1,170 research outputs found
On entanglement evolution across defects in critical chains
We consider a local quench where two free-fermion half-chains are coupled via
a defect. We show that the logarithmic increase of the entanglement entropy is
governed by the same effective central charge which appears in the ground-state
properties and which is known exactly. For unequal initial filling of the
half-chains, we determine the linear increase of the entanglement entropy.Comment: 11 pages, 5 figures, minor changes, reference adde
Detecting many-body entanglements in noninteracting ultracold atomic fermi gases
We explore the possibility of detecting many-body entanglement using
time-of-flight (TOF) momentum correlations in ultracold atomic fermi gases. In
analogy to the vacuum correlations responsible for Bekenstein-Hawking black
hole entropy, a partitioned atomic gas will exhibit particle-hole correlations
responsible for entanglement entropy. The signature of these momentum
correlations might be detected by a sensitive TOF type experiment.Comment: 5 pages, 5 figures, fixed axes labels on figs. 3 and 5, added
reference
Observations Outside the Light-Cone: Algorithms for Non-Equilibrium and Thermal States
We apply algorithms based on Lieb-Robinson bounds to simulate time-dependent
and thermal quantities in quantum systems. For time-dependent systems, we
modify a previous mapping to quantum circuits to significantly reduce the
computer resources required. This modification is based on a principle of
"observing" the system outside the light-cone. We apply this method to study
spin relaxation in systems started out of equilibrium with initial conditions
that give rise to very rapid entanglement growth. We also show that it is
possible to approximate time evolution under a local Hamiltonian by a quantum
circuit whose light-cone naturally matches the Lieb-Robinson velocity.
Asymptotically, these modified methods allow a doubling of the system size that
one can obtain compared to direct simulation. We then consider a different
problem of thermal properties of disordered spin chains and use quantum belief
propagation to average over different configurations. We test this algorithm on
one dimensional systems with mixed ferromagnetic and anti-ferromagnetic bonds,
where we can compare to quantum Monte Carlo, and then we apply it to the study
of disordered, frustrated spin systems.Comment: 19 pages, 12 figure
Stochastic exclusion processes versus coherent transport
Stochastic exclusion processes play an integral role in the physics of
non-equilibrium statistical mechanics. These models are Markovian processes,
described by a classical master equation. In this paper a quantum mechanical
version of a stochastic hopping process in one dimension is formulated in terms
of a quantum master equation. This allows the investigation of coherent and
stochastic evolution in the same formal framework. The focus lies on the
non-equilibrium steady state. Two stochastic model systems are considered, the
totally asymmetric exclusion process and the fully symmetric exclusion process.
The steady state transport properties of these models is compared to the case
with additional coherent evolution, generated by the -Hamiltonian
Edwards-Wilkinson surface over a spherical substrate: noise in the height fluctuations
We study the steady state fluctuations of an Edwards-Wilkinson type surface
with the substrate taken to be a sphere. We show that the height fluctuations
on circles at a given latitude has the effective action of a perfect Gaussian
noise, just as in the case of fixed radius circles on an infinite planar
substrate. The effective surface tension, which is the overall coefficient of
the action, does not depend on the latitude angle of the circles.Comment: 6 page
The components of empirical multifractality in financial returns
We perform a systematic investigation on the components of the empirical
multifractality of financial returns using the daily data of Dow Jones
Industrial Average from 26 May 1896 to 27 April 2007 as an example. The
temporal structure and fat-tailed distribution of the returns are considered as
possible influence factors. The multifractal spectrum of the original return
series is compared with those of four kinds of surrogate data: (1) shuffled
data that contain no temporal correlation but have the same distribution, (2)
surrogate data in which any nonlinear correlation is removed but the
distribution and linear correlation are preserved, (3) surrogate data in which
large positive and negative returns are replaced with small values, and (4)
surrogate data generated from alternative fat-tailed distributions with the
temporal correlation preserved. We find that all these factors have influence
on the multifractal spectrum. We also find that the temporal structure (linear
or nonlinear) has minor impact on the singularity width of the
