# Gordon Baym - Univ. Illinois

## Contact Details

NameGordon Baym |
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AffiliationUniv. Illinois |
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CityUrbana |
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CountryUnited States |
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## Pubs By Year |
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## External Links |
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## Pub CategoriesNuclear Theory (19) High Energy Physics - Phenomenology (15) Physics - Other (10) Physics - Statistical Mechanics (4) Physics - Mesoscopic Systems and Quantum Hall Effect (4) High Energy Astrophysical Phenomena (4) Nuclear Experiment (3) High Energy Physics - Theory (3) Physics - Superconductivity (2) General Relativity and Quantum Cosmology (2) Quantum Physics (2) Physics - Strongly Correlated Electrons (1) Astrophysics (1) High Energy Physics - Lattice (1) Solar and Stellar Astrophysics (1) High Energy Physics - Experiment (1) Physics - Atomic Physics (1) Physics - History of Physics (1) |

## Publications Authored By Gordon Baym

Chiral symmetry is always broken in cold, dense matter, by chiral condensation at low densities and by diquark condensation at high density. We construct here, within a schematic Nambu-Jona-Lasinio (NJL) model, the corresponding generalized Nambu-Goldstone pion, $\pi_G$. As we show, the $\pi_G$ mode naturally emerges as a linear combination of the $\langle \bar{q}q\rangle$ vacuum pion $\pi$ and the $\langle qq \rangle$ diquark pion $\tilde{\pi}$, with $q$ the quark field, and continuously evolves with increasing density from being $\pi$-like in the vacuum to $\tilde{\pi}$-like in the high density diquark pairing phase. Read More

The polarization of direct photons produced in an ultrarelativistic heavy-ion collision reflects the momentum anisotropy of the quark-gluon plasma created in the collision. This paper presents a general framework, based on the photon spectral functions in the plasma, for analyzing the angular distribution and thus the polarization of dileptons in terms of the plasma momentum anisotropies. The rates of dilepton production depend, in general, on four independent spectral functions, corresponding to two transverse polarizations, one longitudinal polarization, and -- in plasmas in which the momentum anisotropy is not invariant under parity in the local rest frame of the matter -- a new spectral function, $\rho_n$, related to the anisotropy direction in the collision. Read More

I first review the early history of the ultrarelativistic heavy ion program, starting with the 1974 Bear Mountain Workshop, and the 1983 Aurora meeting of the U.S. Nuclear Science Committee, just one billion seconds ago, which laid out the initial science goals of an ultrarelativistic collider. Read More

The neutron, in addition to possibly having a permanent electric dipole moment as a consequence of violation of time-reversal invariance, develops an induced electric dipole moment in the presence of an external electric field. We present here a unified non-relativistic description of these two phenomena, in which the dipole moment operator, $\vec{\cal D}$, is not constrained to lie along the spin operator. Although the expectation value of $\vec{\cal D}$ in the neutron is less than $10^{-13}$ of the neutron radius, $r_n$, the expectation value of $\vec {\cal D}\,^2$ is of order $r_n^2$. Read More

We delineate the properties of QCD matter at baryon density n_B=1-10n_0 (n_0: nuclear saturation density), through the construction of neutron star equations of state that satisfy the neutron star mass-radius constraints as well as physical conditions on the speed of sound. The QCD matter is described in the 3-window modeling: at n_B < 2n_0 purely nuclear matter; at n_B > 5n_0 percolated quark matter; and at 2n_0 < n_B < 5n_0 matter intermediate between these two which are constructed by interpolation. Using a schematic quark model with effective interactions inspired from hadron and nuclear physics, we analyze the strength of interactions necessary to describe observed neutron star properties. Read More

