arXiv subjects

A. D. Jackson

Publications and source records attributed to A. D. Jackson.

At least 37 records · Page 2Linked to original sources

arXiv2005

Temperature dependence in random matrix models with pairing condensates

We address a number of issues raised by a manuscript of Klein, Toublan, and Verbaarschot (hep-ph/0405180) in which the authors introduce a random matrix model for QCD with two colors, two flavors, and fermions in the fundamental representation. Their inclusion of temperature terms differs from the approach adopted in previous work on this problem (Phys. Rev. D 64, 074016 (2001).) We demonstrate that the two approaches are related by a transformation that leaves the thermodynamic potential invariant and which therefore has no effect on physical observables.

hep-ph↗

arXiv2004

Life, Death and Preferential Attachment

Scientific communities are characterized by strong stratification. The highly skewed frequency distribution of citations of published scientific papers suggests a relatively small number of active, cited papers embedded in a sea of inactive and uncited papers. We propose an analytically soluble model which allows for the death of nodes. This model provides an excellent description of the citation distributions for live and dead papers in the SPIRES database. Further, this model suggests a novel and general mechanism for the generation of power law distributions in networks whenever the fraction of active nodes is small.

cond-mat.dis-nn↗

arXiv2004

Rotating Bose-Einstein condensates with attractive interactions

We examine the phase diagram of a Bose-Einstein condensate of atoms, interacting with an attractive pseudopotential, in a quadratic-plus-quartic potential trap rotating at a given rate. Investigating the behavior of the gas as a function of interaction strength and rotational frequency of the trap, we find that the phase diagram has three distinct phases, one with vortex excitation, one with center of mass excitation, and an unstable phase in which the gas collapses.

cond-mat.stat-mech↗

arXiv2004

Phases of a rotating Bose-Einstein condensate with anharmonic confinement

We examine an effectively repulsive Bose-Einstein condensate of atoms that rotates in a quadratic-plus-quartic potential. With use of a variational method we identify the three possible phases of the system (multiple quantization, single quantization, and a mixed phase) as a function of the rotational frequency of the gas and of the coupling constant. The derived phase diagram is shown to be universal and the continuous transitions to be exact in the limit of weak coupling and small anharmonicity. The variational results are found to be consistent with numerical solutions of the Gross-Pitaevskii equation.

cond-mat↗

arXiv2003

Vortices in Bose-Einstein condensates with anharmonic confinement

We examine an effectively repulsive Bose-Einstein condensate of atoms, that rotates in a quadratic-plus-quartic trapping potential. We investigate the phase diagram of the system as a function of the angular frequency of rotation and of the coupling constant, demonstrating that there are phase transitions between multiply- and singly-quantized vortex states. The derived phase diagram is shown to be universal and exact in the limits of small anharmonicity and weak coupling constant.

cond-mat.stat-mech↗

arXiv2003

Duality in the Color Flavor Locked Spectrum

We analyze the spectrum of the massive states for the color flavor locked phase (CFL) of QCD. We show that the vector mesons have a mass of the order of the color superconductive gap $Δ$. We also see that the excitations associated with the solitonic sector of the CFL low energy theory have a mass proportional to $F^2_π/Δ$ and hence are expected to play no role for the physics of the CFL phase for large chemical potential. Another interesting point is that the product of the soliton mass and the vector meson mass is independent of the gap. We interpret this behavior as a form of electromagnetic duality in the sense of Montonen and Olive. Our approach for determining the properties of the massive states is non-perturbative in nature and can be applied to any theory with multiple scales.

hep-ph↗

arXiv2003

Citation Networks in High Energy Physics

The citation network constituted by the SPIRES data base is investigated empirically. The probability that a given paper in the SPIRES data base has $k$ citations is well described by simple power laws, $P(k) \propto k^{-α}$, with $α\approx 1.2$ for $k$ less than 50 citations and $α\approx 2.3$ for 50 or more citations. Two models are presented that both represent the data well, one which generates power laws and one which generates a stretched exponential. It is not possible to discriminate between these models on the present empirical basis. A consideration of citation distribution by subfield shows that the citation patterns of high energy physics form a remarkably homogeneous network. Further, we utilize the knowledge of the citation distributions to demonstrate the extreme improbability that the citation records of selected individuals and institutions have been obtained by a random draw on the resulting distribution.

physics.soc-ph↗

arXiv2003

Microscopic spectral density in random matrix models for chiral and diquark condensation

We examine random matrix models of QCD which are capable of supporting both chiral and diquark condensation. A numerical study of the spectral densities near zero virtuality shows that the introduction of color in the interactions does not alter the one-body results imposed by chiral symmetry. A model with three colors has the spectral density predicted for the chiral ensemble with a Dyson index beta = 2; a pseudoreal model with two colors exhibits the spectral density of the chiral ensemble with beta = 1.

hep-ph↗

arXiv2002

Propagation of exciton pulses in semiconductors

Using a toy model, we examine the propagation of excitons in Cu$_2$O, which form localized pulses under certain experimental conditions. The formation of these waves is attributed to the effect of dispersion, non-linearity and the coupling of the excitons to phonons, which acts as a dissipative mechanism.

cond-mat↗

arXiv2002

Lieb Mode in a Quasi One-Dimensional Bose-Einstein Condensate of Atoms

We calculate the dispersion relation associated with a solitary wave in a quasi-one-dimensional Bose-Einstein condensate of atoms confined in a harmonic, cylindrical trap in the limit of weak and strong interactions. In both cases, the dispersion relation is linear for long wavelength excitations and terminates at the point where the group velocity vanishes. We also calculate the dispersion relation of sound waves in both limits of weak and strong coupling.

