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Gordon Baym

Publications and source records attributed to Gordon Baym.

At least 109 records · Page 6Linked to original sources
arXiv2001

Non-analytic dependence of the transition temperature of the homogeneous dilute Bose gas on scattering length

We show that the shift in the transition temperature of the dilute homogeneous Bose gas is non-analytic in the scattering amplitude, $a$. The first correction beyond the positive linear shift in $a$ is negative and of order $a^2\ln a$. This non-universal non-analytic structure indicates how the discrepancies between numerical calculations at finite $a$ can be reconciled with calculations of the limit $a \to0$, since the linearity is apparent only for anomalously small $a$.

cond-mat.stat-mech↗
arXiv2001

Finite size scaling and the role of the thermodynamic ensemble in the transition temperature of a dilute Bose gas

We study the Bose-Einstein condensation phase transition in a weakly interacting gas through a perturbative analysis of finite systems. In both the grand canonical and the canonical ensembles, perturbation theory suffers from infrared divergences and cannot directly determine the transition temperature in the thermodynamic limit. However, in conjunction with finite size scaling, perturbation theory provides a powerful calculation tool. We implement it here to estimate a shift in the transition temperature in the canonical ensemble consistent with grand canonical calculations.

cond-mat.stat-mech↗
arXiv2001

RHIC: From dreams to beams in two decades

This talk traces the history of RHIC over the last two decades, reviewing the scientific motivations underlying its design, and the challenges and opportunities the machine presents.

hep-ph↗
arXiv2000

The superfluid phases of quark matter: Ginzburg-Landau theory and color neutrality

We apply Ginzburg-Landau theory to determine BCS pairing in a strongly-coupled uniform superfluid of three-flavor massless quarks in flavor equilibrium. We elucidate the phase diagram near the critical temperature in the space of the parameters characterizing the thermodynamic potential terms of fourth order in the pairing gap. Within the color and flavor antisymmetric channel with zero total angular momentum, the phase diagram contains an isoscalar (IS) color-antitriplet phase and a color-flavor-locked (CFL) phase, reached by a second order transition from the normal state, as well as states reached by a first order transition. We complement the general Ginzburg-Landau approach by deriving the high-density asymptotic form of the Ginzburg-Landau free energy from the weak-coupling gap equation. The dynamically-screened, long-range color magnetic interactions are taken into account in solving the gap equation. We find that in the limit of weak coupling, the IS phase is less favorable near the transition temperature than the CFL phase. In view of the fact that deconfined quark matter must be color charge neutral, we incorporate the constraint of overall color neutrality into the Ginzburg-Landau theory and the gap equation. This constraint yields a disparity in the chemical potential between colors and reduces the size of the gap, in the presence of the anisotropy of the order parameters in color space. In comparison with the case in which there are no chemical potential differences between colors and hence the superfluid generally has nonzero net color charge, we find that while the constraint of color neutrality has only negligible effects on the gap in the weak coupling regime, it appreciably destabilizes the IS phase in the strong coupling regime without affecting the CFL phase.

hep-ph↗
arXiv2000

Finite Temperature Collapse of a Bose Gas with Attractive Interactions (extended version)

We study the mechanical stability of the weakly interacting Bose gas with attractive interactions, and construct a unified picture of the collapse valid from the low temperature condensed regime to the high temperature classical regime. As we show, the non-condensed particles play a crucial role in determining the region of stability, even providing a mechanism for collapse in the non-condensed cloud. Furthermore, we demonstrate that the mechanical instability prevents BCS-type ``pairing'' in the attractive Bose gas. We extend our results to describe domain formation in spinor condensates.

cond-mat.stat-mech↗
arXiv2000

Self-consistent approximations: application to a quasiparticle description of the thermodynamic properties of relativistic plasmas

We generalize the concept of conserving,Φ-derivable, approximations to relativistic field theories. Treating the interaction field as a dynamical degree of freedom, we derive the thermodynamical potential in terms of fully dressed propagators, an approach which allows us to resolve the entropy of a relativistic plasma into contributions from its interacting elementary excitations. We illustrate the derivation for a hot QED plasma of massless particles. We also discuss how the self-consistency of the treatment manifests itself into relationships between the contributions from interaction and matter fields.

