8 research outputs found
Crossover from Orthogonal to Unitary Symmetry for Ballistic Electron Transport in Chaotic Microstructures
We study the ensemble-averaged conductance as a function of applied magnetic
field for ballistic electron transport across few-channel microstructures
constructed in the shape of classically chaotic billiards. We analyse the
results of recent experiments, which show suppression of weak localization due
to magnetic field, in the framework of random-matrix theory. By analysing a
random-matrix Hamiltonian for the billiard-lead system with the aid of
Landauer's formula and Efetov's supersymmetry technique, we derive a universal
expression for the weak-localization contribution to the mean conductance that
depends only on the number of channels and the magnetic flux. We consequently
gain a theoretical understanding of the continuous crossover from orthogonal
symmetry to unitary symmetry arising from the violation of time-reversal
invariance for generic chaotic systems.Comment: 49 pages, latex, 9 figures as tar-compressed uuencoded fil
Energy averages and fluctuations in the decay out of superdeformed bands
We derive analytic formulae for the energy average (including the energy
average of the fluctuation contribution) and variance of the intraband decay
intensity of a superdeformed band. Our results may be expressed in terms of
three dimensionless variables: , ,
and . Here is
the spreading width for the mixing of a superdeformed (SD) state with the
normally deformed (ND) states whose spin is the same as 's. The
have mean level spacing and mean electromagnetic decay width
whilst has electromagnetic decay width .
The average decay intensity may be expressed solely in terms of the variables
and or, analogously to statistical
nuclear reaction theory, in terms of the transmission coefficients and
describing transmission from the to the SD band via and
to lower ND states.
The variance of the decay intensity, in analogy with Ericson's theory of
cross section fluctuations depends on an additional variable, the correlation
length
\Gamma_N/(\Gamma_S+\Gamma^{\downarrow})=\frac{d}{2\pi}T_N/(\Gamma_S+\Gamma^{\d
ownarrow}). This suggests that analysis of an experimentally obtained variance
could yield the mean level spacing as does analysis of the cross section
autocorrelation function in compound nuclear reactions.
We compare our results with those of Gu and Weidenm\"uller.Comment: revtex4, 14 pages, 4 figures, to appear in Physical Review
Weak Localization and Integer Quantum Hall Effect in a Periodic Potential
We consider magnetotransport in a disordered two-dimensional electron gas in
the presence of a periodic modulation in one direction. Existing quasiclassical
and quantum approaches to this problem account for Weiss oscillations in the
resistivity tensor at moderate magnetic fields, as well as a strong
modulation-induced modification of the Shubnikov-de Haas oscillations at higher
magnetic fields. They do not account, however, for the operation at even higher
magnetic fields of the integer quantum Hall effect, for which quantum
interference processes are responsible. We then introduce a field-theory
approach, based on a nonlinear sigma model, which encompasses naturally both
the quasiclassical and quantum-mechanical approaches, as well as providing a
consistent means of extending them to include quantum interference corrections.
A perturbative renormalization-group analysis of the field theory shows how
weak localization corrections to the conductivity tensor may be described by a
modification of the usual one-parameter scaling, such as to accommodate the
anisotropy of the bare conductivity tensor. We also show how the two-parameter
scaling, conjectured as a model for the quantum Hall effect in unmodulated
systems, may be generalized similarly for the modulated system. Within this
model we illustrate the operation of the quantum Hall effect in modulated
systems for parameters that are realistic for current experiments.Comment: 15 pages, 4 figures, ReVTeX; revised version with condensed
introduction; two figures taken out; reference adde
Magnetoconductance autocorrelation function for few-channel chaotic microstructures.
Using the Landauer formula and a random matrix model, we investigate the
autocorrelation function of the conductance versus magnetic field strength for
ballistic electron transport through few-channel microstructures with the shape
of a classically chaotic billiard coupled to ideal leads. This function depends
on the total number M of channels and the parameter t which measures the
difference in magnetic field strengths. Using the supersymmetry technique, we
calculate for any value of M the leading terms of the asymptotic expansion for
small t. We pay particular attention to the evaluation of the boundary terms.
For small values of M, we supplement this analytical study by a numerical
simulation. We compare our results with the squared Lorentzian suggested by
semiclassical theory and valid for large M. For small M, we present evidence
for non--analytic behavior of the autocorrelation function at t = 0.Comment: 40 pages, 4 figures, submitted to Annals of Physics (NY
A comparison between various expressions for effective interactions and operators in nuclei
Mechanism of enhanced yield of light particles in compound nucleus formation: Diffusion description
A transition in the spectral statistics of quantum optical model by different electromagnetic fields
In this paper, we have considered the effects of different quantized electromagnetic fields on the spectral statistics of two-level atoms. The Berry-Robnik distribution and the maximum likelihood estimation technique are used to analyze the effect of the mean photon numbers, the two level atoms numbers and also the quantum number of considered states on the fluctuation properties of different systems which are described by different sets of the Dicke Hamiltonian’s parameters. Our results describe the obvious effect of mean photon number on the spectral statistics and show more regular dynamics when this quantity reaches 700. Also, we observed universality in the spectral statistics of considered systems when the number of two level atoms approaches an unrealistic limit (NA ~ 200) and there are some suggestions about the effect of the quantum number of selected levels and the atom-field coupling constant on level statistics