Relativistic heavy-ion collisions: An approach based on non-equilibrium thermodynamics

A new theory of particle production in high energy collisions is proposed which is based on non-equilibrium thermodynamics. The non-equilibrium model is a major extension of the equilibrium thermodynamic model of relativistic heavy-ion collisions developed earlier. While the equilibrium thermodynamic theory is appropriate for the formation of light nuclei and for pions, the non-equilibrium theory applies to the creation of particles heavier than the pion, which include such particles as the strange mesons, strange baryons and the anti-nucleons. Using an approach based on the degree of the reaction of kinetic theory, the time evolution of the composition of hadronic systems in incomplete equilibrium is investigated. Densities of produced particles are related to space-time quantities and to the production cross sections of the underlying dynamic processes. An application of the non-equilibrium approach to the production of strange matter is given. The importance of secondary processes, following pion production, in the formation of strange matter is shown. In fact, the secondary production process for kaons is as important as the direct production process arising from initial nucleon-nucleon (NN) collision of a first collision picture. Thus, kaons can be produced in a late stage of the collision of two nuclei and they do not necessarily reflect the early stages of the collision as first thought. Using the experimental number of kaons, the time of reaction is also estimated. No evidence for a long-lived state of the nuclear system is found. Expressions for particle production ratios are developed. The results of an equilibrium theory and a non-equilibrium theory are found to be similar for such ratios. The chemical equilibrium constant is shown to be present in the non-equilibrium theory; the Boltzmann factor in the production threshold energy appears in the equilibrium theory. The K^?/K⁺ ratio is estimated. Surprisingly, reasonable agreement with experiment is found in the K^?/K⁺ ratio using the equilibrium theory, even though the production processes for K⁺'s and K^?'s treated individually, are not ones for which the equilibrium theory applies. It is shown that a fundamental difference between the equilibrium and non-equilibrium theory is lost when particle ratios for non-equilibrium particles are taken. Expressions for the production of complex composite structures made of strange particles are developed. The non-equilibrium model with some modifications may be useful for high energy NN and pion-nucleon collisions.     

Quantum Transport of Particles and Entropy

A unified view on macroscopic thermodynamics and quantum transport is presented. Thermodynamic processes with an exchange of energy between two systems necessarily involve the flow of other balancable quantities. These flows are first analyzed using a simple drift-diffusion model, which includes the thermoelectric effects, and connects the various transport coefficients to certain thermodynamic susceptibilities and a diffusion coefficient. In the second part of the paper, the connection between macroscopic thermodynamics and quantum statistics is discussed. It is proposed to employ not particles, but elementary Fermi- or Bose-systems as the elementary building blocks of ideal quantum gases. In this way, the transport not only of particles but also of entropy can be derived in a concise way, and is illustrated both for ballistic quantum wires, and for diffusive conductors. In particular, the quantum interference of entropy flow is in close correspondence to that of electric current.     

Evolution equations and sl(2, R)-valued Bäcklund forms

Evolution equations, in one variable, which are determined by a Bäcklund equation, on sl(2, R), are classified. A geometrical setting is given for the Gardner construction of conserved quantities. A relation between different constructions of conserved quantities for the KdV equation is found. It is shown that for all evolution equations obtained in this classification, these constructions reduce essentially to the KdV case. The second Poisson structure is derived and a Kac-Moody formulation is given, which allows one to deal with all higher order KdV-flows.     

The electromagnetic two-body problem in special relativity

A system of two point charged particles is considered. Each particle moves in the electromagnetic field created by the other particle according to Maxwell's equations. A scheme of successive approximations is developed to study the field and the motion of the charges. The field (potentials and intensities) are exapanded in powers of c^?1 using a retarded time coordinate. The variables of the motion (position vectors, velocities, etc) are expanded in powers of c^?1 with coefficients depending on t only. The field is evaluated in the first three approximations. The equations of motion are derived in the same approximations and the corresponding conserved quantities are explicitly given. Thus, the usual assumption of an action-at-a-distance principle is avoided and the original nonlinear integrodifferential equations are reduced to a sequence of linear equations.     

