4,899 research outputs found
Fluctuational susceptibility of ultracold bosons in the vicinity of condensation
We study the behaviour of ultracold bosonic gas in the critical region above
the Bose-Einstein condensation in the presence of an artificial magnetic field,
. We show that the condensate fluctuations above the critical
temperature cause the fluctuational susceptibility, ,
of a uniform gas to have a stronger power-law divergence than in an analogous
superconducting system. Measuring such a divergence opens new ways of exploring
critical properties of the ultracold gas and an opportunity of an accurate
determination of . We describe a method of measuring
which requires a constant gradient in and suggest a way of
creating such a field in experiment.Comment: 5 pages, 3 figures, 5 pages of Supplement; the text is rewritten and
rearranged, and the figures are modifie
Dimensional Crossover of the Dephasing Time in Disordered Mesoscopic Rings: From Diffusive through Ergodic to 0D Behavior
We analyze dephasing by electron interactions in a small disordered quasi-one
dimensional (1D) ring weakly coupled to leads, where we recently predicted a
crossover for the dephasing time \tPh(T) from diffusive or ergodic 1D
(\tPh^{-1} \propto T^{2/3}, T^{1}) to behavior (\tPh^{-1} \propto
T^{2}) as drops below the Thouless energy \ETh. We provide a detailed
derivation of our results, based on an influence functional for quantum Nyquist
noise, and calculate all leading and subleading terms of the dephasing time in
the three regimes. Explicitly taking into account the Pauli blocking of the
Fermi sea in the metal allows us to describe the regime on equal footing
as the others. The crossover to , predicted by Sivan, Imry and Aronov for
3D systems, has so far eluded experimental observation. We will show that for
T \ll \ETh, dephasing governs not only the -dependence for the smooth
part of the magnetoconductivity but also for the amplitude of the
Altshuler-Aronov-Spivak oscillations, which result only from electron paths
winding around the ring. This observation can be exploited to filter out and
eliminate contributions to dephasing from trajectories which do not wind around
the ring, which may tend to mask the behavior. Thus, the ring geometry
holds promise of finally observing the crossover to experimentally.Comment: in "Perspectives of Mesoscopic Physics - Dedicated to Yoseph Imry's
70th Birthday", edited by Amnon Aharony and Ora Entin-Wohlman (World
Scientific, 2010), chap. 20, p. 371-396, ISBN-13 978-981-4299-43-
Thermal noise and dephasing due to electron interactions in non-trivial geometries
We study Johnson-Nyquist noise in macroscopically inhomogeneous disordered
metals and give a microscopic derivation of the correlation function of the
scalar electric potentials in real space. Starting from the interacting
Hamiltonian for electrons in a metal and the random phase approximation, we
find a relation between the correlation function of the electric potentials and
the density fluctuations which is valid for arbitrary geometry and
dimensionality. We show that the potential fluctuations are proportional to the
solution of the diffusion equation, taken at zero frequency. As an example, we
consider networks of quasi-1D disordered wires and give an explicit expression
for the correlation function in a ring attached via arms to absorbing leads. We
use this result in order to develop a theory of dephasing by electronic noise
in multiply-connected systems.Comment: 9 pages, 6 figures (version submitted to PRB
Fluctuation-induced traffic congestion in heterogeneous networks
In studies of complex heterogeneous networks, particularly of the Internet,
significant attention was paid to analyzing network failures caused by hardware
faults or overload, where the network reaction was modeled as rerouting of
traffic away from failed or congested elements. Here we model another type of
the network reaction to congestion -- a sharp reduction of the input traffic
rate through congested routes which occurs on much shorter time scales. We
consider the onset of congestion in the Internet where local mismatch between
demand and capacity results in traffic losses and show that it can be described
as a phase transition characterized by strong non-Gaussian loss fluctuations at
a mesoscopic time scale. The fluctuations, caused by noise in input traffic,
are exacerbated by the heterogeneous nature of the network manifested in a
scale-free load distribution. They result in the network strongly overreacting
to the first signs of congestion by significantly reducing input traffic along
the communication paths where congestion is utterly negligible.Comment: 4 pages, 3 figure
Crossover from diffusive to strongly localized regime in two-dimensional systems
We have studied the conductance distribution function of two-dimensional
disordered noninteracting systems in the crossover regime between the diffusive
and the localized phases. The distribution is entirely determined by the mean
