548 research outputs found
Regular Tunnelling Sequences in Mixed Systems
We show that the pattern of tunnelling rates can display a vivid and regular
pattern when the classical dynamics is of mixed chaotic/regular type. We
consider the situation in which the dominant tunnelling route connects to a
stable periodic orbit and this orbit is surrounded by a regular island which
supports a number of quantum states. We derive an explicit semiclassical
expression for the positions and tunnelling rates of these states by use of a
complexified trace formula.Comment: submitted to Physica E as a contribution to the workshop proceedings
of "Dynamics of Complex Systems" held at the Max Planck Institute for the
Physics of Complex Systems in Dresden from March 30 to June 15, 199
Calculation of the Characteristic Functions of Anharmonic Oscillators
The energy levels of quantum systems are determined by quantization
conditions. For one-dimensional anharmonic oscillators, one can transform the
Schrodinger equation into a Riccati form, i.e., in terms of the logarithmic
derivative of the wave function. A perturbative expansion of the logarithmic
derivative of the wave function can easily be obtained. The Bohr-Sommerfeld
quantization condition can be expressed in terms of a contour integral around
the poles of the logarithmic derivative. Its functional form is B_m(E,g) = n +
1/2, where B is a characteristic function of the anharmonic oscillator of
degree m, E is the resonance energy, and g is the coupling constant. A
recursive scheme can be devised which facilitates the evaluation of
higher-order Wentzel-Kramers-Brioullin (WKB) approximants. The WKB expansion of
the logarithmic derivative of the wave function has a cut in the tunneling
region. The contour integral about the tunneling region yields the instanton
action plus corrections, summarized in a second characteristic function
A_m(E,g). The evaluation of A_m(E,g) by the method of asymptotic matching is
discussed for the case of the cubic oscillator of degree m=3.Comment: 11 pages, LaTeX; three further typographical errors correcte
Fermi Edge Singularities in the Mesoscopic Regime: II. Photo-absorption Spectra
We study Fermi edge singularities in photo-absorption spectra of generic
mesoscopic systems such as quantum dots or nanoparticles. We predict deviations
from macroscopic-metallic behavior and propose experimental setups for the
observation of these effects. The theory is based on the model of a localized,
or rank one, perturbation caused by the (core) hole left behind after the
photo-excitation of an electron into the conduction band. The photo-absorption
spectra result from the competition between two many-body responses, Anderson's
orthogonality catastrophe and the Mahan-Nozieres-DeDominicis contribution. Both
mechanisms depend on the system size through the number of particles and, more
importantly, fluctuations produced by the coherence characteristic of
mesoscopic samples. The latter lead to a modification of the dipole matrix
element and trigger one of our key results: a rounded K-edge typically found in
metals will turn into a (slightly) peaked edge on average in the mesoscopic
regime. We consider in detail the effect of the "bound state" produced by the
core hole.Comment: 16 page
Artificial trapping of a stable high-density dipolar exciton fluid
We present compelling experimental evidence for a successful electrostatic
trapping of two-dimensional dipolar excitons that results in stable formation
of a well confined, high-density and spatially uniform dipolar exciton fluid.
We show that, for at least half a microsecond, the exciton fluid sustains a
density higher than the critical density for degeneracy if the exciton fluid
temperature reaches the lattice temperature within that time. This method
should allow for the study of strongly interacting bosons in two dimensions at
low temperatures, and possibly lead towards the observation of quantum phase
transitions of 2D interacting excitons, such as superfluidity and
crystallization.Comment: 11 pages 4 figure
Robustness of adiabatic passage trough a quantum phase transition
We analyze the crossing of a quantum critical point based on exact results
for the transverse XY model. In dependence of the change rate of the driving
field, the evolution of the ground state is studied while the transverse
magnetic field is tuned through the critical point with a linear ramping. The
excitation probability is obtained exactly and is compared to previous studies
and to the Landau-Zener formula, a long time solution for non-adiabatic
transitions in two-level systems. The exact time dependence of the excitations
density in the system allows to identify the adiabatic and diabatic regions
during the sweep and to study the mesoscopic fluctuations of the excitations.
The effect of white noise is investigated, where the critical point transmutes
into a non-hermitian ``degenerate region''. Besides an overall increase of the
excitations during and at the end of the sweep, the most destructive effect of
the noise is the decay of the state purity that is enhanced by the passage
through the degenerate region.Comment: 16 pages, 15 figure
Solitary Adrenal Metastasis from Esophageal Adenocarcinoma: A Case Report and Review of the Literature
Introduction. In patients with extra-adrenal malignancy, an adrenal mass necessitates investigating the possibility of metastatic tumor. Curable adrenal metastasis are considered as a rare event. Case report. A 52-year-old male suffering from lower esophageal adenocarcinoma with a solitary left adrenal metastasis is presented herein, who underwent concomitant transhiatal esophagectomy and left adrenalectomy. The patient remains disease-free 18 months later. Discussion. Adrenal metastases mostly occur in patients with lung, kidney, breast, and gastrointestinal carcinomas. Primary esophageal adenocarcinoma gives adrenal metastatic deposits according to autopsy series with an incidence of about 3%–12%. When no other evidence of metastatic disease in cancer patients exists, several authors advocate adrenalectomy with curative intent. Isolated cases of long-term survival after resection of solitary adrenal metastasis from esophageal adenocarcinoma, like in our case, have been reported only as case reports. Conclusion. This study concludes that surgical resection may result in survival benefit in selected patients with solitary adrenal metastasis from esophageal adenocarcinoma
Sharpenings of Li's criterion for the Riemann Hypothesis
Exact and asymptotic formulae are displayed for the coefficients
used in Li's criterion for the Riemann Hypothesis. For we obtain
that if (and only if) the Hypothesis is true,
(with and explicitly given, also for the case of more general zeta or
-functions); whereas in the opposite case, has a non-tempered
oscillatory form.Comment: 10 pages, Math. Phys. Anal. Geom (2006, at press). V2: minor text
corrections and updated reference
The WKB Approximation without Divergences
In this paper, the WKB approximation to the scattering problem is developed
without the divergences which usually appear at the classical turning points. A
detailed procedure of complexification is shown to generate results identical
to the usual WKB prescription but without the cumbersome connection formulas.Comment: 13 pages, TeX file, to appear in Int. J. Theor. Phy
Fractional Hamiltonian Monodromy from a Gauss-Manin Monodromy
Fractional Hamiltonian Monodromy is a generalization of the notion of
Hamiltonian Monodromy, recently introduced by N. N. Nekhoroshev, D. A.
Sadovskii and B. I. Zhilinskii for energy-momentum maps whose image has a
particular type of non-isolated singularities. In this paper, we analyze the
notion of Fractional Hamiltonian Monodromy in terms of the Gauss-Manin
Monodromy of a Riemann surface constructed from the energy-momentum map and
associated to a loop in complex space which bypasses the line of singularities.
We also prove some propositions on Fractional Hamiltonian Monodromy for 1:-n
and m:-n resonant systems.Comment: 39 pages, 24 figures. submitted to J. Math. Phy
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