900 research outputs found
Binary jumps in continuum. II. Non-equilibrium process and a Vlasov-type scaling limit
Let denote the space of all locally finite subsets (configurations)
in . A stochastic dynamics of binary jumps in continuum is a
Markov process on in which pairs of particles simultaneously hop over
. We discuss a non-equilibrium dynamics of binary jumps. We prove
the existence of an evolution of correlation functions on a finite time
interval. We also show that a Vlasov-type mesoscopic scaling for such a
dynamics leads to a generalized Boltzmann non-linear equation for the particle
density
Tagged particle process in continuum with singular interactions
By using Dirichlet form techniques we construct the dynamics of a tagged
particle in an infinite particle environment of interacting particles for a
large class of interaction potentials. In particular, we can treat interaction
potentials having a singularity at the origin, non-trivial negative part and
infinite range, as e.g., the Lennard-Jones potential.Comment: 27 pages, proof for conservativity added, tightened presentatio
The second law, Maxwell's daemon and work derivable from quantum heat engines
With a class of quantum heat engines which consists of two-energy-eigenstate
systems undergoing, respectively, quantum adiabatic processes and energy
exchanges with heat baths at different stages of a cycle, we are able to
clarify some important aspects of the second law of thermodynamics. The quantum
heat engines also offer a practical way, as an alternative to Szilard's engine,
to physically realise Maxwell's daemon. While respecting the second law on the
average, they are also capable of extracting more work from the heat baths than
is otherwise possible in thermal equilibrium
On the coupling of massless particles to scalar fields
It is investigated if massless particles can couple to scalar fields in a
special relativistic theory with classical particles. The only possible obvious
theory which is invariant under Lorentz transformations and reparametrization
of the affine parameter leads to trivial trajectories (straight lines) for the
massless case, and also the investigation of the massless limit of the massive
theory shows that there is no influence of the scalar field on the limiting
trajectories.
On the other hand, in contrast to this result, it is shown that massive
particles are influenced by the scalar field in this theory even in the
ultra-relativistic limit.Comment: 9 pages, no figures, uses titlepage.sty, LaTeX 2.09 file, submitted
to International Journal of Theoretical Physic
Spherical codes, maximal local packing density, and the golden ratio
The densest local packing (DLP) problem in d-dimensional Euclidean space Rd
involves the placement of N nonoverlapping spheres of unit diameter near an
additional fixed unit-diameter sphere such that the greatest distance from the
center of the fixed sphere to the centers of any of the N surrounding spheres
is minimized. Solutions to the DLP problem are relevant to the realizability of
pair correlation functions for packings of nonoverlapping spheres and might
prove useful in improving upon the best known upper bounds on the maximum
packing fraction of sphere packings in dimensions greater than three. The
optimal spherical code problem in Rd involves the placement of the centers of N
nonoverlapping spheres of unit diameter onto the surface of a sphere of radius
R such that R is minimized. It is proved that in any dimension, all solutions
between unity and the golden ratio to the optimal spherical code problem for N
spheres are also solutions to the corresponding DLP problem. It follows that
for any packing of nonoverlapping spheres of unit diameter, a spherical region
of radius less than or equal to the golden ratio centered on an arbitrary
sphere center cannot enclose a number of sphere centers greater than one more
than the number that can be placed on the region's surface.Comment: 12 pages, 1 figure. Accepted for publication in the Journal of
Mathematical Physic
Universal correlations of trapped one-dimensional impenetrable bosons
We calculate the asymptotic behaviour of the one body density matrix of
one-dimensional impenetrable bosons in finite size geometries. Our approach is
based on a modification of the Replica Method from the theory of disordered
systems. We obtain explicit expressions for oscillating terms, similar to
fermionic Friedel oscillations. These terms are universal and originate from
the strong short-range correlations between bosons in one dimension.Comment: 18 pages, 3 figures. Published versio
Bath generated work extraction and inversion-free gain in two-level systems
The spin-boson model, often used in NMR and ESR physics, quantum optics and
spintronics, is considered in a solvable limit to model a spin one-half
particle interacting with a bosonic thermal bath. By applying external pulses
to a non-equilibrium initial state of the spin, work can be extracted from the
thermalized bath. It occurs on the timescale \T_2 inherent to transversal
(`quantum') fluctuations. The work (partly) arises from heat given off by the
surrounding bath, while the spin entropy remains constant during a pulse. This
presents a violation of the Clausius inequality and the Thomson formulation of
the second law (cycles cost work) for the two-level system.
Starting from a fully disordered state, coherence can be induced by employing
the bath. Due to this, a gain from a positive-temperature (inversion-free)
two-level system is shown to be possible.Comment: 4 pages revte
Markov evolutions and hierarchical equations in the continuum I. One-component systems
General birth-and-death as well as hopping stochastic dynamics of infinite
particle systems in the continuum are considered. We derive corresponding
evolution equations for correlation functions and generating functionals.
General considerations are illustrated in a number of concrete examples of
Markov evolutions appearing in applications.Comment: 47 page
Vlasov scaling for the Glauber dynamics in continuum
We consider Vlasov-type scaling for the Glauber dynamics in continuum with a
positive integrable potential, and construct rescaled and limiting evolutions
of correlation functions. Convergence to the limiting evolution for the
positive density system in infinite volume is shown. Chaos preservation
property of this evolution gives a possibility to derive a non-linear
Vlasov-type equation for the particle density of the limiting system.Comment: 32 page
Longitudinal patterns in an Arkansas River Valley stream: an Application of the River Continuum Concept
The River Continuum Concept (RCC) provides the framework for studying how lotic ecosystems vary from headwater streams to large rivers. The RCC was developed in streams in eastern deciduous forests of North America, but watershed characteristics and land uses differ across ecoregions, presenting unique opportunities to study how predictions of the RCC may differ across regions. Additionally, RCC predictions may vary due to the influence of fishes, but few studies have used fish taxa as a metric for evaluating predictions of the RCC. Our goal was to determine if RCC predictions for stream orders 1 through 5 were supported by primary producer, macroinvertebrate, and fish communities in Cadron Creek of the Arkansas River Valley. We sampled chlorophyll a, macroinvertebrates, and fishes at five stream reaches across a gradient of watershed size. Contrary to RCC predictions, chlorophyll a did not increase in concentration with catchment size. As the RCC predicts, fish and macroinvertebrate diversity increased with catchment size. Shredding and collecting macroinvertebrate taxa supported RCC predictions, respectively decreasing and increasing in composition as catchment area increased. Herbivorous and predaceous fish did not follow RCC predictions; however, surface-water column feeding fish were abundant at all sites as predicted. We hypothesize some predictions of the RCC were not supported in headwater reaches of this system due to regional differences in watershed characteristics and altered resource availability due to land use surrounding sampling sites
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