15,202 research outputs found
Statistical study of the conductance and shot noise in open quantum-chaotic cavities: Contribution from whispering gallery modes
In the past, a maximum-entropy model was introduced and applied to the study
of statistical scattering by chaotic cavities, when short paths may play an
important role in the scattering process. In particular, the validity of the
model was investigated in relation with the statistical properties of the
conductance in open chaotic cavities. In this article we investigate further
the validity of the maximum-entropy model, by comparing the theoretical
predictions with the results of computer simulations, in which the Schroedinger
equation is solved numerically inside the cavity for one and two open channels
in the leads; we analyze, in addition to the conductance, the zero-frequency
limit of the shot-noise power spectrum. We also obtain theoretical results for
the ensemble average of this last quantity, for the orthogonal and unitary
cases of the circular ensemble and an arbitrary number of channels. Generally
speaking, the agreement between theory and numerics is good. In some of the
cavities that we study, short paths consist of whispering gallery modes, which
were excluded in previous studies. These cavities turn out to be all the more
interesting, as it is in relation with them that we found certain systematic
discrepancies in the comparison with theory. We give evidence that it is the
lack of stationarity inside the energy interval that is analyzed, and hence the
lack of ergodicity that gives rise to the discrepancies. Indeed, the agreement
between theory and numerical simulations is improved when the energy interval
is reduced to a point and the statistics is then collected over an ensemble. It
thus appears that the maximum-entropy model is valid beyond the domain where it
was originally derived. An understanding of this situation is still lacking at
the present moment.Comment: Revised version, minor modifications, 28 pages, 7 figure
The problem of quantum chaotic scattering with direct processes reduced to the one without
We show that the study of the statistical properties of the scattering matrix
S for quantum chaotic scattering in the presence of direct processes
(charaterized by a nonzero average S matrix ) can be reduced to the simpler
case where direct processes are absent ( = 0). Our result is verified with a
numerical simulation of the two-energy autocorrelation for two-dimensional S
matrices. It is also used to extend Wigner's time delay distribution for
one-dimensional S matrices, recently found for = 0, to the case not
equal to zero; this extension is verified numerically. As a consequence of our
result, future calculations can be restricted to the simpler case of no direct
processes.Comment: 9 pages (Latex) and 1 EPS figure. Submitted to Europhysics Letters.
The conjecture proposed in the previous version is proved; thus the present
version contains a more satisfactory presentation of the proble
Undulation textures at the phase transitions of some alkyloxybenzoic acids
We observed undulated smectic textures for some compounds of the
4,n-alkyloxybenzoic (nOBAC) acid series, at transitions between the smectic and
the isotropic phase and between the smectic and nematic phase. Studied
compounds were 12OBAC, 16OBAC and a binary mixture of 12- and 16OBAC. The
undulations are dressing a usual Schlieren texture. In the case of the binary
mixture, an interesting fingerprint pattern is observed too
Casimir Densities for a Massive Fermionic Quantum Field in a Global Monopole Background with Spherical Boundary
We investigate the vacuum expectation value of the energy-momentum tensor
associated with a massive fermionic field obeying the MIT bag boundary
condition on a spherical shell in the global monopole spacetime. The asymptotic
behavior of the vacuum densities is investigated near the sphere center and
surface, and at large distances from the sphere. In the limit of strong
gravitational field corresponding to small values of the parameter describing
the solid angle deficit in global monopole geometry, the sphere-induced
expectation values are exponentially suppressed.Comment: 8 pages, 4 figures, 6th Alexander Friedmann International Seminar on
Gravitation and Cosmolog
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