arXiv subjects
Publications and source records attributed to Hai-cang Ren.
Type-I color superconductors display a first-order phase transition due to thermal gauge-field fluctuations. We numerically evaluated the critical temperature of the first-order phase transition and the corresponding discontinuity of the diquark condensate at the critical point.
We study the gauge field fluctuations in dense quark matter and determine the temperature of the induced first-order phase transition to the color-superconducting phase in weak coupling. We find that the local approximation of the coupling between the gauge potential and the order parameter, employed in the Ginzburg-Landau theory, has to be modified by restoring the full momentum dependence of the polarization function of gluons in the superconducting phase.
In order to discern aggregation in solutions, we present a quantum mechanical analog of the photon statistics from fluorescent molecules diffusing through a focused beam. A generating functional is developed to fully describe the experimental physical system as well as the statistics. Histograms of the measured time delay between photon counts are fit by an analytical solution describing the static as well as diffusing regimes. To determine empirical fitting parameters, fluorescence correlation spectroscopy is used in parallel to the photon counting. For expedient analysis, we find that the distribution's deviation from a single Poisson shows a difference between two single fluor moments or a double fluor aggregate of the same total intensities. Initial studies were performed on fixed-state aggregates limited to dimerization. However preliminary results on reactive species suggest that the method can be used to characterize any aggregating system.
At sufficiently high baryon density, a quark matter is expected to become a color superconductor because of the pairing forces mediated by gluons. The theoretical aspect of this novel phase of the strong interaction is reviewed with the emphasis on the perturbation theory of QCD at high chemical potential and low temperature. The derivation of the scaling formula of the superconducting transition temperature at weak coupling is explained in detail. The Ginzburg-Landau theory of the color superconductivity is also discussed.
In a braneworld context, the radion is a massless mode coupling to the trace of the matter stress tensor. Since the radion also governs the separation between branes, it is expected to decouple from the physical spectrum in single brane scenarios, such as the one-brane Randall-Sundrum model. However, contrary to expectations, we demonstrate that the Karch-Randall radion always remains as a physical excitation, even in the single brane case. Here, the radion measures the distance not between branes, but rather between the brane and the anti-de Sitter boundary on the other side of the bulk.
We give a proof of a local relation between the inverse Faddeev-Popov operator and the non-Abelian Coulomb interaction between color charges.
The Weyl-gauge ($A_0^a=0)$ QCD Hamiltonian is unitarily transformed to a representation in which it is expressed entirely in terms of gauge-invariant quark and gluon fields. In a subspace of gauge-invariant states we have constructed that implement the non-Abelian Gauss's law, this unitarily transformed Weyl-gauge Hamiltonian can be further transformed and, under appropriate circumstances, can be identified with the QCD Hamiltonian in the Coulomb gauge. We demonstrate an isomorphism that materially facilitates the application of this Hamiltonian to a variety of physical processes, including the evaluation of $S$-matrix elements. This isomorphism relates the gauge-invariant representation of the Hamiltonian and the required set of gauge-invariant states to a Hamiltonian of the same functional form but dependent on ordinary unconstrained Weyl-gauge fields operating within a space of ``standard'' perturbative states. The fact that the gauge-invariant chromoelectric field is not hermitian has important implications for the functional form of the Hamiltonian finally obtained. When this nonhermiticity is taken into account, the ``extra'' vertices in Christ and Lee's Coulomb-gauge Hamiltonian are natural outgrowths of the formalism. When this nonhermiticity is neglected, the Hamiltonian used in the earlier work of Gribov and others results.
The color superconductivity of a dense quark matter is reviewed with emphasis on the long range nature of the pairing force and the multiplicity of the order parameter. The former gives rise to a non BCS behavior of the superconducting energy scale and the latter modifies the critical value of the Ginzburg-Landau parameter that separates the superconductivity of type I and that of type II.
In terms of the s-wave phase shift of the two-body scattering at thermal wavelength, a systematic perturbative expansion of the virial coefficients is developed for a two-dimensional dilute system of bosons in its gaseous phase at low temperature. The thermodynamic functions are calculated to the second order of the expansion parameter. The observability of the universal low energy limit of the two-dimensional phase shift with a quasi-two dimensional atomic gas in an anisotropic trap is discussed.
We apply the Ginzburg-Landau theory to the colour superconducting phase of a lump of dense quark matter. We calculate the surface energy of a domain wall separating the normal phase from the super phase with the bulk equilibrium maintained by a critical external magnetic field. Because of the symmetry of the problem, we are able to simplify the Ginzburg-Landau equations and express them in terms of two components of the di-quark condensate and one component of the gauge potential. The equations also contain two dimensionless parameters: the Ginzburg-Landau parameter $κ$ and $ρ$. The main result of this paper is a set of inequalities obeyed by the critical value of the Ginzburg-Landau parameter--the value of $κ$ for which the surface energy changes sign--and its derivative with respect to $ρ$. In addition we prove a number of inequalities of the functional dependence of the surface energy on the parameters of the problem and obtain a numerical solution of the Ginzburg-Landau equations. Finally a criterion for the types of colour superconductivity (type I or type II) is established in the weak coupling approximation.
