12,311 research outputs found
Casimir pistons with hybrid boundary conditions
The Casimir effect giving rise to an attractive or repulsive force between
the configuration boundaries that confine the massless scalar field is
reexamined for one to three-dimensional pistons in this paper. Especially, we
consider Casimir pistons with hybrid boundary conditions, where the boundary
condition on the piston is Neumann and those on other surfaces are Dirichlet.
We show that the Casimir force on the piston is always repulsive, in contrast
with the same problem where the boundary conditions are Dirichlet on all
surfaces.Comment: 8 pages, 4 figures,references added, minor typos correcte
Fractional quantum Hall effect at : Ground states, non-Abelian quasiholes, and edge modes in a microscopic model
We present a comprehensive numerical study of a microscopic model of the
fractional quantum Hall system at filling fraction , based on the
disc geometry. Our model includes Coulomb interaction and a semi-realistic
confining potential. We also mix in some three-body interaction in some cases
to help elucidate the physics. We obtain a phase diagram, discuss the
conditions under which the ground state can be described by the Moore-Read
state, and study its competition with neighboring stripe phases. We also study
quasihole excitations and edge excitations in the Moore-Read--like state. From
the evolution of edge spectrum, we obtain the velocities of the charge and
neutral edge modes, which turn out to be very different. This separation of
velocities is a source of decoherence for a non-Abelian quasihole/quasiparticle
(with charge ) when propagating at the edge; using numbers obtained
from a specific set of parameters we estimate the decoherence length to be
around four microns. This sets an upper bound for the separation of the two
point contacts in a double point contact interferometer, designed to detect the
non-Abelian nature of such quasiparticles. We also find a state that is a
potential candidate for the recently proposed anti-Pfaffian state. We find the
speculated anti-Pfaffian state is favored in weak confinement (smooth edge)
while the Moore-Read Pfaffian state is favored in strong confinement (sharp
edge).Comment: 15 pages, 9 figures; Estimate of e/4 quasiparticle/hole coherence
length when propagating along the edge modified in response to a recent
revision of Ref. 25, and minor changes elsewher
The Casimir force of Quantum Spring in the (D+1)-dimensional spacetime
The Casimir effect for a massless scalar field on the helix boundary
condition which is named as quantum spring is studied in our recent
paper\cite{Feng}. In this paper, the Casimir effect of the quantum spring is
investigated in -dimensional spacetime for the massless and massive
scalar fields by using the zeta function techniques. We obtain the exact
results of the Casimir energy and Casimir force for any , which indicate a
symmetry of the two space dimensions. The Casimir energy and Casimir
force have different expressions for odd and even dimensional space in the
massless case but in both cases the force is attractive. In the case of
odd-dimensional space, the Casimir energy density can be expressed by the
Bernoulli numbers, while in the even case it can be expressed by the
-function. And we also show that the Casimir force has a maximum value
which depends on the spacetime dimensions. In particular, for a massive scalar
field, we found that the Casimir force varies as the mass of the field changes.Comment: 9 pages, 5 figures, v2, massive case added, refs. adde
A Variational Principle Based Study of KPP Minimal Front Speeds in Random Shears
Variational principle for Kolmogorov-Petrovsky-Piskunov (KPP) minimal front
speeds provides an efficient tool for statistical speed analysis, as well as a
fast and accurate method for speed computation. A variational principle based
analysis is carried out on the ensemble of KPP speeds through spatially
stationary random shear flows inside infinite channel domains. In the regime of
small root mean square (rms) shear amplitude, the enhancement of the ensemble
averaged KPP front speeds is proved to obey the quadratic law under certain
shear moment conditions. Similarly, in the large rms amplitude regime, the
enhancement follows the linear law. In particular, both laws hold for the
Ornstein-Uhlenbeck process in case of two dimensional channels. An asymptotic
ensemble averaged speed formula is derived in the small rms regime and is
explicit in case of the Ornstein-Uhlenbeck process of the shear. Variational
principle based computation agrees with these analytical findings, and allows
further study on the speed enhancement distributions as well as the dependence
of enhancement on the shear covariance. Direct simulations in the small rms
regime suggest quadratic speed enhancement law for non-KPP nonlinearities.Comment: 28 pages, 14 figures update: fixed typos, refined estimates in
section
Nonlinear Non-Hermitian Landau-Zener-St\"uckelberg-Majorana interferometry
In this work, we have studied the non-Hermitian nonlinear LZSM interferometry
in a non-Hermitian N-body interacting boson system in which the non-Hermicity
is from the nonreciprocal tunnelings between the bosons. By using the
mean-field approximation and projective Hilbert space, the effect of
nonreciprocity and nonlinearity on the energy spectrum, the dynamics, and the
