1,605 research outputs found
Local Versus Global Thermal States: Correlations and the Existence of Local Temperatures
We consider a quantum system consisting of a regular chain of elementary
subsystems with nearest neighbor interactions and assume that the total system
is in a canonical state with temperature . We analyze under what condition
the state factors into a product of canonical density matrices with respect to
groups of subsystems each, and when these groups have the same temperature
. While in classical mechanics the validity of this procedure only depends
on the size of the groups , in quantum mechanics the minimum group size
also depends on the temperature ! As examples, we apply our
analysis to a harmonic chain and different types of Ising spin chains. We
discuss various features that show up due to the characteristics of the models
considered. For the harmonic chain, which successfully describes thermal
properties of insulating solids, our approach gives a first quantitative
estimate of the minimal length scale on which temperature can exist: This
length scale is found to be constant for temperatures above the Debye
temperature and proportional to below.Comment: 12 pages, 5 figures, discussion of results extended, accepted for
publication in Phys. Rev.
Multipartite entanglement in fermionic systems via a geometric measure
We study multipartite entanglement in a system consisting of
indistinguishable fermions. Specifically, we have proposed a geometric
entanglement measure for N spin-1/2 fermions distributed over 2L modes (single
particle states). The measure is defined on the 2L qubit space isomorphic to
the Fock space for 2L single particle states. This entanglement measure is
defined for a given partition of 2L modes containing m >= 2 subsets. Thus this
measure applies to m <= 2L partite fermionic system where L is any finite
number, giving the number of sites. The Hilbert spaces associated with these
subsets may have different dimensions. Further, we have defined the local
quantum operations with respect to a given partition of modes. This definition
is generic and unifies different ways of dividing a fermionic system into
subsystems. We have shown, using a representative case, that the geometric
measure is invariant under local unitaries corresponding to a given partition.
We explicitly demonstrate the use of the measure to calculate multipartite
entanglement in some correlated electron systems. To the best of our knowledge,
there is no usable entanglement measure of m > 3 partite fermionic systems in
the literature, so that this is the first measure of multipartite entanglement
for fermionic systems going beyond the bipartite and tripartite cases.Comment: 25 pages, 8 figure
Switch Points of Bi-Persistence Matching Distance
In multi-parameter persistence, the matching distance is defined as the
supremum of weighted bottleneck distances on the barcodes given by the
restriction of persistence modules to lines with a positive slope. In the case
of finitely presented bi-persistence modules, all the available methods to
compute the matching distance are based on restricting the computation to lines
through pairs from a finite set of points in the plane. Some of these points
are determined by the filtration data as they are entrance values of critical
simplices. However, these critical values alone are not sufficient for the
matching distance computation and it is necessary to add so-called switch
points, i.e. points such that on a line through any of them, the bottleneck
matching switches the matched pair.
This paper is devoted to the algorithmic computation of the set of switch
points given a set of critical values. We find conditions under which a
candidate switch point is erroneous or superfluous. The obtained conditions are
turned into algorithms that have been implemented. With this, we analyze how
the size of the set of switch points increases as the number of critical values
increases, and how it varies depending on the distribution of critical values.
Experiments are carried out on various types of bi-persistence modules.Comment: 30 pages, 10 figures. Comments welcom
Entanglement in the interaction between two quantum oscillator systems
The fundamental quantum dynamics of two interacting oscillator systems are
studied in two different scenarios. In one case, both oscillators are assumed
to be linear, whereas in the second case, one oscillator is linear and the
other is a non-linear, angular-momentum oscillator; the second case is, of
course, more complex in terms of energy transfer and dynamics. These two
scenarios have been the subject of much interest over the years, especially in
developing an understanding of modern concepts in quantum optics and quantum
electronics. In this work, however, these two scenarios are utilized to
consider and discuss the salient features of quantum behaviors resulting from
the interactive nature of the two oscillators, i.e., coherence, entanglement,
spontaneous emission, etc., and to apply a measure of entanglement in analyzing
the nature of the interacting systems. ... For the coupled linear and
angular-momentum oscillator system in the fully quantum-mechanical description,
we consider special examples of two, three, four-level angular momentum
systems, demonstrating the explicit appearances of entanglement. We also show
that this entanglement persists even as the coupled angular momentum oscillator
is taken to the limit of a large number of levels, a limit which would go over
to the classical picture for an uncoupled angular momentum oscillator
Effects of upward and downward social comparison information on the efficacy of an appearance-based sun protection intervention: a randomized, controlled experiment
