Siu A. Chin

A relativistic many-body theory of high density matter

Abstract A fully relativistic quantum many-body theory is applied to the study of high-density matter. The latter is identified with the zero-temperature ground state of a system of interacting baryons. In accordance with the observed short-range repulsive and long-range attractive character of the nucleon-nucleon force, baryons are described as interacting with each other via a massive scalar and a massive vector meson exchange. In the Hartree approximation, the theory yields the same result as the mean-field theory, but with additional vacuum fluctuation corrections. The resultant equation of state for neutron matter is used to determine properties of neutron stars. The relativistic exchange energy, its corresponding single-particle excitation spectrum, and its effect on the neutron matter equation of state, are calculated. The correlation energy from summing the set of ring diagrams is derived directly from the energy-momentum tensor, with renormalization carried out by adding counterterms to the original Lagrangian and subtracting purely vacuum expectation values. Terms of order g4lng2 are explicitly given. Effects of scalarvector mixing are discussed. Collective modes corresponding to macroscopic density fluctuation are investigated. Two basic modes are found, a plasma-like mode and zero sound, with the latter dominant at high density. The stability and damping of these modes are studied. Last, the effect of vacuum polarization in high-density matter is examined.

Can a neutron star be a giant MIT bag

Abstract We show, on the basis of the M.I.T. bag model of hadrons, that a neutron matter-quark phase transition is energetically favorable at densities around ten to twenty times nuclear matter density. It is unlikely, however, that quark matter can be found within stable neutron stars, or that it may form a third family of dense stellar objects.

Symplectic integrators from composite operator factorizations

Abstract I derive fourth order symplectic integrators by factorizing the exponential of two operators in terms of an additional higher order composite operator with positive coefficients. One algorithm requires only one evaluation of the force and one evaluation of the force and its gradient. When applied to Keplers problem, the energy error function associated with these algorithms are approximately 10 to 80 times smaller than the fourth order Forest-Ruth, Candy-Rozmus integrator.

Landau theory of relativistic Fermi liquids

Abstract A relativistic extension of the Landau Fermi liquid theory, applicable to the study of high density matter, is developed. Consequences of Lorentz invariance in the theory are explored. The formalism is illustrated by a study of relativistic Fermi systems weakly interacting via scalar and vector meson exchange. Second order exchange energies for both massless scalar and massless vector interactions are calculated in terms of Landau parameters on the Fermi surface. Zero sound and “color-plasma oscillations” are studied in quark matter with SU(3) color gluon coupling.

TRANSITION TO HOT QUARK MATTER IN RELATIVISTIC HEAVY-ION COLLISION *

Abstract The nuclear matter-quark matter phase transition density is calculated as a function of temperature. The result suggests a transition to quark matter in heavy-ion collision at laboratory kinetic energies of a few GeV per nucleon. The transition may be inferred by observing a limiting temperature for the hadrons produced by the collision.

Gradient symplectic algorithms for solving the Schrödinger equation with time-dependent potentials

We show that the method of factorizing the evolution operator to fourth order with purely positive coefficients, in conjunction with Suzuki’s method of implementing time-ordering of operators, produces a new class of powerful algorithms for solving the Schrodinger equation with time-dependent potentials. When applied to the Walker–Preston model of a diatomic molecule in a strong laser field, these algorithms can have fourth order error coefficients that are three orders of magnitude smaller than the Forest–Ruth algorithm using the same number of fast Fourier transforms. Compared to the second order split-operator method, some of these algorithms can achieve comparable convergent accuracy at step sizes 50 times as large. Morever, we show that these algorithms belong to a one-parameter family of algorithms, and that the parameter can be further optimized for specific applications.

Effects of geometry and impurities on quantum rings in magnetic fields

We investigate the effects of impurities and changing ring geometry on the energetics of quantum rings under different magnetic field strengths. We show that as the magnetic field and/or the electron number are/is increased, both the quasiperiodic Aharonov-Bohm oscillations and various magnetic phases become insensitive to whether the ring is circular or square in shape. This is in qualitative agreement with experiments. However, we also find that the Aharonov-Bohm oscillation can be greatly phase-shifted by only a few impurities and can be completely obliterated by a high level of impurity density. In the many-electron calculations we use a recently developed fourth-order imaginary time projection algorithm that can exactly compute the density matrix of a free-electron in a uniform magnetic field.

Fourth order gradient symplectic integrator methods for solving the time-dependent Schrödinger equation

We show that the method of splitting the operator ee(T+V) to fourth order with purely positive coefficients produces excellent algorithms for solving the time-dependent Schrodinger equation. These algorithms require knowing the potential and the gradient of the potential. One fourth order algorithm only requires four fast Fourier transformations per iteration. In a one dimensional scattering problem, the fourth order error coefficients of these new algorithms are roughly 500 times smaller than fourth order algorithms with negative coefficient, such as those based on the traditional Forest–Ruth symplectic integrator. These algorithms can produce converged results of conventional second or fourth order algorithms using time steps 5 to 10 times as large. Iterating these positive coefficient algorithms to sixth order also produced better converged algorithms than iterating the Forest–Ruth algorithm to sixth order or using Yoshida’s sixth order algorithm A directly.

Many-body theory of confined quarks and excluded pions: A perturbative study of the chiral bag

Abstract Relativistic many-body theory is developed for quarks confined to and pions excluded from a spherical cavity. Green functions for confined quarks and excluded pions are constructed to study the chiral bag perturbatively. Explicit expressions are obtained for the pion field of a general multiquark state and g A of an arbitrary nucleon configuration. The second-order energy is derived with the consistent inclusion of the self-energy and is evaluated for the case of closed shell quark configurations. The self-energy is shown numerically to be linearly divergent and its associated difficulties are discussed.

Dilepton production from hot quark matter in an ultra-relativistic heavy-ion collision

Abstract The dilepton production mass spectrum from the decay of hot quark matter in an ultra-relativistic heavy-ion collision is calculated. Relativistic hydrodynamic equations are solved to obtain the space-time evolution of the quark matter fireball. Distinct enhancements of the dilepton mass spectrum below 600 MeV are predicted for a deconfinement transition temperature T c ⪅200MeV.