We present a comprehensive study of spectroscopic radius measurements of twelve neutron stars obtained during thermonuclear bursts or in quiescence. We incorporate, for the first time, a large number of systematic uncertainties in the measurement of the apparent angular sizes, Eddington fluxes, and distances, in the composition of the interstellar medium, and in the flux calibration of X-ray detectors. We also take into account the results of recent theoretical calculations of rotational effects on neutron star radii, of atmospheric effects on surface spectra, and of relativistic corrections to the Eddington critical flux. Read More

We calculate the effect of a heat current on transporting $^3$He dissolved in superfluid $^4$He at ultralow concentration, as will be utilized in a proposed experimental search for the electric dipole moment of the neutron (nEDM). In this experiment, a phonon wind will generated to drive (partly depolarized) $^3$He down a long pipe. In the regime of $^3$He concentrations $\tilde < 10^{-9}$ and temperatures $\sim 0. Read More

We construct an equation of state for massive neutron stars based on quantum chromodynamics phenomenology. Our primary purpose is to delineate the relevant ingredients of equations of state that simultaneously have the required stiffness and satisfy constraints from thermodynamics and causality. These ingredients are: (i) a repulsive density-density interaction, universal for all flavors; (ii) the color-magnetic interaction active from low to high densities; (iii) confining effects, which become increasingly important as the baryon density decreases; (iv) non-perturbative gluons, which are not very sensitive to changes of the quark density. Read More

We report microscopic calculations of the thermal conductivity, diffusion constant and thermal diffusion constant for classical solutions of $^3$He in superfluid $^4$He at temperatures $T \la 0.6$~K, where phonons are the dominant excitations of the $^4$He. We focus on solutions with $^3$He concentrations $\la \,10^{-3}$, for which the main scattering mechanisms are phonon-phonon scattering via 3-phonon Landau and Beliaev processes, which maintain the phonons in a drifting equilibrium distribution, and the slower process of $^3$He-phonon scattering, which is crucial for determining the $^3$He distribution function in transport. Read More

We study, in the PNJL model, how the entropy of interacting quarks reflects the change in the effective degrees of freedom as the temperature increases through the quark-hadron phase transition. With inclusion of mesonic correlations, the effective degrees of freedom change from those of pi and sigma mesons at low temperatures to those of free quarks at high temperatures, with a resultant second order phase deconfinement transition in the chiral limit. Read More

We show how anisotropy in momentum of the gluon distribution in ultrarelativistic heavy ion collisions gives rise to polarization of direct photons produced via gluon-quark Compton scattering, as well as by quark-antiquark annihilation into a gluon-photon pair. We estimate the polarization asymmetry from the Compton process within a toy model where the polarized photons are produced from thermal gluons scattered by heavy-quark scattering centers moving with Bjorken boost-invariant flow, and find that it could be as large as 10%. We conclude that polarization measurements of directly produced photons can shed light on gluon pressure anisotropy in the early stages of collisions. Read More

We compute---at finite quark chemical potentials---the color screening of cold quark matter at the one-loop level, comparing the normal, BCS-paired U(1)em (or Higgs) phase and a singlet phase with color-singlet condensate near the Fermi surface. The latter phase is computed using the example of two-color QCD with a color-singlet diquark condensate. In contrast to the normal and Higgs phases, neither electric nor magnetic screening masses appear in the singlet phase. Read More

We calculate the normal mass density of a paired Fermi gas at unitarity. The dominant contribution near the superfluid transition is from fermionic quasiparticle excitations, and is thus sensitive to the pairing gap. A comparison with the recent experiment of Sidorenkov et al. Read More

We show how the configuration-space form of the Bogoliubov ground state wave function of a bosonic condensate with a single vortex in a harmonic trap can be described in terms of bosonic Jastrow correlations. We then generalize this result to study the first effects of such correlations on a mean-field vortex lattice state and show that the included correlations lower the energy below that of the mean-field state. Although the reduction is relatively small, it is a precursor of the more general expected effect of correlations in describing the melting of the vortex lattice at large angular momentum per particle. Read More

