Geometric inequalities from phase space translations

We establish a quantum version of the classical isoperimetric inequality relating the Fisher information and the entropy power of a quantum state. The key tool is a Fisher information inequality for a state which results from a certain convolution operation: the latter maps a classical probability distribution on phase space and a quantum state to a quantum state. We show that this inequality also gives rise to several related inequalities whose counterparts are well-known in the classical setting: in particular, it implies an entropy power inequality for the mentioned convolution operation as well as the isoperimetric inequality, and establishes concavity of the entropy power along trajectories of the quantum heat diffusion semigroup. As an application, we derive a Log-Sobolev inequality for the quantum Ornstein-Uhlenbeck semigroup, and argue that it implies fast convergence towards the fixed point for a large class of initial states.Comment: 37 pages; updated to match published versio

Pressure effects on charge, spin, and metal-insulator transitions in narrow bandwidth manganite Pr1−x_{1-x}Cax_{x}MnO3_{3}

Pressure effects on the charge and spin states and the relation between the ferromagnetic and metallic states were explored on the small bandwidth manganite Pr$_{1-x}$Ca$_{x}$MnO$_{3}$ (x = 0.25, 0.3, 0.35). Under pressure, the charge ordering state is suppressed and a ferromagnetic metallic state is induced in all three samples. The metal-insulator transition temperature (T$_{MI}$) increases with pressure below a critical point P*, above which T$_{MI}$ decreases and the material becomes insulating as at the ambient pressure. The e$_{g}$ electron bandwidth and/or band-filling mediate the pressure effects on the metal-insulator transition and the magnetic transition. In the small bandwidth and low doping concentration compound (x = 0.25), the T$_{MI}$ and Curie temperature (T$_{C}$) change with pressure in a reverse way and do not couple under pressure. In the x = 0.3 compound, the relation of T$_{MI}$ and T$_{C}$ shows a critical behavior: They are coupled in the range of $\sim$0.8-5 GPa and decoupled outside of this range. In the x = 0.35 compound, T$_{MI}$ and T$_{C}$ are coupled in the measured pressure range where a ferromagnetic state is present

Structured optical receivers to attain superadditive capacity and the Holevo limit

When classical information is sent over a quantum channel, attaining the ultimate limit to channel capacity requires the receiver to make joint measurements over long codeword blocks. For a pure-state channel, we construct a receiver that can attain the ultimate capacity by applying a single-shot unitary transformation on the received quantum codeword followed by simultaneous (but separable) projective measurements on the single-modulation-symbol state spaces. We study the ultimate limits of photon-information-efficient communications on a lossy bosonic channel. Based on our general results for the pure-state quantum channel, we show some of the first concrete examples of codes and structured joint-detection optical receivers that can achieve fundamentally higher (superadditive) channel capacity than conventional receivers that detect each modulation symbol individually.Comment: 4 pages, 4 figure

Universality of collapsing two-dimensional self-avoiding trails

Results of a numerically exact transfer matrix calculation for the model of Interacting Self-Avoiding Trails are presented. The results lead to the conclusion that, at the collapse transition, Self-Avoiding Trails are in the same universality class as the O(n=0) model of Blote and Nienhuis (or vertex-interacting self-avoiding walk), which has thermal exponent $\nu=12/23$, contrary to previous conjectures.Comment: Final version, accepted for publication in Journal of Physics A; 9 pages; 3 figure

Temperature dependent optical studies of Ti1−x_{1-x}Cox_xO2_2

We present the results of Raman and photoluminescence (PL) studies on epitaxial anatase phase Ti$_{1-x}$Co$_x$O$_2$ films for $x$ = 0-0.07, grown by pulsed laser deposition. The low doped system ($x$=0.01 and 0.02) shows a Curie temperature of ~700 K in the as-grown state. The Raman spectra from the doped and undoped films confirm their anatase phase. The photoluminescence spectrum is characterized by a broad emission from self-trapped excitons (STE) at 2.3 eV at temperatures below 120 K. This peak is characteristic of the anatase-phase TiO$_2$ and shows a small blueshift with increasing doping concentration. In addition to the emission from STE, the Co-doped samples show two emission lines at 2.77 eV and 2.94 eV that are absent in the undoped film indicative of a spin-flip energy.Comment: 8 pages, 4 figure

A note on multi-dimensional Camassa-Holm type systems on the torus

We present a $2n$-component nonlinear evolutionary PDE which includes the $n$-dimensional versions of the Camassa-Holm and the Hunter-Saxton systems as well as their partially averaged variations. Our goal is to apply Arnold's [V.I. Arnold, Sur la g\'eom\'etrie diff\'erentielle des groupes de Lie de dimension infinie et ses applications \`a l'hydrodynamique des fluides parfaits. Ann. Inst. Fourier (Grenoble) 16 (1966) 319-361], [D.G. Ebin and J.E. Marsden, Groups of diffeomorphisms and the motion of an incompressible fluid. Ann. of Math. 92(2) (1970) 102-163] geometric formalism to this general equation in order to obtain results on well-posedness, conservation laws or stability of its solutions. Following the line of arguments of the paper [M. Kohlmann, The two-dimensional periodic $b$-equation on the diffeomorphism group of the torus. J. Phys. A.: Math. Theor. 44 (2011) 465205 (17 pp.)] we present geometric aspects of a two-dimensional periodic $\mu$-$b$-equation on the diffeomorphism group of the torus in this context.Comment: 14 page

PASTEURELLOSIS IN DUCK IN WEST BENGAL

Two hundred sixty four samples were collected from heart blood, liver, spleen and femur of 85 khaki Campbell ducks of which P. multocida could be isolated from 4 (4.70%) birds. Out of 4 samples, organisms could be isolated from heart blood of one ducklings liver and femur of one duck each. All the isolates were found positive to catalase, oxidase, indole, nitrate reduction test and negative to methyl red, Voges-Proskaur, citrate utilization, H2S production and triple sugar iron test. The isolates fermented glucose and manitol without production of gas and non-fermented lactose, salicin, dulcitol and inositol. The isolates were non-motile and pathogenic to mice. All isolates of P. multocida were sensitive to amoxiclav, chloramphenicol, gentamicin and three isolates were sensitive to co-trimoxazole. All were moderately sensitive to amikacin, cefotaxime, neomycin and norfloxacin and resistant to ciprofloxacin and lomefloxacin