Multiparameter deformed and non-standard Y(glM) Yangian symmetry in a novel class of spin Calogero-Sutherland models

It is well known through a recent work of Bernard, Gaudin, Haldane and Pasquier (BGHP) that the usual spin Calogero-Sutherland (CS) model, containing particles with M internal degrees of freedom, respects the Y(gl_M) Yangian symmetry. By following and suitably modifying the approach of BGHP, in this article we construct a novel class of spin CS models which exhibit multiparameter deformed or ‘non-standard’ variants of Y(gl_M) Yangian symmetry. An interesting feature of such CS Hamiltonians is that they contain many-body spin-dependent interactions, which can be calculated directly from the associated rational solutions of the Yang-Baxter equation. Moreover, these spin-dependent interactions often lead to ‘anyon-like’ representations of the permutation algebra on the combined internal space of all particles. We also find the general forms of conserved quantities as well as Lax pairs for the above-mentioned class of spin CS models, and describe the method of constructing their exact wave functions.     

Activated Random Walkers: Facts, Conjectures and Challenges

We study a particle system with hopping (random walk) dynamics on the integer lattice ? ^d . The particles can exist in two states, active or inactive (sleeping); only the former can hop. The dynamics conserves the number of particles; there is no limit on the number of particles at a given site. Isolated active particles fall asleep at rate λ>0, and then remain asleep until joined by another particle at the same site. The state in which all particles are inactive is absorbing. Whether activity continues at long times depends on the relation between the particle density ζ and the sleeping rate λ. We discuss the general case, and then, for the one-dimensional totally asymmetric case, study the phase transition between an active phase (for sufficiently large particle densities and/or small λ) and an absorbing one. We also present arguments regarding the asymptotic mean hopping velocity in the active phase, the rate of fixation in the absorbing phase, and survival of the infinite system at criticality. Using mean-field theory and Monte Carlo simulation, we locate the phase boundary. The phase transition appears to be continuous in both the symmetric and asymmetric versions of the process, but the critical behavior is very different. The former case is characterized by simple integer or rational values for critical exponents (β=1, for example), and the phase diagram is in accord with the prediction of mean-field theory. We present evidence that the symmetric version belongs to the universality class of conserved stochastic sandpiles, also known as conserved directed percolation. Simulations also reveal an interesting transient phenomenon of damped oscillations in the activity density.     

The Camassa Holm equation: conserved quantities and the initial value problem

Using a Miura–Gardner–Kruskal type construction, we show that the Camassa–Holm equation has an infinite number of local conserved quantities. We explore the implications of these conserved quantities for global well-posedness.     

由宇宙线(1011—1014电子伏)引起的高能核作用

这篇总结性文章叙论了由能量高到10¹¹—10¹⁴电子伏的粒子在乳胶和云室中所引起的高能核作用。文中首先提出和讨论了在测量上较困难的一些问题,例如,初能量的测量,次粒子的辨认和靶质量的估计。一些可能揭示碰撞机构从而显示核子内部结构的物理量的物理意义,也适当地加以讨论和阐明。除了不同次粒子的多重性外,主要的物理量是:次粒子的角分布、它们的横动量和非弹性系数。关于这些量的测量原理,实验准确度和实验结果的物理意义,特别是后面一点,都有了较充分的检查和讨论。末了,“一个发射中心”和两个发射中心”的各种模型也从物理观点作了较定性的描述和讨论,并和实验结果作了比较。希望通过这篇文章对高能核作用目前发展的概况、尚存在的问题及今后工作的方向能有一定的了解。     

Canonical structure of soliton equations. I

The canonical structure of the nonlinear evolution equations in 1 + 1 dimensions solvable in terms of an N × N inverse scattering problem is discussed. The simplest form of the scattering problems, that is those containing the spectral parameter linearly, is considered. It applies to most of the known soliton equations, like the Korteweg-de Vries eq., the sine-Gordon eq. and the Boussinesq eq. Discussion of various possible reductions of the number of dependent variables by imposing constraints consistent with the Hamiltonian flows is given together with the canonical structure of the reduced systems. A direct proof of the involutive character of the infinite number of conserved quantities is given for the general case as well as the reduced case. The relation between the conserved quantities and symmetry transformations (Lie-Bäcklund transformations) becomes very simple in this framework.     