We investigate the effects of realistic quark masses and local color neutrality on quark pairing in the three-flavor Polyakov--Nambu--Jona-Lasinio model. While prior studies have indicated the presence of light flavor quark (2SC) or symmetric color-flavor-locked (CFL) pairing at low temperatures, we find that in the absence of a local color neutrality constraint the inclusion of the Polyakov loop gives rise to phases in which all quark colors and flavors pair, but with unequal magnitudes. We study this asymmetric color-flavor-locked (ACFL) phase, which can exist even for equal mass quarks, identifying its location in the phase diagram, the order of the associated phase transitions, and its symmetry breaking pattern, which proves to be the intersection of the symmetry groups of the 2SC and CFL phases. Read More

A longstanding goal of Akira Tonomura was to observe Hanbury Brown--Twiss anti-correlations between electrons in a field-emission free electron beam. The experimental results were reported in his 2011 paper with Tetsuji Kodama and Nobuyuki Osakabe [Phys. Rev. Read More

Motivated by a proposed experimental search for the electric dipole moment of the neutron (nEDM) utilizing neutron-$^3$He capture in a dilute solution of $^3$He in superfluid $^4 $He, we derive the transport properties of dilute solutions in the regime where the $^3$He are classically distributed and rapid $^3$He-$^3$He scatterings keep the $^3$He in equilibrium. Our microscopic framework takes into account phonon-phonon, phonon-$^3$He, and $^3$He-$^3$He scatterings. We then apply these calculations to measurements by Rosenbaum et al. Read More

We study the stability and dynamics of an ultra-cold bosonic gas trapped in a toroidal geometry and driven by rotation, in the absence of dissipation. We first delineate, via the Bogoliubov mode expansion, the regions of stability and the nature of instabilities of the system for both repulsive and attractive interaction strengths. To study the response of the system to variations in the rotation rate, we introduce a "disorder" potential, breaking the rotational symmetry. Read More

We review the history of neutron star physics in the 1930s that is related to L. Landau. According to recollections of Rosenfeld (1974, Proc. Read More

We study the Bose-Einstein condensate phase transition of three-dimensional ultracold bosons with isotropic Rashba spin-orbit coupling. Investigating the structure of Ginzburg-Landau free energy as a function of the condensate density, we show, within the Bogoliubov approximation, that the condensate phase transition is first order with a jump in the condensate density. We calculate the transition temperature and the jump in the condensate density at the transition for large spin-orbit coupling, where the transition temperature depends linearly on the density of particles. Read More

The flow of a uniform Bose gas at speeds greater than the Landau critical velocity, v_c, does not necessarily destroy superfluidity, but rather need only lead to a decrease of the superfluid mass density, {\rho}_s. Analyzing a weakly interacting Bose gas with a finite range interparticle interaction that leads to a Landau critical velocity at non-zero quasiparticle momentum, we explicitly construct the (non-uniform) condensate for fluid flow faster than v_c and calculate the accompanying decrease in {\rho}_s. We briefly comment on the relation of the physics to other problems in superfluids, e. Read More

**Affiliations:**

^{1}Colorado School of Mines,

^{2}RIKEN,

^{3}Univ. Illinois

We show that an antiferrosmectic-C phase has lower energy at high densities than the non-magnetized Fermi gas and ferronematic phases in an ultracold gas of fermionic atoms, or molecules, with large magnetic dipole moments. This phase, which is analogous to meson condensation in dense nuclear matter, is a one-dimensional periodic structure in which the fermions localize in layers with their pseudospin direction aligned parallel to the layers, and staggered layer by layer. Read More

The striped state of ultracold bosons with Rashba spin-orbit coupling in a homogeneous infinite system has, as we show, a constant particle flow, which in a finite-size system would accumulate particles at the boundaries; it is thus not a physical steady state of the system. We propose, as a variational ansatz, a condensate wave function for a weakly trapped system which behaves similarly to the striped state near the center, but does not have particle flow at the boundaries. This state has a line of unquantized coreless vortices. Read More

