Thermodynamic geometry of holographic superconductors

We obtain the thermodynamic geometry of a (2+1) dimensional strongly coupled quantum field theory at a finite temperature in a holographic set up, through the gauge/gravity correspondence. The bulk dual gravitational theory is described by a (3+1) dimensional charged AdS black hole in the presence of a massive charged scalar field. The holographic free energy of the (2+1) dimensional strongly coupled boundary field theory is computed analytically through the bulk boundary correspondence. The thermodynamic metric and the corresponding scalar curvature is then obtained from the holographic free energy. The thermodynamic scalar curvature characterizes the superconducting phase transition of the boundary field theory.Comment: 7 Pages and 3 Figure

Particle Dynamics and Lie-algebraic type of Non-commutativity of space-time

In this paper, we present the results of our investigation relating particle dynamics and non-commutativity of space-time by using Dirac's constraint analysis. In this study, we re-parameterise the time $t=t(\tau)$ along with $x=x(\tau)$ and treat both as configuration space variables. Here, $\tau$ is a monotonic increasing parameter and the system evolves with this parameter. After constraint analysis, we find the deformed Dirac brackets similar to the $\kappa$-deformed space-time and also, get the deformed Hamilton's equations of motion. Moreover, we study the effect of non-commutativity on the generators of Galilean group and Poincare group and find undeformed form of the algebra. Also, we work on the extended space analysis in the Lagrangian formalism. We find the primary as well as the secondary constraints. Strikingly on calculating the Dirac brackets among the phase space variables, we obtain the classical version of $\kappa$-Minkowski algebra.Comment: 15 page

Our Trysts with `Bal' and Noncommutative Geometry

This contributory article begins with our fond and sincere reminiscences about our beloved Prof. A.P. Balachandran. In the main part, we discuss our recent formulation of quantum mechanics on (1+1)D noncommutative space-time using Hilbert-Schmidt operators. As an application, we demonstrate how geometrical phase in a system of time-dependent forced harmonic oscillator living in the Moyal space-time can emerge.Comment: In Honor of A.P.Balachandran on the Occasion of His 85th Birthday (To be published in the Festschrift volume: Particles, Fields and Topology by World Scientific, Singapore

Low frequency gravitational waves emerge Berry phase

The detection of low frequency gravitational waves (LFGWs) astronomy has marked an advent of new era in the domain of astrophysics and general relativity. Using the framework of interaction between GWs and a point two-particles like detector, within linearized gravity approach, we propose a toy detector model whose quantum state is being investigated at a low-frequency of GWs. The detector is in simultaneous interaction with GWs and an external time-dependent (tuneable) two-dimensional harmonic potential. We observe that the interaction with low frequency GWs naturally provides adiabatic approximation in the calculation, and thereby can lead to a quantal geometric phase in the quantum states of the detector. Moreover this can be controlled by tuning the frequency of the external harmonic potential trap. We argue that such geometric phase detection may serve as a manifestation of the footprint of GWs. More importantly, our theoretical model may be capable of providing a layout for the detection of very small frequency GWs through Berry phase.Comment: Revised version, title changed, to appear in Phys. Rev.

Notch Dosage Haploinsufficiency Is Associated With Reduced Neuronal Division and Disruption of Periglomerular Interneurons in Mice

Neural stem cells in the lateral ganglionic eminence (LGE) generate progenitors that migrate through the rostral migratory stream (RMS) to repopulate olfactory bulb (OB) interneurons, but the regulation of this process is poorly defined. The evolutionarily conserved Notch pathway is essential for neural development and maintenance of neural stem cells. Jagged1, a Notch ligand, is required for stem cell maintenance. In humans, heterozygous mutations in JAGGED1 cause Alagille syndrome, a genetic disorder characterized by complications such as cognitive impairment and reduced number of bile ducts in the liver, suggesting the presence of a JAGGED1 haploinsufficient phenotype. Here, we examine the role of Jagged1 using a conditional loss-of-function allele in the nervous system. We show that heterozygous mice possess a haploinsufficient phenotype that is associated with a reduction in size of the LGE, a reduced proliferative state, and fewer progenitor cells in the LGE and RMS. Moreover, loss of Jagged1 leads to deficits in periglomerular interneurons in the OB. Our results support a dose-dependent role for Jagged1 in maintaining progenitor division within the LGE and RMS

Symmetries of κ-Minkowski space-time: a possibility of exotic momentum space geometry?

Abstract The quest for a quantum gravity phenomenology has inspired a quantum notion of space-time, which motivates us to study the fate of the relativistic symmetries of a particular model of quantum space-time, as well as its intimate connection with the plausible emergent curved “physical momentum space”. We here focus on the problem of Poincare symmetry of κ-Minkowski type non-commutative (quantum) space-time, where the Poincare algebra, on its own, remains undeformed, but in order to preserve the structure of the space-time non-commutative (NC) algebra, the actions of the algebra generators on the operator-valued space-time manifold must be enveloping algebra valued that lives in entire phase space i.e. the cotangent bundle on the space-time manifold (at classical level). Further, we constructed a model for a spin-less relativistic massive particle enjoying the deformed Poincare symmetry, using the first order form of geometric Lagrangian, that satisfies a new deformed dispersion relation and explored a feasible regime of a future Quantum Gravity theory in which the momentum space becomes curved. In this scenario there is only a mass scale (Planck mass m p ), but no length scale. Finally, we relate the deformed mass shell to the geodesic distance in this curved momentum space, where the mass of the particle gets renormalized as a result of noncommutativity. We show, that under some circumstances, the Planck mass provides an upper bound for the observed renormalized mass

Developmental and functional significance of the CSF-1 proteoglycan chondroitin sulfate chain

The primary macrophage growth factor, colony-stimulating factor-1 (CSF-1), is homodimeric and exists in 3 biologically active isoforms: a membrane-spanning, cell-surface glycoprotein (csCSF-1) and secreted glycoprotein (sgCSF-1) and proteoglycan (spCSF-1) isoforms. To investigate the in vivo role of the chondroitin sulfate glycosaminoglycan (GAG) chain of spCSF-1, we created mice that exclusively express, in a normal tissue-specific and developmental manner, either the secreted precursor of spCSF-1 or the corresponding precursor in which the GAG addition site was mutated. The reproductive, hematopoietic tooth eruption and tissue macrophage defects of CSF-1-deficient, osteopetrotic Csf1op/Csf1op mice were corrected by transgenic expression of the precursors of either sgCSF-1 or spCSF-1. Furthermore, in contrast to the transgene encoding csCSF-1, both failed to completely correct growth retardation, suggesting a role for csCSF-1 in the regulation of body weight. However, spCSF-1, in contrast to sgCSF-1, completely resolved the osteopetrotic phenotype. Furthermore, in transgenic lines expressing different concentrations of sgCSF-1 or spCSF-1, spCSF-1 more efficiently corrected Csf1op/Csf1op defects of tooth eruption, eyelid opening, macrophage morphology, and B-cell deficiency than sgCSF-1. These results indicate an important role of the CSF-1 chondroitin sulfate proteoglycan in in vivo signaling by secreted CSF-1. (Blood. 2006;107:786-795