiently interesting
structure, although the method can also be extended to higher dimensional
systems.Comment: 15 pages, 15 figure

### Comment on "Gravity Waves, Chaos, and Spinning Compact Binaries"

In this comment, I argue that chaotic effects in binary black hole inspiral
will not strongly impact the detection of gravitational waves from such
systems.Comment: 1 page, comment on gr-qc/991004

### Entanglement induced by nonadiabatic chaos

We investigate entanglement between electronic and nuclear degrees of freedom
for a model nonadiabatic system. We find that entanglement (measured by the von
Neumann entropy of the subsystem for the eigenstates) is large in a statistical
sense when the system shows ``nonadiabatic chaos'' behavior which was found in
our previous work [Phys. Rev. E {\bf 63}, 066221 (2001)]. We also discuss
non-statistical behavior of the eigenstates for the regular cases.Comment: 4 pages, 6 figures, submitted to Phys. Rev.

### Long-Time Coherence in Echo Spectroscopy with $\pi/2$--$\pi$--$\pi/2$ Pulse Sequence

Motivated by atom optics experiments, we investigate a new class of fidelity
functions describing the reconstruction of quantum states by time-reversal
operations as $M_{\mathrm{Da}}(t) = | <\psi | e^{i H_2 t / 2} e^{i H_1 t / 2}
e^{-i H_2 t / 2} e^{-i H_1 t / 2} | \psi >|^2$. We show that the decay of
$M_{\mathrm{Da}}$ is quartic in time at short times, and that it freezes well
above the ergodic value at long times, when $H_2-H_1$ is not too large. The
long-time saturation value of $M_{\mathrm{Da}}$ contains easily extractable
information on the strength of decoherence in these systems.Comment: 5 pages, 3 figure

### Periodic orbit quantization of a Hamiltonian map on the sphere

In a previous paper we introduced examples of Hamiltonian mappings with phase
space structures resembling circle packings. It was shown that a vast number of
periodic orbits can be found using special properties. We now use this
information to explore the semiclassical quantization of one of these maps.Comment: 23 pages, REVTEX

### Semiclassical theory of spin-orbit interactions using spin coherent states

We formulate a semiclassical theory for systems with spin-orbit interactions.
Using spin coherent states, we start from the path integral in an extended
phase space, formulate the classical dynamics of the coupled orbital and spin
degrees of freedom, and calculate the ingredients of Gutzwiller's trace formula
for the density of states. For a two-dimensional quantum dot with a spin-orbit
interaction of Rashba type, we obtain satisfactory agreement with fully
quantum-mechanical calculations. The mode-conversion problem, which arose in an
earlier semiclassical approach, has hereby been overcome.Comment: LaTeX (RevTeX), 4 pages, 2 figures, accepted for Physical Review
Letters; final version (v2) for publication with minor editorial change

### Significance of Ghost Orbit Bifurcations in Semiclassical Spectra

Gutzwiller's trace formula for the semiclassical density of states in a
chaotic system diverges near bifurcations of periodic orbits, where it must be
replaced with uniform approximations. It is well known that, when applying
these approximations, complex predecessors of orbits created in the bifurcation
("ghost orbits") can produce pronounced signatures in the semiclassical spectra
in the vicinity of the bifurcation. It is the purpose of this paper to
demonstrate that these ghost orbits themselves can undergo bifurcations,
resulting in complex, nongeneric bifurcation scenarios. We do so by studying an
example taken from the Diamagnetic Kepler Problem, viz. the period quadrupling
of the balloon orbit. By application of normal form theory we construct an
analytic description of the complete bifurcation scenario, which is then used
to calculate the pertinent uniform approximation. The ghost orbit bifurcation
turns out to produce signatures in the semiclassical spectrum in much the same
way as a bifurcation of real orbits would.Comment: 20 pages, 6 figures, LATEX (IOP style), submitted to J. Phys.

### Symmetry Decomposition of Chaotic Dynamics

Discrete symmetries of dynamical flows give rise to relations between
periodic orbits, reduce the dynamics to a fundamental domain, and lead to
factorizations of zeta functions. These factorizations in turn reduce the labor
and improve the convergence of cycle expansions for classical and quantum
spectra associated with the flow. In this paper the general formalism is
developed, with the $N$-disk pinball model used as a concrete example and a
series of physically interesting cases worked out in detail.Comment: CYCLER Paper 93mar01

### Point perturbations of circle billiards

The spectral statistics of the circular billiard with a point-scatterer is
investigated. In the semiclassical limit, the spectrum is demonstrated to be
composed of two uncorrelated level sequences. The first corresponds to states
for which the scatterer is located in the classically forbidden region and its
energy levels are not affected by the scatterer in the semiclassical limit
while the second sequence contains the levels which are affected by the
point-scatterer. The nearest neighbor spacing distribution which results from
the superposition of these sequences is calculated analytically within some
approximation and good agreement with the distribution that was computed
numerically is found.Comment: 9 pages, 2 figure

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