conductance, g, in agreement with the strong version of the single-parameter
scaling hypothesis. The distribution seems to change drastically at a critical
value very close to one. For conductances larger than this critical value, the
distribution is roughly Gaussian while for smaller values it resembles a
log-normal distribution. The two distributions match at the critical point with
an often appreciable change in behavior. This matching implies a jump in the
first derivative of the distribution which does not seem to disappear as system
size increases. We have also studied 1/g corrections to the skewness to
quantify the deviation of the distribution from a Gaussian function in the
diffusive regime.Comment: 4 pages, 4 figure
The Zipf law for random texts with unequal probabilities of occurrence of letters and the Pascal pyramid
We model the generation of words with independent unequal probabilities of
occurrence of letters. We prove that the probability of occurrence of
words of rank has a power asymptotics. As distinct from the paper published
earlier by B. Conrad and M. Mitzenmacher, we give a brief proof by elementary
methods and obtain an explicit formula for the exponent of the power law.Comment: 4 page
Decoherence of charge qubit coupled to interacting background charges
The major contribution to decoherence of a double quantum dot or a Josephson
junction charge qubit comes from the electrostatic coupling to fluctuating
background charges hybridized with the conduction electrons in the reservoir.
However, estimations according to previously developed theories show that
finding a sufficient number of effective fluctuators in a realistic
experimental layout is quite improbable. We show that this paradox is resolved
by allowing for a short-range Coulomb interaction of the fluctuators with the
electrons in the reservoir. This dramatically enhances both the number of
effective fluctuators and their contribution to decoherence, resulting in the
most dangerous decoherence mechanism for charge qubits.Comment: 4 pages, 1 figur
Asymptotically exact probability distribution for the Sinai model with finite drift
We obtain the exact asymptotic result for the disorder-averaged probability
distribution function for a random walk in a biased Sinai model and show that
it is characterized by a creeping behavior of the displacement moments with
time, ~ t^{\mu n} where \mu is dimensionless mean drift. We employ a
method originated in quantum diffusion which is based on the exact mapping of
the problem to an imaginary-time Schr\"{odinger} equation. For nonzero drift
such an equation has an isolated lowest eigenvalue separated by a gap from
quasi-continuous excited states, and the eigenstate corresponding to the former
governs the long-time asymptotic behavior.Comment: 4 pages, 2 figure
Temporal Correlations of Local Network Losses
We introduce a continuum model describing data losses in a single node of a
packet-switched network (like the Internet) which preserves the discrete nature
of the data loss process. {\em By construction}, the model has critical
behavior with a sharp transition from exponentially small to finite losses with
increasing data arrival rate. We show that such a model exhibits strong
fluctuations in the loss rate at the critical point and non-Markovian power-law
correlations in time, in spite of the Markovian character of the data arrival
process. The continuum model allows for rather general incoming data packet
distributions and can be naturally generalized to consider the buffer server
idleness statistics
Optics with Quantum Hall Skyrmions
A novel type of charged excitation, known as a Skyrmion, has recently been
discovered in quantum Hall systems with filling factor near \nu = 1. A Skyrmion
-- which can be thought of as a topological twist in the spin density of the
electron gas -- has the same charge as an electron, but a much larger spin. In
this review we present a detailed theoretical investigation of the optical
properties of Skyrmions. Our results provide means for the optical detection of
Skyrmions using photoluminescence (PL) spectroscopy. We first consider the
optical properties of Skyrmions in disordered systems. A calculation of the
luminescence energy reveals a special optical signature which allows us to
distinguish between Skyrmions and ordinary electrons. Two experiments to
measure the optical signature are proposed. We then turn to the optical
properties of Skyrmions in pure systems. We show that, just like an ordinary
electron, a Skyrmion may bind with a hole to form a Skyrmionic exciton. The
Skyrmionic exciton can have a lower energy than the ordinary magnetoexciton.
The optical signature of Skyrmions is found to be a robust feature of the PL
spectrum in both disordered and pure systems.Comment: 31 pages, LaTex, 11 eps figures. ijmpb style file included. Review
article submitted to Int. J. Mod. Phys.
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