Bell Inequalities in Phase Space and their Violation in Quantum Mechanics

We derive ``Bell inequalities'' in four dimensional phase space and prove the following ``three marginal theorem'' for phase space densities $\rho(\overrightarrow{q},\overrightarrow{p})$, thus settling a long standing conjecture : ``there exist quantum states for which more than three of the quantum probability distributions for $(q_1,q_2)$, $(p_1,p_2)$, $(q_1,p_2)$ and $(p_1,q_2)$ cannot be reproduced as marginals of a positive $\rho(\overrightarrow{q},\overrightarrow{p})$''. We also construct the most general positive $\rho(\overrightarrow{q},\overrightarrow{p})$ which reproduces any three of the above quantum probability densities for arbitrary quantum states. This is crucial for the construction of a maximally realistic quantum theory.Comment: 11 pages, latex, no figure

Group theoretic dimension of stationary symmetric \alpha-stable random fields

The growth rate of the partial maximum of a stationary stable process was first studied in the works of Samorodnitsky (2004a,b), where it was established, based on the seminal works of Rosi\'nski (1995,2000), that the growth rate is connected to the ergodic theoretic properties of the flow that generates the process. The results were generalized to the case of stable random fields indexed by Z^d in Roy and Samorodnitsky (2008), where properties of the group of nonsingular transformations generating the stable process were studied as an attempt to understand the growth rate of the partial maximum process. This work generalizes this connection between stable random fields and group theory to the continuous parameter case, that is, to the fields indexed by R^d.Comment: To appear in Journal of Theoretical Probability. Affiliation of the authors are update

Constraining the Randall-Sundrum modulus in the light of recent PVLAS data

Recent PVLAS data put stringent constraints on the measurement of birefringence and dichroism of electromagnetic waves travelling in a constant and homogeneous magnetic field. There have been theoretical predictions in favour of such phenomena when appropriate axion-electromagnetic coupling is assumed. Origin of such a coupling can be traced in a low energy string action from the requirement of quantum consistency. The resulting couplings in such models are an artifact of the compactification of the extra dimensions present inevitably in a string scenario. The moduli parameters which encode the compact manifold therefore play a crucial role in determining the axion-photon coupling. In this work we examine the possible bounds on the value of compact modulus that emerge from the experimental limits on the coupling obtained from the PVLAS data. In particular we focus into the Randall-Sundrum (RS) type of warped geometry model whose modulus parameter is already restricted from the requirement of the resolution of gauge hierarchy problem in connection with the mass of the Higgs. We explore the bound on the modulus for a wide range of the axion mass for both the birefringence and the dichroism data in PVLAS. We show that the proposed value of the modulus in the RS scenario can only be accommodated for axion mass \gsim 0.3 eV.Comment: 26 pages, 1 figure, LaTex; added references, typos corrected. Minor changes in the text, a comment added in the Conclusio

Motion of a spin 1/2 particle in shape invariant scalar and magnetic fields

We study the motion of a spin 1/2 particle in a scalar as well as a magnetic field within the framework of supersymmetric quantum mechanics(SUSYQM). We also introduce the concept of shape invariant scalar and magnetic fields and it is shown that the problem admits exact analytical solutions when such fields are considered.Comment: 14 page

Electron localization and possible phase separation in the absence of a charge density wave in single-phase 1T-VS2_2

We report on a systematic study of the structural, magnetic and transport properties of high-purity 1T-VS$_2$ powder samples prepared under high pressure. The results differ notably from those previously obtained by de-intercalating Li from LiVS$_2$. First, no Charge Density Wave (CDW) is found by transmission electron microscopy down to 94 K. Though, \textit{ab initio} phonon calculations unveil a latent CDW instability driven by an acoustic phonon softening at the wave vector ${\bf q}_{CDW} \approx$ (0.21,0.21,0) previously reported in de-intercalated samples. A further indication of latent lattice instability is given by an anomalous expansion of the V-S bond distance at low temperature. Second, infrared optical absorption and electrical resistivity measurements give evidence of non metallic properties, consistent with the observation of no CDW phase. On the other hand, magnetic susceptibility and NMR data suggest the coexistence of localized moments with metallic carriers, in agreement with \textit{ab initio} band structure calculations. This discrepancy is reconciled by a picture of electron localization induced by disorder or electronic correlations leading to a phase separation of metallic and non-metallic domains in the nm scale. We conclude that 1T-VS$_2$ is at the verge of a CDW transition and suggest that residual electronic doping in Li de-intercalated samples stabilizes a uniform CDW phase with metallic properties.Comment: 22 pages, 10 Figures. Full resolution pictures available at http://journals.aps.org/prb/abstract/10.1103/PhysRevB.89.23512

Timescale for equilibration of N/Z gradients in dinuclear systems

Equilibration of N/Z in binary breakup of an excited and transiently deformed projectile-like fragment (PLF*), produced in peripheral collisions of 64Zn + 27Al, 64Zn, 209Bi at E/A = 45 MeV, is examined. The composition of emitted light fragments (3<=Z<=6) changes with the decay angle of the PLF*. The most neutron-rich fragments observed are associated with a small rotation angle. A clear target dependence is observed with the largest initial N/Z correlated with the heavy, neutron-rich target. Using the rotation angle as a clock, we deduce that N/Z equilibration persists for times as long as 3-4 zs (1zs = 1 x 10^-21 s = 300 fm/c). The rate of N/Z equilibration is found to depend on the initial neutron gradient within the PLF*.Comment: 6 pages, 4 figure

Symbolic Magnifying Lens Abstraction in Markov Decision Processes

In this paper, we combine abstraction-refinement and symbolic techniques to fight the state-space explosion problem when model checking Markov decision processes (MDPs). The abstract-refinement technique, called "magnifying-lens abstraction" (MLA), partitions the state-space into regions and computes upper and lower bounds for reachability and safety properties on the regions, rather than the states. To compute such bounds, MLA iterates over the regions, analyzing the concrete states of each region in turn - as if one was sliding a magnifying lens across the system to view the states. The algorithm adaptively refines the regions, using smaller regions where more detail is required, until the difference between the bounds is below a specified accuracy. The symbolic technique is based on multi-terminal binary decision diagrams (MTBDDs) which have been used extensively to provide compact encodings of probabilistic models. We introduce a symbolic version of the MLA algorithm, called "symbolic MLA", which combines the power of both practical techniques when verifying MDPs. An implementation of symbolic MLA in the probabilistic model checker PRISM and experimental results to illustrate the advantages of our approach are presented

Identifying Collective Modes via Impurities in the Cuprate Superconductors

We show that the pinning of collective charge and spin modes by impurities in the cuprate superconductors leads to qualitatively different fingerprints in the local density of states (LDOS). In particular, in a pinned (static) spin droplet, the creation of a resonant impurity state is suppressed, the spin-resolved LDOS exhibits a characteristic spatial pattern, and the LDOS undergoes significant changes with increasing magnetic field. Since all of these fingerprints are absent in a charge droplet, impurities are a new probe for identifying the nature and relative strength of collective modes.Comment: 4 pages, 4 figure

Highly efficient room temperature spin injection in a metal-insulator-semiconductor light emitting diode

We demonstrate highly efficient spin injection at low and room temperature in an AlGaAs/GaAs semiconductor heterostructure from a CoFe/AlOx tunnel spin injector. We use a double-step oxide deposition for the fabrication of a pinhole-free AlOx tunnel barrier. The measurements of the circular polarization of the electroluminescence in the Oblique Hanle Effect geometry reveal injected spin polarizations of at least 24% at 80K and 12% at room temperature