Quark-hadron phase transition and strangeness conservation constraints

The implications of the strangeness conservation in a hadronic resonance gas (HRG) on the expected phase transition to the quark gluon plasma (QGP) are investigated. It is assumed that under favourable conditions a first order hadron-quark matter phase transition may occur in the hot hadronic matter such as those produced in the ultra-relativistic heavy-ion collisions at CERN and BNL. It is however shown that the criteria of strict strangeness conservation in the HRG may not permit the occurrence of a strict first order equilibrium quark-hadron phase transition unlike a previous study. This emerges as a consequence of the application of a realistic equation of state (EOS) for the HRG and QGP phases, which account for the finite-size effect arising from the short range hard-core hadronic repulsion in the HRG phase and the perturbative QCD interactions in the QGP phase. For a first order hadron-quark matter phase transition to occur one will therefore require large fluctuations in the critical thermal parameters, which might arise due to superheating, supercooling or other nonequlibrium effects. We also discuss a scenario proposed earlier, leading to a possible strangeness separation process during hadronization. Received: 25 August 1997 / Revised version: 25 March 1998 / Published online: 26 August 1998     

Thermodynamic geometry: Evolution, correlation and phase transition

Under the fluctuation of the electric charge and atomic mass, this paper considers the theory of the thin film depletion layer formation of an ensemble of finitely excited, non-empty d/f-orbital heavy materials, from the thermodynamic geometric perspective. At each state of the local adiabatic evolutions, we examine the nature of the thermodynamic parameters, viz., electric charge and mass, changing at each respective embedding. The definition of the intrinsic Riemannian geometry and differential topology offers the properties of (i) local heat capacities, (ii) global stability criterion and (iv) global correlation length. Under the Gaussian fluctuations, such an intrinsic geometric consideration is anticipated to be useful in the statistical coating of the thin film layer of a desired quality-fine high cost material on a low cost durable coatant. From the perspective of everyday applications, thermodynamic geometry is thus intrinsically self-consistent with the theory of local and global economic optimizations. Following the above procedure, the quality of the thin layer depletion could self-consistently be examined to produce quality products economically.     

Dye laser statistics and the phase transition

By an analytic examination of the photon probability distribution derived by Schaefer and Willis it is shown that, under the conditions for a second order phase transition, the dye laser statistics may be indistinguishable from those of a conventional laser, despite the presence of the triplet states. Under the conditions for a first order phase transition the statistics change, and for some combinations of parameters the change is manifest in the behavior of the normalized second factorial moment of the photon number. Curves are presented that should be directly verifiable by photoelectric counting experiments.     

Torsion and conservation laws

The interaction of spinor and electromagnetic fields with the torsion of space-time is studied within the framework of the Einstein-Cartan theory. The equivalent nonlinear theory in Riemann space is obtained. The conservation laws for the vector and pseudovector currents are investigated in the nonlinear theory.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 50–52, February, 1986.     

Syzygies and conservation laws

We show how the notion of syzygies of a system of partial differential equations allows to derive some conservation laws, for the case of Maxwell and Proca systems. More in general, we apply some classical tools in algebraic analysis to derive properties of the solutions of the previous systems like their integral representations.     

Noether equations and conservation laws

The purpose of the paper is to present a rigorous derivation of the relation between conservation laws and transformations leaving invariant the action integral. The (space-)time development of a physical system is represented by a cross section of a product bundleM. A Lagrange function is defined as a mapping where is the bundle space of the first jet extension ofM. A symmetry transformation is defined as a bundle automorphism ofM, carrying solutions of the Euler-Lagrange equation into solutions of the same equation. An important class of symmetry transformations is that of generalized invariant transformations: they are defined by specifying their action on the Euler-Lagrange equation. The generators of generalized invariant transformations are solutions of a system of linear, homogeneous partial differential equation (Noether equations). The set of all solutions of these equations has a natural structure of Lie algebra. In a simple manner, the Noether equations give rise to differential conservation laws.Supported by Air Force Office of Scientifie Research and Aeronautical Research Laboratories.On leave of absence from the Institute of Theoretical Physics, Warsaw University, Warsaw, Poland.     

