6,201 research outputs found
Superfluid gap formation in a fermionic optical lattice with spin imbalanced populations
We investigate the attractive Hubbard model in infinite spatial dimensions at
quarter filling. By combining dynamical mean-field theory with continuous-time
quantum Monte Carlo simulations in the Nambu formalism, we directly deal with
the superfluid phase in the population imbalanced system. We discuss the low
energy properties in the polarized superfluid state and the pseudogap behavior
in the vicinity of the critical temperature.Comment: 4 pages, 1 figure, To appear in J. Phys.: Conf. Ser. for SCES201
Origin and reduction of wakefields in photonic crystal accelerator cavities
Photonic crystal (PhC) defect cavities that support an accelerating mode tend
to trap unwanted higher-order modes (HOMs) corresponding to zero-group-velocity
PhC lattice modes at the top of the bandgap. The effect is explained quite
generally from photonic band and perturbation theoretical arguments. Transverse
wakefields resulting from this effect are observed in a hybrid dielectric PhC
accelerating cavity based on a triangular lattice of sapphire rods. These
wakefields are, on average, an order of magnitude higher than those in the
waveguide-damped Compact Linear Collider (CLIC) copper cavities. The avoidance
of translational symmetry (and, thus, the bandgap concept) can dramatically
improve HOM damping in PhC-based structures.Comment: 11 pages, 18 figures, 2 table
Casimir-dissipation stabilized stochastic rotating shallow water equations on the sphere
We introduce a structure preserving discretization of stochastic rotating
shallow water equations, stabilized with an energy conserving Casimir (i.e.
potential enstrophy) dissipation. A stabilization of a stochastic scheme is
usually required as, by modeling subgrid effects via stochastic processes,
small scale features are injected which often lead to noise on the grid scale
and numerical instability. Such noise is usually dissipated with a standard
diffusion via a Laplacian which necessarily also dissipates energy. In this
contribution we study the effects of using an energy preserving selective
Casimir dissipation method compared to diffusion via a Laplacian. For both, we
analyze stability and accuracy of the stochastic scheme. The results for a test
case of a barotropically unstable jet show that Casimir dissipation allows for
stable simulations that preserve energy and exhibit more dynamics than
comparable runs that use a Laplacian
Multiple Schramm-Loewner evolutions for conformal field theories with Lie algebra symmetries
We provide multiple Schramm-Loewner evolutions (SLEs) to describe the scaling
limit of multiple interfaces in critical lattice models possessing Lie algebra
symmetries. The critical behavior of the models is described by
Wess-Zumino-Witten (WZW) models. Introducing a multiple Brownian motion on a
Lie group as well as that on the real line, we construct the multiple SLE with
additional Lie algebra symmetries. The connection between the resultant SLE and
the WZW model can be understood via SLE martingales satisfied by the
correlation functions in the WZW model. Due to interactions among SLE traces,
these Brownian motions have drift terms which are determined by partition
functions for the corresponding WZW model. As a concrete example, we apply the
formula to the su(2)k-WZW model. Utilizing the fusion rules in the model, we
conjecture that there exists a one-to-one correspondence between the partition
functions and the topologically inequivalent configurations of the SLE traces.
Furthermore, solving the Knizhnik-Zamolodchikov equation, we exactly compute
the probabilities of occurrence for certain configurations (i.e. crossing
probabilities) of traces for the triple SLE.Comment: 21 pages, 8 figures, typos corrected, references added, published
versio
A Fast Algorithm for Simulating the Chordal Schramm-Loewner Evolution
The Schramm-Loewner evolution (SLE) can be simulated by dividing the time
interval into N subintervals and approximating the random conformal map of the
SLE by the composition of N random, but relatively simple, conformal maps. In
the usual implementation the time required to compute a single point on the SLE
curve is O(N). We give an algorithm for which the time to compute a single
point is O(N^p) with p<1. Simulations with kappa=8/3 and kappa=6 both give a
value of p of approximately 0.4.Comment: 17 pages, 10 figures. Version 2 revisions: added a paragraph to
introduction, added 5 references and corrected a few typo
2D growth processes: SLE and Loewner chains
This review provides an introduction to two dimensional growth processes.
Although it covers a variety processes such as diffusion limited aggregation,
it is mostly devoted to a detailed presentation of stochastic Schramm-Loewner
evolutions (SLE) which are Markov processes describing interfaces in 2D
critical systems. It starts with an informal discussion, using numerical
simulations, of various examples of 2D growth processes and their connections
with statistical mechanics. SLE is then introduced and Schramm's argument
mapping conformally invariant interfaces to SLE is explained. A substantial
part of the review is devoted to reveal the deep connections between
statistical mechanics and processes, and more specifically to the present
context, between 2D critical systems and SLE. Some of the SLE remarkable
properties are explained, as well as the tools for computing with SLE. This
review has been written with the aim of filling the gap between the
mathematical and the physical literatures on the subject.Comment: A review on Stochastic Loewner evolutions for Physics Reports, 172
pages, low quality figures, better quality figures upon request to the
authors, comments welcom
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