hep-ph↗
arXiv1999

Finite Temperature Collapse of a Bose Gas with Attractive Interactions

We study the mechanical stability of the weakly interacting Bose gas with attractive interactions, and construct a unified picture of the collapse valid from the low temperature condensed region to the high temperature classical regime. As we show, the non-condensed particles play a crucial role in determining the region of stability. We extend our results to describe domain formation in spinor condensates.

cond-mat.stat-mech↗
arXiv1999

The quantum mechanics of particle-correlation measurements in high-energy heavy-ion collisions

The Hanbury Brown--Twiss (HBT) effect in two-particle correlations is a fundamental wave phenomenon that occurs at the sensitive elements of detectors; it is one of the few processes in elementary particle detection that depends on the wave mechanics of the produced particles. We analyze here, within a quantum mechanical framework for computing correlations among high-energy particles, how particle detectors produce the HBT effect. We focus on the role played by the wave functions of particles created in collisions and the sensitivity of the HBT effect to the arrival times of pairs at the detectors, and show that the two detector elements give an enhanced signal when the single-particle wave functions of the detected particles overlap at both elements within the characteristic atomic transition time of the elements. The measured pair correlation function is reduced when the delay in arrival times between pairs at the detectors is of order of or larger than the transition time.

nucl-th↗
arXiv1999

The transition temperature of the dilute interacting Bose gas

We show that the critical temperature of a uniform dilute Bose gas must increase linearly with the s-wave scattering length describing the repulsion between the particles. Because of infrared divergences, the magnitude of the shift cannot be obtained from perturbation theory, even in the weak coupling regime; rather, it is proportional to the size of the critical region in momentum space. By means of a self-consistent calculation of the quasiparticle spectrum at low momenta at the transition, we find an estimate of the effect in reasonable agreement with numerical simulations.

cond-mat.stat-mech↗
arXiv1999

The transition temperature of the dilute interacting Bose gas for $N$ internal degrees of freedom

We calculate explicitly the variation $δT_c$ of the Bose-Einstein condensation temperature $T_c$ induced by weak repulsive two-body interactions to leading order in the interaction strength. As shown earlier by general arguments, $δT_c/T_c$ is linear in the dimensionless product $an^{1/3}$ to leading order, where $n$ is the density and $a$ the scattering length. This result is non-perturbative, and a direct perturbative calculation of the amplitude is impossible due to infrared divergences familiar from the study of the superfluid helium lambda transition. Therefore we introduce here another standard expansion scheme, generalizing the initial model which depends on one complex field to one depending on $N$ real fields, and calculating the temperature shift at leading order for large $N$. The result is explicit and finite. The reliability of the result depends on the relevance of the large $N$ expansion to the situation N=2, which can in principle be checked by systematic higher order calculations. The large $N$ result agrees remarkably well with recent numerical simulations.

cond-mat.stat-mech↗
arXiv1998

The physics of Hanbury Brown--Twiss intensity interferometry: from stars to nuclear collisions

In the 1950's Hanbury Brown and Twiss showed that one could measure the angular sizes of astronomical radio sources and stars from correlations of signal intensities, rather than amplitudes, in independent detectors. Their subsequent correlation experiments demonstrating quantum bunching of photons in incoherent light beams were seminal in the development of quantum optics. Since that time the technique of "intensity interferometry" has become a valuable probe of high energy nuclear and particle collisions, providing information on the space-time geometry of the collision. The effect is one of the few measurements in elementary particle detection that depends on the wave mechanics of the produced particles. Here we discuss the basic physics of intensity interferometry, and its current applications in high energy nuclear physics, as well as recent applications in condensed matter and atomic physics.

nucl-th↗
arXiv1998

Self-consistent approximations in relativistic plasmas: Quasiparticle analysis of the thermodynamic properties

