Spectral properties of zero temperature dynamics in a model of a compacting granular column

The compacting of a column of grains has been studied using a one-dimensional Ising model with long range directed interactions in which down and up spins represent orientations of the grain having or not having an associated void. When the column is not shaken (zero 'temperature') the motion becomes highly constrained and under most circumstances we find that the generator of the stochastic dynamics assumes an unusual form: many eigenvalues become degenerate, but the associated multi-dimensional invariant spaces have but a single eigenvector. There is no spectral expansion and a Jordan form must be used. Many properties of the dynamics are established here analytically; some are not. General issues associated with the Jordan form are also taken up.Comment: 34 pages, 4 figures, 3 table

Supersymmetric Model of a 2D Long-Range Bose Liquid

The model Hamiltonian of a two-dimensional Bose liquid (proposed earlier by Kane, Kivelson, Lee and Zhang as the Hamiltonian which has Jastrow-type wavefunctions as the ground-state solution), is shown to possess nonrelativistic supersymmetry. For the special value of the coupling constant $\alpha=1/2$ the quantum mechanics described by this Hamiltonian is shown to be equivalent to the dynamics of (complex) eigenvalues of random Gaussian ensemble of normal complex matrices. For general $\alpha$, an exact relation between the equal-time current-current and density-density correlation functions is obtained, and used to derive an asymptotically exact (at low wavevectors q) spectrum of single-particle excitations beyond the superfluid ground-state (realized at low $\alpha$'s). The ground-state at very large $\alpha$ is shown to be of ``Quantum Hexatic" type, possessing long-range orientational order and quasi-long-range translational order but with zero shear modulus. Possible scenaria of the ground-state phase transitions as function of $\alpha$ are discussed.Comment: Revtex; 12 pages, 1 Postscript figur

Are you suggesting that’s my hand? The relation between hypnotic suggestibility and the rubber hand illusion

Hypnotic suggestibility (HS) is the ability to respond automatically to suggestions and to experience alterations in perception and behaviour. Hypnotically suggestible participants are also better able to focus and sustain their attention on an experimental stimulus. The present study explores the relation between HS and susceptibility to the rubber hand illusion (RHI). Based on previous research with visual illusions, it was predicted that higher HS would lead to a stronger RHI illusion. Two behavioural output measures of the RHI, an implicit (proprioceptive drift) and an explicit (RHI questionnaire) measure were correlated against HS scores. Hypnotic suggestibility correlated positively with the implicit RHI measure contributing to 30% of the variation. However, there was no relation between HS and the explicit RHI questionnaire measure, or with compliance control items. High hypnotic suggestibility may facilitate, via attentional mechanisms, the multisensory integration of visuoproprioceptive inputs that leads to greater perceptual mislocalisation of a participant’s hand. These results may provide insight into the multisensory brain mechanisms involved in our sense of embodiment

Heavy quark production via leptoquarks at a neutrino factory

The proposed neutrino factory (NF) based on a muon storage ring (MSR) is an ideal place to look for heavy quark production via neutral current (NC) and charged current (CC) interactions. In this article, we address the issue of contribution coming from mediating leptoquarks (LQ) in $\nu_\mu (\bar\nu_e)-{\rm N}$ interactions leading to the production of $b(\bar b)$ at a MSR and investigate the region where LQ interactions are significant in the near-site experiments.Comment: 12 pages latex, 10 ps figures, uses axocolour.sty, Slightly revised version to appear in PR

Quantum mechanics with a time-dependent random unitary Hamiltonian: A perturbative study of the nonlinear Keldysh sigma-model

We analyze the perturbative series of the Keldysh-type sigma-model proposed recently for describing the quantum mechanics with time-dependent Hamiltonians from the unitary Wigner-Dyson random-matrix ensemble. We observe that vertices of orders higher than four cancel, which allows us to reduce the calculation of the energy-diffusion constant to that in a special kind of the matrix \phi^4 model. We further verify that the perturbative four-loop correction to the energy-diffusion constant in the high-velocity limit cancels, in agreement with the conjecture of one of the authors.Comment: 27 pages, 15 figures; typos corrected, one reference adde

Stability conditions and positivity of invariants of fibrations

We study three methods that prove the positivity of a natural numerical invariant associated to $1-$parameter families of polarized varieties. All these methods involve different stability conditions. In dimension 2 we prove that there is a natural connection between them, related to a yet another stability condition, the linear stability. Finally we make some speculations and prove new results in higher dimension.Comment: Final version, to appear in the Springer volume dedicated to Klaus Hulek on the occasion of his 60-th birthda

Vortex dissipation and level dynamics for the layered superconductors with impurities

We study parametric level statistics of the discretized excitation spectra inside a moving vortex core in layered superconductors with impurities. The universal conductivity is evaluated numerically for the various values of rescaled vortex velocities $\kappa$ from the clean case to the dirty limit case. The random matrix theoretical prediction is verified numerically in the large $\kappa$ regime. On the contrary in the low velocity regime, we observe $\sigma_{xx} \propto \kappa^{2/3}$ which is consistent with the theoretical result for the super-clean case, where the energy dissipation is due to the Landau-Zener transition which takes place at the points called ``avoided crossing''.Comment: 10 pages, 4 figures, REVTeX3.

Statistical analysis and the equivalent of a Thouless energy in lattice QCD Dirac spectra

Random Matrix Theory (RMT) is a powerful statistical tool to model spectral fluctuations. This approach has also found fruitful application in Quantum Chromodynamics (QCD). Importantly, RMT provides very efficient means to separate different scales in the spectral fluctuations. We try to identify the equivalent of a Thouless energy in complete spectra of the QCD Dirac operator for staggered fermions from SU(2) lattice gauge theory for different lattice size and gauge couplings. In disordered systems, the Thouless energy sets the universal scale for which RMT applies. This relates to recent theoretical studies which suggest a strong analogy between QCD and disordered systems. The wealth of data allows us to analyze several statistical measures in the bulk of the spectrum with high quality. We find deviations which allows us to give an estimate for this universal scale. Other deviations than these are seen whose possible origin is discussed. Moreover, we work out higher order correlators as well, in particular three--point correlation functions.Comment: 24 pages, 24 figures, all included except one figure, missing eps file available at http://pluto.mpi-hd.mpg.de/~wilke/diff3.eps.gz, revised version, to appear in PRD, minor modifications and corrected typos, Fig.4 revise

Statistics of Coulomb blockade peak spacings for a partially open dot

We show that randomness of the electron wave functions in a quantum dot contributes to the fluctuations of the positions of the conductance peaks. This contribution grows with the conductance of the junctions connecting the dot to the leads. It becomes comparable with the fluctuations coming from the randomness of the single particle spectrum in the dot while the Coulomb blockade peaks are still well-defined. In addition, the fluctuations of the peak spacings are correlated with the fluctuations of the conductance peak heights.Comment: 13 pages, 1 figur