We study the stability of Bose condensates with Rashba-Dresselhaus spin-orbit coupling in three dimensions against quantum and thermal fluctuations. The ground state depletion of the plane-wave condensate due to quantum fluctuations is, as we show, finite, and therefore the condensate is stable. We also calculate the corresponding shift of the ground state energy. Read More

We investigate the phase structure of massless three-flavor QCD by extending the Nambu-Jona- Lasinio model to include the effects of confinement and the axial anomaly. We study the interplay between the chiral and diquark condensates induced by the axial anomaly, as well as their relationship with the Polyakov loop, which parameterizes confinement. By minimizing the thermodynamic potential we construct the QCD phase diagram and investigate the possibility of realizing a recently discovered low temperature critical point and an associated BEC-BCS crossover. Read More

We study ultracold bosons in three dimensions with an anisotropic Rashba-Dresselhaus spin-orbit coupling. We first carry out the exact summation of ladder diagrams for the two-boson t-matrix at zero energy. Then, with the t-matrix as the effective interaction, we find the ground-state phase diagrams of bosons in mean field as a function of the spin-orbit coupling, the anisotropy, and the scattering lengths between particles in the same and in different pseudospin states. Read More

Interactions of ultracold atoms with Rashba spin-orbit coupling, currently being studied with simulated (artificial) gauge fields, have nontrivial ultraviolet and infrared behavior. Examining the ultraviolet structure of the Bethe-Salpeter equation, we show that the linear ultraviolet divergence in the bare interaction can be renormalized as usual in terms of low-energy scattering lengths, and that for both bosons and fermions ultraviolet logarithmic divergences are absent. Calculating the leading order effective interaction with full dependence on the spin-orbit coupling strength and the center-of-mass momentum of the colliding pair, we elucidate the relation between mean-field interactions and physical three-dimensional scattering lengths. Read More

We investigate the phase diagram and the BCS-BEC crossover of a homogeneous three-component ultracold Fermi gas with a U(3) invariant attractive interaction. We show that the system at sufficiently low temperatures exhibits population imbalance, as well as fermionic pairing. We describe the crossover in this system, connecting the weakly interacting BCS regime of the partially population-imbalanced fermion pairing state and the BEC limit with three weakly interacting species of molecules, including pairing fluctuations within a t-matrix calculation of the particle self-energies. Read More

We study the QCD phase structure in the three-flavor Nambu--Jona-Lasinio model, incorporating the chiral-diquark interplay due to the axial anomaly. We demonstrate that for a certain range of model parameters, the low temperature critical point predicted by a Ginzburg-Landau analysis appears in the phase diagram. In addition, we show that the axial anomaly presents a new scenario for a possible BEC-BCS crossover in the color-flavor locked phase of QCD. Read More

We investigate the effects of correlations on the properties of the ground state of the rotating harmonically-trapped Bose gas by adding Bogoliubov fluctuations to the mean-field ground state of an $N$-particle single-vortex system. We demonstrate that the fluctuation-induced correlations lower the energy compared to that of the mean-field ground state, that the vortex core is pushed slightly away from the center of the trap, and that an unstable mode with negative energy (for rotations slower than a critical frequency) emerges in the energy spectrum, thus, pointing to a better state for slow rotation. We construct mean-field ground states of 0-, 1-, and 2-vortex states as a function of rotation rate and determine the critical frequencies for transitions between these states, as well as the critical frequency for appearance of a metastable state with an off-center vortex and its image vortex in the evanescent tail of the cloud. Read More

We study the QCD phase structure in the three-flavor Nambu-Jona-Lasinio model, incorporating the interplay between the chiral and diquark condensates induced by the axial anomaly. We demonstrate that for an appropriate range of parameters of the model, the interplay leads to the low temperature critical point in the phase structure predicted by a previous Ginzburg-Landau analysis. We also show that a Bose-Einstein condensate (BEC) of diquark molecules emerges in the intermediate density region, and as a result, a BEC-BCS crossover is realized with increasing quark chemical potential. Read More