Energy conservation laws and antimatter

In field theory, an energy-momentum tensor fails to be conserved if internal symmetries are broken. This revised version was published online in August 2006 with corrections to the Cover Date.     

Nonlocal integral conservation laws and tetradic currents in the Einstein-Cartan theory I. Nonlocal conservation laws

Nonlocal integral conservation laws in the Einstein-Cartan theory for the energy-momentum tensor of general-form sources, in essence being an integral equivalent of convoluted Bianchi identities, are obtained.     

Superradiant laser: First-order phase transition and non-stationary regime

We solve the superradiant laser model in two limiting cases. First the stationary low-pumping regime is considered where a first-order phase transition in the semiclassical solution occurs. This discontinuity is smeared out in the quantum regime. Second, we solve the model in the non-stationary regime where we find a temporally periodic solution. For a certain parameter range well-separated pulses may occur. Received: 19 June 1998 / Accepted: 19 October 1998     

Hyperbolic regularizations of conservation laws

One of the problems of the kinetics of nonequilibrium processes is related to the lack of information concerning most of the nonequilibrium variables, namely, those which have no intuitive physical meaning, i.e., cannot be defined from the experiment. Moreover, the number of nonequilibrium variables is so large that a reasonable amount (from the physical point of view) of boundary conditions is insufficient for posing the mixed problem. What do the initial data for the Cauchy problem and the boundary conditions for the mixed problem mean in this case? In fact, we must assume that the initial-boundary data for most of the nonequilibrium variables (the higher-order momenta) are arbitrary! The British physicists Chapman and Enskog conjectured that, for “physically correct” models of continuum mechanics, the influence of the higher-order momenta is “inessential.” There are some postulates of physical correctness, but we do not dwell on them. For us it is of importance to understand what the fact that the influence of the higher-order momenta is “inessential” means from the mathematical point of view. The paper is devoted to this very topic.     

Singular Lyapunov spectra and conservation laws

We give analytic arguments and numerical evidence to show that the presence of conservation laws can produce a singularity in the spectrum of Lyapunov exponents for extended dynamical systems of low spatial dimensionality. This phenomenon can be used, e.g., for finding hidden conservation laws. (c) 1995 American Institute of Physics.     

Strong correlation to weak correlation phase transition in bilayer quantum Hall systems

At small layer separations, the ground state of a nu = 1 bilayer quantum Hall system exhibits spontaneous interlayer phase coherence. The evolution of this state with increasing layer separation d has been a matter of controversy. We report on small system exact diagonalization calculations which suggest that a single-phase transition, likely of first order, separates incompressible states with strong interlayer correlations from compressible states with weak interlayer correlations. We find a dependence of the phase boundary on d and interlayer tunneling amplitude that is in very good agreement with recent experiments.     

Toda lattice hierarchy and conservation laws

Time evolutions of the Toda lattice hierarchies of Ueno and Takasaki are induced by Hamiltonians which are conservation laws for the original (one and two dimensional) Toda lattice obtained by Olive and Turok. Moreover these Hamiltonians for two dimensional Toda lattice hierarchy are also conserved quantities of the two component KP hierarchy in which that system is embedded. The one dimensional Toda lattice hierarchy is characterized by the bilinear relations, and a new version of the one dimensional Toda lattice hierarchy is constructed. Generalized Toda lattice hierarchies associated to all affine Lie algebras are presented.     

Nonequilibrium phase transition in v-group semimetals,induced by ultrashort laser pulses

Coherent, totally symmetric large-amplitude phonons in bismuth and antimony were investigated by the pump—probe method using femtosecond laser pulses. The obtained results are compared to time-resolved Raman data. It is shown that intense photoexcitation by laser pulses with a duration shorter than the lifetime and reverse phonon frequency in Bi and Sb can lead to a nonequilibrium semimetal—metal phase transition, most likely caused by the instability of the crystal’s electron subsystem.     

Symmetries and conservation laws of the classical Boussinesq equation

A recursion operator for the classical Boussinesq equation is given, which yields infinitely many symmetries and conservation laws. It is also shown that these symmetries define a hierarchy of the classical Boussinesq equation each of which is a hamiltonian system.