430 research outputs found
Scar Intensity Statistics in the Position Representation
We obtain general predictions for the distribution of wave function
intensities in position space on the periodic orbits of chaotic ballistic
systems. The expressions depend on effective system size N, instability
exponent lambda of the periodic orbit, and proximity to a focal point of the
orbit. Limiting expressions are obtained that include the asymptotic
probability distribution of rare high-intensity events and a perturbative
formula valid in the limit of weak scarring. For finite system sizes, a single
scaling variable lambda N describes deviations from the semiclassical N ->
infinity limit.Comment: To appear in Phys. Rev. E, 10 pages, including 4 figure
Artificial trapping of a stable high-density dipolar exciton fluid
We present compelling experimental evidence for a successful electrostatic
trapping of two-dimensional dipolar excitons that results in stable formation
of a well confined, high-density and spatially uniform dipolar exciton fluid.
We show that, for at least half a microsecond, the exciton fluid sustains a
density higher than the critical density for degeneracy if the exciton fluid
temperature reaches the lattice temperature within that time. This method
should allow for the study of strongly interacting bosons in two dimensions at
low temperatures, and possibly lead towards the observation of quantum phase
transitions of 2D interacting excitons, such as superfluidity and
crystallization.Comment: 11 pages 4 figure
Spectral zeta functions of a 1D Schr\"odinger problem
We study the spectral zeta functions associated to the radial Schr\"odinger
problem with potential V(x)=x^{2M}+alpha x^{M-1}+(lambda^2-1/4)/x^2. Using the
quantum Wronskian equation, we provide results such as closed-form evaluations
for some of the second zeta functions i.e. the sum over the inverse eigenvalues
squared. Also we discuss how our results can be used to derive relationships
and identities involving special functions, using a particular 5F_4
hypergeometric series as an example. Our work is then extended to a class of
related PT-symmetric eigenvalue problems. Using the fused quantum Wronskian we
give a simple method for calculating the related spectral zeta functions. This
method has a number of applications including the use of the ODE/IM
correspondence to compute the (vacuum) nonlocal integrals of motion G_n which
appear in an associated integrable quantum field theory.Comment: 15 pages, version
Fractional Hamiltonian Monodromy from a Gauss-Manin Monodromy
Fractional Hamiltonian Monodromy is a generalization of the notion of
Hamiltonian Monodromy, recently introduced by N. N. Nekhoroshev, D. A.
Sadovskii and B. I. Zhilinskii for energy-momentum maps whose image has a
particular type of non-isolated singularities. In this paper, we analyze the
notion of Fractional Hamiltonian Monodromy in terms of the Gauss-Manin
Monodromy of a Riemann surface constructed from the energy-momentum map and
associated to a loop in complex space which bypasses the line of singularities.
We also prove some propositions on Fractional Hamiltonian Monodromy for 1:-n
and m:-n resonant systems.Comment: 39 pages, 24 figures. submitted to J. Math. Phy
Classical, semiclassical, and quantum investigations of the 4-sphere scattering system
A genuinely three-dimensional system, viz. the hyperbolic 4-sphere scattering
system, is investigated with classical, semiclassical, and quantum mechanical
methods at various center-to-center separations of the spheres. The efficiency
and scaling properties of the computations are discussed by comparisons to the
two-dimensional 3-disk system. While in systems with few degrees of freedom
modern quantum calculations are, in general, numerically more efficient than
semiclassical methods, this situation can be reversed with increasing dimension
of the problem. For the 4-sphere system with large separations between the
spheres, we demonstrate the superiority of semiclassical versus quantum
calculations, i.e., semiclassical resonances can easily be obtained even in
energy regions which are unattainable with the currently available quantum
techniques. The 4-sphere system with touching spheres is a challenging problem
for both quantum and semiclassical techniques. Here, semiclassical resonances
are obtained via harmonic inversion of a cross-correlated periodic orbit
signal.Comment: 12 pages, 5 figures, submitted to Phys. Rev.