We present the first astrophysical measurement of the pressure of cold matter above nuclear saturation density, based on recently determined masses and radii of three neutron stars. The pressure at higher densities are below the predictions of equations of state that account only for nucleonic degrees of freedom, and thus present a challenge to the microscopic theory of neutron star matter. Read More

**Category:**

To clarify the relation of energy shifts to scattering phase shifts in one-body and many-body problems, we examine their relation in a number of different situations. We derive, for a particle in a container of arbitrary shape with a short-range scattering center, a general result for the energy eigenvalues in terms of the s-wave scattering phase shift and the eigenstates in the absence of the scatterer. We show that, while the energy shifts for a spherical container are proportional to the phase shift over large ranges, those for a cubic container have a more complicated behavior. Read More

We relate short-range correlations in ultracold atomic Fermi gases to the entropy of the system over the entire temperature, $T$, vs. coupling strength, $-1/k_Fa$, plane. In the low temperature limit the entropy is dominated by phonon excitations and the correlations increase as $T^4$. Read More

We delineate, as an analog of two-flavor dense quark matter, the phase structure of a many-body mixture of atomic bosons and fermions in two internal states with a tunable boson-fermion attraction. The bosons b correspond to diquarks, and the fermions f to unpaired quarks. For weak b-f attraction, the system is a mixture of a Bose-Einstein condensate and degenerate fermions, while for strong attraction composite b-f fermions N, analogs of the nucleon, are formed, which are superfluid due to the N-N attraction in the spin-singlet channel. Read More

We analyze Niels Bohr's proposed two-slit interference experiment with highly charged particles that argues that the consistency of elementary quantum mechanics requires that the electromagnetic field must be quantized. In the experiment a particle's path through the slits is determined by measuring the Coulomb field that it produces at large distances; under these conditions the interference pattern must be suppressed. The key is that as the particle's trajectory is bent in diffraction by the slits it must radiate and the radiation must carry away phase information. Read More

We describe thermal melting of the two-dimensional vortex lattice in a rotating superfluid by generalizing the Halperin and Nelson theory of dislocation-mediated melting. and derive a melting temperature proportional to the renormalized shear modulus of the vortex lattice. The rigid-body rotation of the superfluid attenuates the effects of lattice compression on the energy of dislocations and hence the melting temperature, while not affecting the shearing. Read More

The QCD axial anomaly, by coupling the chiral condensate and BCS pairing fields of quarks in dense matter, leads to a new critical point in the QCD phase diagram \cite{HTYB,chiral2}, which at sufficiently low temperature should terminate the line of phase transitions between chirally broken hadronic matter and color superconducting quark matter. The critical point indicates that matter at low temperature should cross over smoothly from the hadronic to the quark phase, as suggested earlier on the basis of symmetry. We review here the arguments, based on a general Ginzburg-Landau effective Lagrangian, for the existence of the new critical point, as well as discuss possible connections between the QCD phase structure and the BEC-BCS crossover in ultracold trapped atomic fermion systems at unitarity. Read More

Using arguments based on sum rules, we derive a general result for the average shifts of rf lines in Fermi gases in terms of interatomic interaction strengths and two-particle correlation functions. We show that near an interaction resonance shifts vary inversely with the atomic scattering length, rather than linearly as in dilute gases, thus accounting for the experimental observation that clock shifts remain finite at Feshbach resonances. Read More

Using a general Ginzburg-Landau effective Lagrangian, we study the topological structure and low-lying collective modes of dense QCD having both chiral and diquark condensates, for two and three massless flavors. As we found earlier, the QCD axial anomaly acts as an external field applied to the chiral condensate in a color superconductor and, as a new critical point emerges, leads to a crossover between the broken chiral symmetry and color superconducting phases. At intermediate densities where both chiral and diquark condensates are present, we derive a generalized Gell-Mann- Oakes-Renner relation between the masses of pseudoscalar bosons and the magnitude of the chiral and diquark-condensates. Read More

