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 $T\to 0$. The ambiguity in the coefficient $C_{d/2}$ 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 $(1+2)$-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