formation of the interference fringes have been studied. The different
symmetries and the impact of the two different types of reciprocity, i.e. the
in-phase tunneling and anti-phase tunneling, on the energy spectrum and the
phase transition between the Josephson oscillation and the self-trapping have
been investigated. For the LZSM interferometry, the strength of the
nonreciprocity is found to take an essential role in the population of the
projective state and the strengths of the interference patterns in the
projective space. While the conditions of destructive and constructive
interference under the weak-coupling approximation still only depend on the
strength of nonlinearity. Our result provides an application of the nonlinear
non-Hermitian LZSM interferometry in studying the parameters of a non-Hermitian
nonlinear two-level system which related to the nonlinearity and the
non-Hermicity.Comment: 11 pages, 12 figures, and comments are welcom
Scaling and non-Abelian signature in fractional quantum Hall quasiparticle tunneling amplitude
We study the scaling behavior in the tunneling amplitude when quasiparticles
tunnel along a straight path between the two edges of a fractional quantum Hall
annulus. Such scaling behavior originates from the propagation and tunneling of
charged quasielectrons and quasiholes in an effective field analysis. In the
limit when the annulus deforms continuously into a quasi-one-dimensional ring,
we conjecture the exact functional form of the tunneling amplitude for several
cases, which reproduces the numerical results in finite systems exactly. The
results for Abelian quasiparticle tunneling is consistent with the scaling
anaysis; this allows for the extraction of the conformal dimensions of the
quasiparticles. We analyze the scaling behavior of both Abelian and non-Abelian
quasiparticles in the Read-Rezayi Z_k-parafermion states. Interestingly, the
non-Abelian quasiparticle tunneling amplitudes exhibit nontrivial k-dependent
corrections to the scaling exponent.Comment: 16 pages, 4 figure
Casimir effect for the massless Dirac field in two-dimensional Reissner-Nordstr\"{o}m spacetime
In this paper, the two-dimensional Reissner-Nordstr\"{o}m black hole is
considered as a system of the Casimir type. In this background the Casimir
effect for the massless Dirac field is discussed. The massless Dirac field is
confined between two ``parallel plates'' separated by a distance and there
is no particle current drilling through the boundaries. The vacuum expectation
values of the stress tensor of the massless Dirac field at infinity are
calculated separately in the Boulware state, the Hartle-Hawking state and the
Unruh state.Comment: 10 pages, no figure. Accepted for publication in IJMP
On the Conductance Sum Rule for the Hierarchical Edge States of the Fractional Quantum Hall Effect
The conductance sum rule for the hierarchical edge channel currents of a
Fractional Quantum Hall Effect state is derived analytically within the
Haldane-Halperin hierarchy scheme. We provide also an intuitive interpretation
for the hierarchical drift velocities of the edge excitations.Comment: 11 pages, no figure, Revtex 3.0, IC/93/329, ASITP-93-5
Confidence and Backaction in the Quantum Filter Equation
We study the confidence and backaction of state reconstruction based on a
continuous weak measurement and the quantum filter equation. As a physical
example we use the traditional model of a double quantum dot being continuously
monitored by a quantum point contact. We examine the confidence of the estimate
of a state constructed from the measurement record, and the effect of
backaction of that measurement on that state. Finally, in the case of general
measurements we show that using the relative entropy as a measure of confidence
allows us to define the lower bound on the confidence as a type of quantum
discord.Comment: 9 pages, 6 figure
A new parametric equation of state and quark stars
It is still a matter of debate to understand the equation of state of cold
supra-nuclear matter in compact stars because of unknown on-perturbative strong
interaction between quarks. Nevertheless, it is speculated from an
astrophysical view point that quark clusters could form in cold quark matter
due to strong coupling at realistic baryon densities. Although it is hard to
calculate this conjectured matter from first principles, one can expect the
inter-cluster interaction to share some general features to nucleon-nucleon
interaction. We adopt a two-Gaussian component soft-core potential with these
general features and show that quark clusters can form stable simple cubic
crystal structure if we assume Gaussian form wave function. With this
parameterizing, Tolman-Oppenheimer-Volkoff equation is solved with reasonable
constrained parameter space to give mass-radius relation of crystalline solid
quark star. With baryon densities truncated at 2 times nuclear density at
surface and range of interaction fixed at 2fm we can reproduce similar
mass-radius relation to that obtained with bag model equations of state. The
maximum mass ranges from about 0.5 to 3 solar mass. Observed maximum pulsar
mass (about 2 solar mass) is then used to constrain parameters of this simple
interaction potential.Comment: 5 pages, 2 figure
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