multifractal spectrum while the fat tails have major impact on ,
which confirms the earlier results. In addition, the linear correlation is
found to have only a horizontal translation effect on the multifractal spectrum
in which the distance is approximately equal to the difference between its DFA
scaling exponent and 0.5. Our method can also be applied to other financial or
physical variables and other multifractal formalisms.Comment: 6 epl page
The magnetofection method: Using magnetic force to enhance gene delivery
In order to enhance and target gene delivery we have previously established a novel method, termed magnetofection, which uses magnetic force acting on gene vectors that are associated with magnetic particles. Here we review the benefits, the mechanism and the potential of the method with regard to overcoming physical limitations to gene delivery. Magnetic particle chemistry and physics are discussed, followed by a detailed presentation of vector formulation and optimization work. While magnetofection does not necessarily improve the overall performance of any given standard gene transfer method in vitro, its major potential lies in the extraordinarily rapid and efficient transfection at low vector doses and the possibility of remotely controlled vector targeting in vivo
Entanglement entropy and quantum phase transitions in quantum dots coupled to Luttinger liquid wires
We study a quantum phase transition which occurs in a system composed of two
impurities (or quantum dots) each coupled to a different interacting
(Luttinger-liquid) lead. While the impurities are coupled electrostatically,
there is no tunneling between them. Using a mapping of this system onto a Kondo
model, we show analytically that the system undergoes a
Berezinskii-Kosterlitz-Thouless quantum phase transition as function of the
Luttinger liquid parameter in the leads and the dot-lead interaction. The phase
with low values of the Luttinger-liquid parameter is characterized by an abrupt
switch of the population between the impurities as function of a common applied
gate voltage. However, this behavior is hard to verify numerically since one
would have to study extremely long systems. Interestingly though, at the
transition the entanglement entropy drops from a finite value of to
zero. The drop becomes sharp for infinite systems. One can employ finite size
scaling to extrapolate the transition point and the behavior in its vicinity
from the behavior of the entanglement entropy in moderate size samples. We
employ the density matrix renormalization group numerical procedure to
calculate the entanglement entropy of systems with lead lengths of up to 480
sites. Using finite size scaling we extract the transition value and show it to
be in good agreement with the analytical prediction.Comment: 12 pages, 9 figure
Fluctuation scaling in complex systems: Taylor's law and beyond
Complex systems consist of many interacting elements which participate in
some dynamical process. The activity of various elements is often different and
the fluctuation in the activity of an element grows monotonically with the
average activity. This relationship is often of the form "", where the exponent is predominantly in
the range . This power law has been observed in a very wide range of
disciplines, ranging from population dynamics through the Internet to the stock
market and it is often treated under the names \emph{Taylor's law} or
\emph{fluctuation scaling}. This review attempts to show how general the above
scaling relationship is by surveying the literature, as well as by reporting
some new empirical data and model calculations. We also show some basic
principles that can underlie the generality of the phenomenon. This is followed
by a mean-field framework based on sums of random variables. In this context
the emergence of fluctuation scaling is equivalent to some corresponding limit
theorems. In certain physical systems fluctuation scaling can be related to
finite size scaling.Comment: 33 pages, 20 figures, 2 tables, submitted to Advances in Physic
Comprehensive Analysis of Market Conditions in the Foreign Exchange Market: Fluctuation Scaling and Variance-Covariance Matrix
We investigate quotation and transaction activities in the foreign exchange
market for every week during the period of June 2007 to December 2010. A
scaling relationship between the mean values of number of quotations (or number
of transactions) for various currency pairs and the corresponding standard
deviations holds for a majority of the weeks. However, the scaling breaks in
some time intervals, which is related to the emergence of market shocks. There
is a monotonous relationship between values of scaling indices and global
averages of currency pair cross-correlations when both quantities are observed
for various window lengths .Comment: 13 pages, 10 figure
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