Casimir energy of a massive field in a genus-1 surface
We review the definition of the Casimir energy steming naturally from the
concept of functional determinant through the zeta function prescription. This
is done by considering the theory at finite temperature and by defining then
the Casimir energy as its energy in the limit . The ambiguity in the
coefficient is understood to be a result of the necessary
renormalization of the free energy of the system. Then, as an exact, explicit
example never calculated before, the Casimir energy for a massive scalar field
living in a general -dimensional toroidal spacetime (i.e., a general
surface of genus one) with flat spatial geometry ---parametrized by the
corresponding Teichm\"uller parameters--- and its precise dependence on these
parameters and on the mass of the field is obtained under the form of an
analytic function.Comment: Changes everywhere: title, abstract, contents and figures. Version to
appear in Physics Letters
Virtual turning points and bifurcation of Stokes curves for higher order ordinary differential equations
For a higher order linear ordinary differential operator P, its Stokes curve
bifurcates in general when it hits another turning point of P. This phenomenon
is most neatly understandable by taking into account Stokes curves emanating
from virtual turning points, together with those from ordinary turning points.
This understanding of the bifurcation of a Stokes curve plays an important role
in resolving a paradox recently found in the Noumi-Yamada system, a system of
linear differential equations associated with the fourth Painleve equation.Comment: 7 pages, 4 figure
The Local Time Distribution of a Particle Diffusing on a Graph
We study the local time distribution of a Brownian particle diffusing along
the links on a graph. In particular, we derive an analytic expression of its
Laplace transform in terms of the Green's function on the graph. We show that
the asymptotic behavior of this distribution has non-Gaussian tails
characterized by a nontrivial large deviation function.Comment: 8 pages, two figures (included
Spectral networks
We introduce new geometric objects called spectral networks. Spectral
networks are networks of trajectories on Riemann surfaces obeying certain local
rules. Spectral networks arise naturally in four-dimensional N=2 theories
coupled to surface defects, particularly the theories of class S. In these
theories spectral networks provide a useful tool for the computation of BPS
degeneracies: the network directly determines the degeneracies of solitons
living on the surface defect, which in turn determine the degeneracies for
particles living in the 4d bulk. Spectral networks also lead to a new map
between flat GL(K,C) connections on a two-dimensional surface C and flat
abelian connections on an appropriate branched cover Sigma of C. This
construction produces natural coordinate systems on moduli spaces of flat
GL(K,C) connections on C, which we conjecture are cluster coordinate systems.Comment: 87 pages, 48 figures; v2: typos, correction to general rule for signs
of BPS count
Galvanic vestibular stimulation produces cross-modal improvements in visual thresholds
Background: Stochastic resonance (SR) refers to a faint signal being enhanced
with the addition of white noise. Previous studies have found that vestibular
perceptual thresholds are lowered with noisy galvanic vestibular stimulation
(i.e., "in-channel" SR). Auditory white noise has been shown to improve tactile
and visual thresholds, suggesting "cross-modal" SR. Objective: We aimed to
study the cross-modal impact of noisy galvanic vestibular stimulation (nGVS)
(n=9 subjects) on visual and auditory thresholds. Methods: We measured auditory
and visual perceptual thresholds of human subjects across a swath of different
nGVS levels in order to determine if a subject-specific best nGVS level
elicited a reduction in thresholds as compared the no noise condition (sham).
Results: We found an 18% improvement in visual thresholds (p = 0.026). Among
the 7 of 9 subjects with reduced thresholds, the average improvement was 26%.
Subjects with higher (worse) visual thresholds with no stimulation (sham)
improved more than those with lower thresholds (p = 0.005). Auditory thresholds
were unchanged by vestibular stimulation. Conclusions: These results are the
first demonstration of cross-modal improvement with nGVS, indicating galvanic
vestibular white noise can produce cross-modal improvements in some sensory
channels, but not all.Comment: 15 pages, 7 figure
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