We generalize the concept of conserving, Phi-derivable, approximations to relativistic field theories. Treating the interaction field as a dynamical degree of freedom, we derive the thermodynamic potential in terms of fully dressed propagators, an approach which allows us to resolve the entropy of a relativistic plasma into contributions from its interacting elementary excitations. We illustrate the derivation for a hot relativistic system governed by electromagnetic interactions.

hep-ph↗
arXiv1997

The Electrical Conductivity in the Early Universe

We calculate the electrical conductivity in the early universe at temperatures below as well as above the electroweak vacuum scale, $T_c\simeq 100$GeV. Debye and dynamical screening of electric and magnetic interactions leads to a finite conductivity, $σ_{el}\sim T/α\ln(1/α)$, at temperatures well below $T_c$. At temperatures above, $W^\pm$ charge-exchange processes -- analogous to color exchange through gluons in QCD -- effectively stop left-handed charged leptons. However, right-handed leptons can carry current, resulting in $σ_{el}/T$ being only a factor $\sim \cos^4θ_W$ smaller than at temperatures below $T_c$.

astro-ph↗
arXiv1996

The Maximum Mass of a Neutron Star

Observational identification of black holes as members of binary systems requires the knowledge of the upper limit on the gravitational mass of a neutron star. We use modern equations of state for neutron star matter, fitted to experimental nucleon-nucleon scattering data and the properties of light nuclei, to calculate, within the framework of Rhoades & Ruffini (1974), the minimum upper limit on a neutron star mass. Regarding the equation of state as valid up to twice nuclear matter saturation density, rho_{nm}, we obtain a secure upper bound on the neutron star mass equal to 2.9 solar masses. We also find that in order to reach the lowest possible upper bound of 2.2 solar masses, we need understand the physical properties of neutron matter up to a density of about 4 times rho_{nm}.

astro-ph↗
arXiv1996

Fine structure of excitons in Cu$_2$O

Three experimental observations on 1s-excitons in Cu$_2$O are not consistent with the picture of the exciton as a simple hydrogenic bound state: the energies of the 1s-excitons deviate from the Rydberg formula, the total exciton mass exceeds the sum of the electron and hole effective masses, and the triplet-state excitons lie above the singlet. Incorporating the band structure of the material, we calculate the corrections to this simple picture arising from the fact that the exciton Bohr radius is comparable to the lattice constant. By means of a self-consistent variational calculation of the total exciton mass as well as the ground-state energy of the singlet and the triplet-state excitons, we find excellent agreement with experiment.

cond-mat↗
arXiv1996

Auger decay of degenerate and Bose-condensed excitons in Cu$_2$O

We study the non-radiative Auger decay of excitons in Cu$_2$O, in which two excitons scatter to an excited electron and hole. The exciton decay rate for the direct and the phonon-assisted processes is calculated from first principles; incorporating the band structure of the material leads to a relatively shorter lifetime of the triplet state ortho excitons. We compare our results with the Auger decay rate extracted from data on highly degenerate triplet excitons and Bose-condensed singlet excitons in Cu$_2$O.

cond-mat↗
arXiv1995

Quantum saturation and condensation of excitons in Cu$_2$O: a theoretical study

Recent experiments on high density excitons in Cu$_2$O provide evidence for degenerate quantum statistics and Bose-Einstein condensation of this nearly ideal gas. We model the time dependence of this bosonic system including exciton decay mechanisms, energy exchange with phonons, and interconversion between ortho (triplet-state) and para (singlet-state) excitons, using parameters for the excitonic decay, the coupling to acoustic and low-lying optical phonons, Auger recombination, and ortho-para interconversion derived from experiment. The single adjustable parameter in our model is the optical-phonon cooling rate for Auger and laser-produced hot excitons. We show that the orthoexcitons move along the phase boundary without crossing it (i.e., exhibit a ``quantum saturation''), as a consequence of the balance of entropy changes due to cooling of excitons by phonons and heating by the non-radiative Auger two-exciton recombination process. The Auger annihilation rate for para-para collisions is much smaller than that for ortho-para and ortho-ortho collisions, explaining why, under the given experimental conditions, the paraexcitons condense while the orthoexcitons fail to do so.

cond-mat↗