This experiment examined the impact of adding upward and/or downward social comparison information on the efficacy of an appearance-based sun protection intervention (UV photos and photoaging information). Southern California college students (N = 126) were randomly assigned to one of four conditions: control, intervention, intervention plus upward social comparison, intervention plus downward social comparison. The results demonstrated that all those who received the basic UV photo/photoaging intervention reported greater perceived susceptibility to photoaging (d = .74), less favorable tanning cognitions (d = .44), and greater intentions to sun protect (d = 1.32) relative to controls. Of more interest, while the basic intervention increased sun protective behavior during the subsequent 5 weeks relative to controls (d = .44), the addition of downward comparison information completely negated this benefit. Upward comparison information produced sun protection levels that were only slightly (and nonsignificantly) greater than in the basic intervention condition and, as such, does not appear to be a cost-effective addition. Possible mechanisms that may have reduced the benefits of upward comparison information and contributed to the undermining effects of downward comparison information are discussed
Dynamics of a Quantum Control-Not Gate for an Ensemble of Four-Spin Molecules at Room Temperature
We investigate numerically a single-pulse implementation of a quantum
Control-Not (CN) gate for an ensemble of Ising spin systems at room
temperature. For an ensemble of four-spin ``molecules'' we simulate the
time-evolution of the density matrix, for both digital and superpositional
initial conditions. Our numerical calculations confirm the feasibility of
implementation of quantum CN gate in this system at finite temperature, using
electromagnetic -pulse.Comment: 7 pages 3 figure
Phase transitions for -adic Potts model on the Cayley tree of order three
In the present paper, we study a phase transition problem for the -state
-adic Potts model over the Cayley tree of order three. We consider a more
general notion of -adic Gibbs measure which depends on parameter
\rho\in\bq_p. Such a measure is called {\it generalized -adic quasi Gibbs
measure}. When equals to -adic exponent, then it coincides with the
-adic Gibbs measure. When , then it coincides with -adic quasi
Gibbs measure. Therefore, we investigate two regimes with respect to the value
of . Namely, in the first regime, one takes for some
J\in\bq_p, in the second one . In each regime, we first find
conditions for the existence of generalized -adic quasi Gibbs measures.
Furthermore, in the first regime, we establish the existence of the phase
transition under some conditions. In the second regime, when we prove the existence of a quasi phase transition. It turns out that
if and \sqrt{-3}\in\bq_p, then one finds the existence
of the strong phase transition.Comment: 27 page
The monomer-dimer problem and moment Lyapunov exponents of homogeneous Gaussian random fields
We consider an "elastic" version of the statistical mechanical monomer-dimer
problem on the n-dimensional integer lattice. Our setting includes the
classical "rigid" formulation as a special case and extends it by allowing each
dimer to consist of particles at arbitrarily distant sites of the lattice, with
the energy of interaction between the particles in a dimer depending on their
relative position. We reduce the free energy of the elastic dimer-monomer (EDM)
system per lattice site in the thermodynamic limit to the moment Lyapunov
exponent (MLE) of a homogeneous Gaussian random field (GRF) whose mean value
and covariance function are the Boltzmann factors associated with the monomer
energy and dimer potential. In particular, the classical monomer-dimer problem
becomes related to the MLE of a moving average GRF. We outline an approach to
recursive computation of the partition function for "Manhattan" EDM systems
where the dimer potential is a weighted l1-distance and the auxiliary GRF is a
Markov random field of Pickard type which behaves in space like autoregressive
processes do in time. For one-dimensional Manhattan EDM systems, we compute the
MLE of the resulting Gaussian Markov chain as the largest eigenvalue of a
compact transfer operator on a Hilbert space which is related to the
annihilation and creation operators of the quantum harmonic oscillator and also
recast it as the eigenvalue problem for a pantograph functional-differential
equation.Comment: 24 pages, 4 figures, submitted on 14 October 2011 to a special issue
of DCDS-
RELICS: The Reionization Lensing Cluster Survey and the Brightest High-z Galaxies
Massive foreground galaxy clusters magnify and distort the light of objects behind them, permitting a view into both the extremely distant and intrinsically faint galaxy populations. We present here the z ~ 6-8 candidate high-redshift galaxies from the Reionization Lensing Cluster Survey (RELICS), a Hubble and Spitzer Space Telescope survey of 41 massive galaxy clusters spanning an area of ≈200 arcmin². These clusters were selected to be excellent lenses, and we find similar high-redshift sample sizes and magnitude distributions as the Cluster Lensing And Supernova survey with Hubble (CLASH). We discover 257, 57, and eight candidate galaxies at z ~ 6, 7, and 8 respectively, (322 in total). The observed (lensed) magnitudes of the z ~ 6 candidates are as bright as AB mag ~23, making them among the brightest known at these redshifts, comparable with discoveries from much wider, blank-field surveys. RELICS demonstrates the efficiency of using strong gravitational lenses to produce high-redshift samples in the epoch of reionization. These brightly observed galaxies are excellent targets for follow-up study with current and future observatories, including the James Webb Space Telescope
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