Smoothed Particle Hydrodynamics for Relativistic Heavy Ion Collisions

The method of smoothed particle hydrodynamics (SPH) is developped appropriately for the study of relativistic heavy ion collision processes. In order to describe the flow of a high energy but low baryon number density fluid, the entropy is taken as the SPH base. We formulate the method in terms of the variational principle. Several examples show that the method is very promising for the study of hadronic flow in RHIC physics.Comment: 14 pages, 8figure

Molecular formations in ultracold mixtures of interacting and noninteracting atomic gases

Atom-molecule equilibrium for molecular formation processes is discussed for boson-fermion, fermion-fermion, and boson-boson mixtures of ultracold atomic gases in the framework of quasichemical equilibrium theory. After presentation of the general formulation, zero-temperature phase diagrams of the atom-molecule equilibrium states are calculated analytically; molecular, mixed, and dissociated phases are shown to appear for the change of the binding energy of the molecules. The temperature dependences of the atom or molecule densities are calculated numerically, and finite-temperature phase structures are obtained of the atom-molecule equilibrium in the mixtures. The transition temperatures of the atom or molecule Bose-Einstein condensations are also evaluated from these results. Quantum-statistical deviations of the law of mass action in atom-molecule equilibrium, which should be satisfied in mixtures of classical Maxwell-Boltzmann gases, are calculated, and the difference in the different types of quantum-statistical effects is clarified. Mean-field calculations with interparticle interactions (atom-atom, atom-molecule, and molecule-molecule) are formulated, where interaction effects are found to give the linear density-dependent term in the effective molecular binding energies. This method is applied to calculations of zero-temperature phase diagrams, where new phases with coexisting local-equilibrium states are shown to appear in the case of strongly repulsive interactions.Comment: 35 pages, 14 figure

Condensation of Ideal Bose Gas Confined in a Box Within a Canonical Ensemble

We set up recursion relations for the partition function and the ground-state occupancy for a fixed number of non-interacting bosons confined in a square box potential and determine the temperature dependence of the specific heat and the particle number in the ground state. A proper semiclassical treatment is set up which yields the correct small-T-behavior in contrast to an earlier theory in Feynman's textbook on Statistical Mechanics, in which the special role of the ground state was ignored. The results are compared with an exact quantum mechanical treatment. Furthermore, we derive the finite-size effect of the system.Comment: 18 pages, 8 figure

Differential flow in heavy-ion collisions at balance energies

A strong differential transverse collective flow is predicted for the first time to occur in heavy-ion collisions at balance energies. We also give a novel explanation for the disappearance of the total transverse collective flow at the balance energies. It is further shown that the differential flow especially at high transverse momenta is a useful microscope capable of resolving the balance energy's dual sensitivity to both the nuclear equation of state and in-medium nucleon-nucleon cross sections in the reaction dynamics.Comment: Phys. Rev. Lett. (1999) in pres

Critical Enhancement of the In-medium Nucleon-Nucleon Cross Section at low Temperatures

The in-medium nucleon-nucleon cross section is calculated starting from the thermodynamic T-matrix at finite temperatures. The corresponding Bethe-Salpeter-equation is solved using a separable representation of the Paris nucleon-nucleon-potential. The energy-dependent in-medium N-N cross section at a given density shows a strong temperature dependence. Especially at low temperatures and low total momenta, the in-medium cross section is strongly modified by in-medium effects. In particular, with decreasing temperature an enhancement near the Fermi energy is observed. This enhancement can be discussed as a precursor of the superfluid phase transition in nuclear matter.Comment: 10 pages with 4 figures (available on request from the authors), MPG-VT-UR 34/94 accepted for publication in Phys. Rev.

Bose-Fermi variational theory of the BEC-Tonks crossover

A number-conserving hybrid Bose-Fermi variational theory is developed and applied to investigation of the BEC-Tonks gas crossover in toroidal and long cylindrical traps of high aspect ratio, where strong many-body correlations and condensate depletion occur.Comment: 4 pages RevTeX including 2 figures, uses epsfig. Submitted to Phys. Rev. Let

Dielectronic Recombination of Ground-State and Metastable Li+ Ions

Dielectronic recombination has been investigated for Delta-n = 1 resonances of ground-state Li+(1s^2) and for Delta-n = 0 resonances of metastable Li+(1s2s ^3S). The ground-state spectrum shows three prominent transitions between 53 and 64 eV, while the metastable spectrum exhibits many transitions with energies < 3.2 eV. Reasonably good agreement of R-matrix, LS coupling calculations with the measured recombination rate coefficient is obtained. The time dependence of the recombination rate yields a radiative lifetime of 52.2 +- 5.0 s for the 2 ^3S level of Li+.Comment: Submitted to Phys. Rev. A; REVTeX, 4 pages, 3 figure

Remarks on Shannon's Statistical Inference and the Second Law in Quantum Statistical Mechanics

We comment on a formulation of quantum statistical mechanics, which incorporates the statistical inference of Shannon. Our basic idea is to distinguish the dynamical entropy of von Neumann, $H = -k Tr \hat{\rho}\ln\hat{\rho}$, in terms of the density matrix $\hat{\rho}(t)$, and the statistical amount of uncertainty of Shannon, $S= -k \sum_{n}p_{n}\ln p_{n}$, with $p_{n}=$ in the representation where the total energy and particle numbers are diagonal. These quantities satisfy the inequality $S\geq H$. We propose to interprete Shannon's statistical inference as specifying the {\em initial conditions} of the system in terms of $p_{n}$. A definition of macroscopic observables which are characterized by intrinsic time scales is given, and a quantum mechanical condition on the system, which ensures equilibrium, is discussed on the basis of time averaging. An interesting analogy of the change of entroy with the running coupling in renormalization group is noted. A salient feature of our approach is that the distinction between statistical aspects and dynamical aspects of quantum statistical mechanics is very transparent.Comment: 16 pages. Minor refinement in the statements in the previous version. This version has been published in Journal of Phys. Soc. Jpn. 71 (2002) 6

On Virtual Displacement and Virtual Work in Lagrangian Dynamics

The confusion and ambiguity encountered by students, in understanding virtual displacement and virtual work, is discussed in this article. A definition of virtual displacement is presented that allows one to express them explicitly for holonomic (velocity independent), non-holonomic (velocity dependent), scleronomous (time independent) and rheonomous (time dependent) constraints. It is observed that for holonomic, scleronomous constraints, the virtual displacements are the displacements allowed by the constraints. However, this is not so for a general class of constraints. For simple physical systems, it is shown that, the work done by the constraint forces on virtual displacements is zero. This motivates Lagrange's extension of d'Alembert's principle to system of particles in constrained motion. However a similar zero work principle does not hold for the allowed displacements. It is also demonstrated that d'Alembert's principle of zero virtual work is necessary for the solvability of a constrained mechanical problem. We identify this special class of constraints, physically realized and solvable, as {\it the ideal constraints}. The concept of virtual displacement and the principle of zero virtual work by constraint forces are central to both Lagrange's method of undetermined multipliers, and Lagrange's equations in generalized coordinates.Comment: 12 pages, 10 figures. This article is based on an earlier article physics/0410123. It includes new figures, equations and logical conten