Adiabatic elimination in quantum stochastic models

We consider a physical system with a coupling to bosonic reservoirs via a quantum stochastic differential equation. We study the limit of this model as the coupling strength tends to infinity. We show that in this limit the solution to the quantum stochastic differential equation converges strongly to the solution of a limit quantum stochastic differential equation. In the limiting dynamics the excited states are removed and the ground states couple directly to the reservoirs.Comment: 17 pages, no figures, corrected mistake

Sharp Trace Hardy-Sobolev-Maz'ya Inequalities and the Fractional Laplacian

In this work we establish trace Hardy and trace Hardy-Sobolev-Maz'ya inequalities with best Hardy constants, for domains satisfying suitable geometric assumptions such as mean convexity or convexity. We then use them to produce fractional Hardy-Sobolev-Maz'ya inequalities with best Hardy constants for various fractional Laplacians. In the case where the domain is the half space our results cover the full range of the exponent $s \in (0,1)$ of the fractional Laplacians. We answer in particular an open problem raised by Frank and Seiringer \cite{FS}.Comment: 42 page

Diffusive limit for a quantum linear Boltzmann dynamics

In this article, I study the diffusive behavior for a quantum test particle interacting with a dilute background gas. The model I begin with is a reduced picture for the test particle dynamics given by a quantum linear Boltzmann equation in which the gas particle scattering is assumed to occur through a hard-sphere interaction. The state of the particle is represented by a density matrix that evolves according to a translation-covariant Lindblad equation. The main result is a proof that the particle's position distribution converges to a Gaussian under diffusive rescaling.Comment: 51 pages. I have restructured Sections 2-4 from the previous version and corrected an error in the proof of Proposition 7.

Impaired functional communication between the L-type calcium channel and mitochondria contributes to metabolic inhibition in the mdx heart

Duchenne muscular dystrophy is a fatal X-linked disease characterized by the absence of dystrophin. Approximately 20% of boys will die of dilated cardiomyopathy that is associated with cytoskeletal protein disarray, contractile dysfunction, and reduced energy production. However, the mechanisms for altered energy metabolism are not yet fully clarified. Calcium influx through the L-type Ca2+ channel is critical for maintaining cardiac excitation and contraction. The L-type Ca2+ channel also regulates mitochondrial function and metabolic activity via transmission of movement of the auxiliary beta subunit through intermediate filament proteins. Here, we find that activation of the L-type Ca2+ channel is unable to induce increases in mitochondrial membrane potential and metabolic activity in intact cardiac myocytes from the murine model of Duchenne muscular dystrophy (mdx) despite robust increases recorded in wt myocytes. Treatment of mdx mice with morpholino oligomers to induce exon skipping of dystrophin exon 23 (that results in functional dystrophin accumulation) or application of a peptide that resulted in block of voltage-dependent anion channel (VDAC) “rescued” mitochondrial membrane potential and metabolic activity in mdx myocytes. The mitochondrial VDAC coimmunoprecipitated with the L-type Ca2+ channel. We conclude that the absence of dystrophin in the mdx ventricular myocyte leads to impaired functional communication between the L-type Ca2+ channel and mitochondrial VDAC. This appears to contribute to metabolic inhibition. These findings provide new mechanistic and functional insight into cardiomyopathy associated with Duchenne muscular dystrophy

Granular discharge and clogging for tilted hoppers

We measure the flux of spherical glass beads through a hole as a systematic function of both tilt angle and hole diameter, for two different size beads. The discharge increases with hole diameter in accord with the Beverloo relation for both horizontal and vertical holes, but in the latter case with a larger small-hole cutoff. For large holes the flux decreases linearly in cosine of the tilt angle, vanishing smoothly somewhat below the angle of repose. For small holes it vanishes abruptly at a smaller angle. The conditions for zero flux are discussed in the context of a {\it clogging phase diagram} of flow state vs tilt angle and ratio of hole to grain size

Electrical transport studies of quench condensed Bi films at the initial stage of film growth: Structural transition and the possible formation of electron droplets

The electrical transport properties of amorphous Bi films prepared by sequential quench deposition have been studied in situ. A superconductor-insulator (S-I) transition was observed as the film was made increasingly thicker, consistent with previous studies. Unexpected behavior was found at the initial stage of film growth, a regime not explored in detail prior to the present work. As the temperature was lowered, a positive temperature coefficient of resistance (dR/dT > 0) emerged, with the resistance reaching a minimum before the dR/dT became negative again. This behavior was accompanied by a non-linear and asymmetric I-V characteristic. As the film became thicker, conventional variable-range hopping (VRH) was recovered. We attribute the observed crossover in the electrical transport properties to an amorphous to granular structural transition. The positive dR/dT found in the amorphous phase of Bi formed at the initial stage of film growth was qualitatively explained by the formation of metallic droplets within the electron glass.Comment: 7 pages, 6 figure

Study of Thermodynamic Quantities in Generalized Gravity Theories

In this work, we have studied the thermodynamic quantities like temperature of the universe, heat capacity and squared speed of sound in generalized gravity theories like Brans-Dicke, Ho$\check{\text r}$ava-Lifshitz and $f(R)$ gravities. We have considered the universe filled with dark matter and dark energy. Also we have considered the equation of state parameters for open, closed and flat models. We have observed that in all cases the equation of state behaves like quintessence. The temperature and heat capacity of the universe are found to decrease with the expansion of the universe in all cases. In Brans-Dicke and $f(R)$ gravity theories the squared speed of sound is found to exhibit increasing behavior for open, closed and flat models and in Ho$\check{\text r}$ava-Lifshitz gravity theory it is found to exhibit decreasing behavior for open and closed models with the evolution of the universe. However, for flat universe, the squared speed of sound remains constant in Ho$\check{\text r}$ava-Lifshitz gravity.Comment: 15 pages, 12 figure

The ZEPLIN II dark matter detector: data acquisition system and data reduction

ZEPLIN-II is a two-phase (liquid/gas) xenon dark matter detector searching for WIMP-nucleon interactions. In this paper we describe the data acquisition system used to record the data from ZEPLIN-II and the reduction procedures which parameterise the data for subsequent analysis.Comment: 11 pages, 10 figure