cond-mat↗

arXiv2002

Products of Random Matrices

We derive analytic expressions for infinite products of random 2x2 matrices. The determinant of the target matrix is log-normally distributed, whereas the remainder is a surprisingly complicated function of a parameter characterizing the norm of the matrix and a parameter characterizing its skewness. The distribution may have importance as an uncommitted prior in statistical image analysis.

physics.data-an↗

arXiv2001

Explosive Decomposition in Ultrarelativistic Heavy Ion Collision

Recent results from Au+Au collisions at BNL-RHIC energy hint at explosive hadron production at the QCD transition rather than soft hydrodynamic evolution. We speculate that this is due to a rapid variation of the effective potential for QCD close to Tc. Performing real-time lattice simulations of an effective theory we show that the fast evolution of the potential leads to ``explosive'' spinodal decomposition rather than bubble nucleation or critical slowing down.

hep-ph↗

arXiv2001

Random matrix study of the phase structure of QCD with two colors

We apply a random matrix model to the study of the phase diagram of QCD with two colors, two flavors, and a small quark mass. Although the effects of temperature are only included schematically, this model reproduces most of the ground state predictions of chiral perturbation theory and also gives a qualitative picture of the phase diagram at all temperatures. It leads, however, to an unphysical behavior of the chiral order parameter and the baryon density in vacuum and does not support diquark condensation at arbitrarily high densities. A better treatment of temperature dependence leads to correct vacuum and small temperature properties. We compare our results at both high and low densities with the results of microscopic calculations using the Nambu-Jona-Lasinio model and discuss the effects of large momentum scales on the variations of condensation fields with chemical potential.

hep-ph↗

arXiv2001

The zeros of the QCD partition function

We establish a relationship between the zeros of the partition function in the complex mass plane and the spectral properties of the Dirac operator in QCD. This relation is derived within the context of chiral Random Matrix Theory and applies to QCD when chiral symmetry is spontaneously broken. Further, we introduce and examine the concept of normal modes in chiral spectra. Using this formalism we study the consequences of a finite Thouless energy for the zeros of the partition function. This leads to the demonstration that certain features of the QCD partition function are universal.

hep-th↗

arXiv2001

Anomalous Multiplicity Fluctuations from Phase Transitions in Heavy Ion Collisions

Event-by-event fluctuations and correlations between particles produced in relativistic nuclear collisions are studied. The fluctuations in positive, negative, total and net charge are closely related through correlations. In the event of a phase transitions to a quark-gluon plasma, fluctuations in total and net charge can be enhanced and reduced respectively which, however, is very sensitive to the acceptance and centrality. If the colliding system experiences strong density fluctuations due, e.g., to droplet formation in a first-order phase transition, all fluctuations can be enhanced substantially. The importance of fluctuations and correlations is exemplified by event-by-event measurement of the multiplicities of $J/Ψ$'s and charged particles since these observables should anti-correlate in the presence of co-mover or anomalous absorption.

nucl-th↗

arXiv2001

First-Order Chiral Phase Transition in High-Energy Collisions: Can Nucleation Prevent Spinodal Decomposition?

We discuss homogeneous nucleation in a first-order chiral phase transition within an effective field theory approach to low-energy QCD. Exact decay rates and bubble profiles are obtained numerically and compared to analytic results obtained with the thin-wall approximation. The thin-wall approximation overestimates the nucleation rate for any degree of supercooling. The time scale for critical thermal fluctuations is calculated and compared to typical expansion times for high-energy hadronic or heavy-ion collisions. We find that significant supercooling is possible, and the relevant mechanism for phase conversion might be that of spinodal decomposition. Some potential experimental signatures of supercooling, such as an increase in the correlation length of the scalar condensate, are also discussed.

hep-ph↗

arXiv2000

Random matrix theory for systems with an approximate symmetry and widths of acoustic resonances in thin chaotic plates

We discuss a random matrix model of systems with an approximate symmetry and present the spectral fluctuation statistics and eigenvector characteristics for the model. An acoustic resonator like, e.g., an aluminium plate may have an approximate symmetry. We have measured the frequency spectrum and the widths for acoustic resonances in thin aluminium plates, cut in the shape of the so-called three-leaf clover. Due to the mirror symmetry through the middle plane of the plate, each resonance of the plate belongs to one of two mode classes and we show how to separate the modes into these two classes using their measured widths. We compare the spectral statistics of each mode class with results for the Gaussian orthogonal ensemble. By cutting a slit of increasing depth on one face of the plate, we gradually break the mirror symmetry and study the transition that takes place as the two classes are mixed. Presenting the spectral fluctuation statistics and the distribution of widths for the resonances, we find that this transition is well described by the random matrix model.

cond-mat↗

arXiv2000

Hydrodynamic Models for Heavy-Ion Collisions, and beyond

A generic property of a first-order phase transition in equilibrium, and in the limit of large entropy per unit of conserved charge, is the smallness of the isentropic speed of sound in the ``mixed phase''. A specific prediction is that this should lead to a non-isotropic momentum distribution of nucleons in the reaction plane (for energies around 40 AGeV in our model calculation). On the other hand, we show that from present effective theories for low-energy QCD one does not expect the thermal transition rate between various states of the effective potential to be much larger than the expansion rate, questioning the applicability of the idealized Maxwell/Gibbs construction. Experimental data could soon provide essential information on the dynamics of the phase transition.

nucl-th↗