We derive the Josephson relation in a superfluid between the condensate density, the superfluid mass density, and the infrared structure of the single particle Green's function by means of diagrammatic perturbation theory. The derivation is valid for finite systems and two dimensions. Read More

Recent observations of neutron star masses close to the maximum predicted by nucleonic equations of state begin to challenge our understanding of dense matter in neutron stars, and constrain the possible presence of quark matter in their deep interiors. Read More

We derive a general framework, in terms of elastic theory, for describing the distortion of the vortex lattice in a rotating Bose-Einstein condensate at arbitrary rotation speed and determining the dependence of the distortion on the density inhomogeneity of the system. In the rapidly rotating limit, we derive the energetics in terms of Landau levels, including excitation to higher levels; the distortion depends on the excitation of higher levels as well as on the density gradient. As we show, the dominant effect of higher Landau levels in a distorted lattice in equilibrium is simply to renormalize the frequency entering the lowest Landau level condensate wave function -- from the transverse trap frequency, $\omega$, to the rotational frequency, $\Omega$, of the system. Read More

We propose a Bragg spectroscopy experiment to measure the onset of superfluid pairing in ultracold trapped Fermi gases. In particular, we study two component Fermi gases in the weak coupling BCS and BEC limits as well as in the strong coupling unitarity limit. The low temperature Bragg spectrum exhibits a gap directly related to the pair-breaking energy. Read More

We calculate the structure of individual vortices in rotating Bose-Einstein condensates in a transverse harmonic trap. Making a Wigner-Seitz approximation for the unit cell of the vortex lattice, we derive the Gross-Pitaevskii equation for the condensate wave function in each cell of the lattice, including effects of varying coarse grained density. We calculate the Abrikosov parameter, the fractional core area, and the energy of individual cells. Read More

**Affiliations:**

^{1}Cornell,

^{2}OSU,

^{3}Tokyo Institute of Technology,

^{4}UIUC

We present the theory of bosonic systems with multiple condensates, unifying disparate models which are found in the literature, and discuss how degeneracies, interactions, and symmetries conspire to give rise to this unusual behavior. We show that as degeneracies multiply, so do the types of fragmentation, eventually leading to strongly correlated states with no trace of condensation. Read More

We study the interplay between chiral and diquark condensates within the framework of the Ginzburg-Landau free energy, and classify possible phase structures of two and three-flavor massless QCD. The QCD axial anomaly acts as an external field applied to the chiral condensate in a color superconductor and leads to a crossover between the broken chiral symmetry and the color superconducting phase, and, in particular, to a new critical point in the QCD phase diagram. Read More

We present a unified overview, from the mean-field to the unitarity regime, of the stability of a trapped Fermi gas with short range attractive interactions. Unlike in a system of bosons, a Fermi gas is always stable in these regimes, no matter how large the particle number. However, when the interparticle spacing becomes comparable to the range of the interatomic interactions, instability is not precluded. Read More

The spin response functions measured in multi-component fermion gases by means of rf transitions between hyperfine states are strongly constrained by the symmetry of the interatomic interactions. Such constraints are reflected in the spin f-sum rule that the response functions must obey. In particular, only if the effective interactions are not fully invariant in SU(2) spin space, are the response functions sensitive to mean field and pairing effects. Read More

We derive, from the Gross-Pitaevskii equation, an exact expression for the velocity of any vortex in a Bose-Einstein condensate, in equilibrium or not, in terms of the condensate wave function at the center of the vortex. In general, the vortex velocity is a sum of the local superfluid velocity, plus a correction related to the density gradient near the vortex. A consequence is that in rapidly rotating harmonically trapped Bose-Einstein condensates, unlike in the usual situation in slowly rotating condensates and in hydrodynamics, vortices do not move with the local fluid velocity. Read More