We present a linearized gravity investigation of the bent braneworld, where an AdS_4 brane is embedded in AdS_5. While we focus on static spherically symmetric mass distributions on the brane, much of the analysis continues to hold for more general configurations. In addition to the identification of the massive Karch-Randall graviton and a tower of Kaluza-Klein gravitons, we find a radion mode that couples to the trace of the energy-momentum tensor on the brane. The Karch-Randall radion arises as a property of the embedding of the brane in the bulk space, even in the context of a single brane model.
In crystalline color superconductivity, quark pairs form at non-zero total momentum. This crystalline order potentially enlarges the domain of color superconductivity in cold dense quark matter. We present a perturbative calculation of the parameters governing the crystalline phase and show that this is indeed the case. Nevertheless, the enhancement is modest, and to lowest order is independent of the strength of the color interaction.
We solve the Einstein equations in the Dvali-Gabadadze-Porrati model with a static, spherically symmetric matter distribution on the physical brane and obtain an exact expression for the gravitational field outside the source to the first order in the gravitational coupling. Although when confined on the physical brane this expression reproduces the correct 4D Newtonian potential for distances r_s << r << λ, where λ is a characteristic length scale of the model, it does not coincide with the standard linearized form of the 4D Schwarzschild metric. The solution reproduces the 5D Schwarzschild metric in the linearized approximation for r >> λ.
We derive the Ginzburg-Landau free energy functional of color superconductivity in terms of the thermal diagrams of QCD in its perturbative region. The zero mode of the quadratic term coefficient yields the same transition temperature, including the pre-exponential factor, as the one obtained previously from the Fredholm determinant of the two quark scattering amplitude. All coefficients of the free energy can be made identical to those of a BCS model by setting the Fermi velocity of the latter equal to the speed of light. We also calculate the induced symmetric color condensate near $T_c$ and find that it scales as the cubic power of the dominant antisymmetric color component. We show that in the presence of an inhomogeneity and a nonzero gauge potential, while the color-flavor locked condensate dominates in the bulk, the unlocked condensate, the octet, emerges as a result of a simultaneous color-flavor rotation in the core region of a vortex filament or at the junction of super and normal phases.
We solve the Einstein equations in the Randall-Sundrum framework using an isotropic ansatz for the metric and obtain an exact expression to first order in the gravitational coupling. The solution is free from metric singularities away from the source and it satisfies the Israel matching condition on a straight brane. At distances far away from the source and on the physical brane this solution coincides with the 4-D Schwarzschild metric in isotropic coordinates. Furthermore we show that the extension of the standard Schwarzschild horizon in the bulk is tubular for any diagonal form of the metric while there is no restriction for the extension of the Schwarzschild horizon in isotropic coordinates.
We show that, in the absence of matter in the bulk, the Einstein equations and the Gauss-normal form of the metric place stringent restrictions on the form of the event horizon in a brane world. As a consequence, the off-brane extension of the standard 4-D Schwarzschild horizon in the Randall-Sundrum $AdS_5$ spacetime, as it is viewed from the brane can only be of a tubular shape, instead of a pancake shape. When it is viewed from the $AdS_5$ horizon, such a tubular horizon is absent.
We solve the Einstein equations in the Randall-Sundrum framework with a static, spherically symmetric matter distribution on the {\it physical brane} and obtain an approximate expression for the gravitational field outside the source to second order in the gravitational coupling. This expression when confined on the {\it physical brane} coincides with the standard form of the Schwarzschild metric. Therefore, the Randall-Sundrum scenario is consistent with the Mercury precession test of General Relativity.
At sufficiently high baryon densities, the physics of a dense quark-gluon plasma may be investigated through the tools of perturbative QCD. This approach has recently been successfully applied to the study of color superconductivity, where the dominant di-quark pairing interaction arises from one gluon exchange. Screening in the plasma leads to novel behaviour, including a remarkable non-BCS scaling of T_C, the transition temperature to the color superconducting phase. Radiative corrections to one gluon exchange were previously considered and found to affect T_C. In particular, the quark self-energy in a plasma leads to non-Fermi liquid behaviour and suppresses T_C. However, at the same time, the quark-gluon vertex was shown not to modify the result at leading order. This dichotomy between the effects of the radiative corrections at first appears rather surprising, as the BRST identity connects the self-energy to the vertex corrections. Nevertheless, as we demonstrate, there is in fact no contradiction with the BRST identity, at least to leading log order. This clarifies some of the previous statements on the importance of the higher order corrections to the determination of T_C and the zero temperature gap in color superconductivity.