Exact solutions and conserved quantities in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) Gravity

This paper explores Noether and Noether gauge symmetries of anisotropic universe model in f(R, T) gravity. We consider two particular models of this gravity and evaluate their symmetry generators as well as associated conserved quantities. We also find exact solution by using cyclic variable and investigate its behavior via cosmological parameters. The behavior of cosmological parameters turns out to be consistent with recent observations which indicates accelerated expansion of the universe. Next we study Noether gauge symmetry and corresponding conserved quantities for both isotropic and anisotropic universe models. We conclude that symmetry generators and the associated conserved quantities appear in all cases.     

Light-particle emission in the reaction 32S + 27A1 AT 135 and 190 MeV

The properties oflight particles emitted by the ³²S + ²⁷Al reaction at 135and 190 MeV bombarding energies were studied by means of a coincidence spectrometer. The spectrometer consisted of two large-area ionization chambers which measured the energy, momentum, mass and nuclear charge of the heavy reaction products. By requiring the conservation of those quantities the energy, momentum, mass and charge deficits were determined which are representative of the unobserved light particles. The analysis of the momentum deficit in the event plane did not yield an indication for a fast, direct process of light-particle emission. The alternative analysis in the fragments rest system confirmed the statistical nature of the emission process. The out-of-plane angular correlations were used to determine the spins of the particle-emitting fragments.     

32S-induced reactions at 10 MeV/u bombarding energy

The deep-inelastic processes of the reactions ³²S + ²⁸Si, ^natS, ⁴⁰Ca, ⁵⁸Ni, ⁷⁴Ge are studied at 10 MeV/u bombarding energy employing a kinematical coincidence spectrometer. From the measured energies, momenta, masses and atomic numbers of two heavy fragments the corresponding parameters for the unobserved reaction products and the reaction Q-values are deduced. It is found that the reactions generally show the pattern of a normal deep-inelastic process which is followed by the evaporation of several light particles. But with much less intensities other processes also seem to occur: three-fragment exit channels and incomplete energy damping which is correlated with the emission of a few light particles of high momenta.     

Kinematic waves in a liquefied paste

Paste means a dense mass of small unconsolidated (i.e., not joined together) solid particles with the pore-spaces completely filled with either gas or liquid. Liquefaction, here, means the conversion of its nature from that of a solid to that of a fluid by the application of mechanical motion; it can have, individually, either industrial applications or catastrophic consequences. The range of volume concentrations of the solid is very narrow in the liquefied state, and the liquefaction process requires that the mechanical motions be of relatively large amplitude and low frequency. The actual mechanism of the process is obscure; one is postulated here. It involves kinematic travelling waves, one in each phase, that do not utilize elastic processes, the energy and pressure amplitudes being much less than elastic dilatational waves would entail. Coupling between the waves is by conservative (inertial) forces and the dilatational phenomenon in each arises from the longitudinal spacing of the particles. The mass of each particle is its virtual mass. A plane sinusoidal wave is considered and expressions for wave velocity, phase constant, stress and concentration (as well as quantities analogous to “elasticity” and “elastic condensation”) are deduced. Some measured values of wave velocity and pressure amplitudes are reported and discussed in the light of the hypothesis.     

Pair creation by a photon in an electric field

The process of pair creation by a photon in a constant and homogeneous electric field is investigated basing on the polarization operator in the field. The total probability of the process is found in a relatively simple form. At high energy the quasiclassical approximation is valid. The corrections to the standard quasiclassical approximation (SQA) are calculated. In the region of relatively low photon energies, where SQA is unapplicable, the new approximation is used. It is shown that in this energy interval the probability of pair creation by a photon in electric field exceeds essentially the corresponding probability in a magnetic field. This approach is valid at the photon energy much larger than the “vacuum” energy in electric field: ω?eE/m. For smaller photon energies the low energy approximation is developed. At ω?eE/m the found probability describes the absorption of soft photon by the particles created by an electric field.     

Structure and melting of dipole clusters

Two-dimensional clusters of particles, repelling due to dipole-dipole interactions and confined by an external parabolic potential, are considered. The model describes different physical systems, particularly electrons in semiconductor structures, or electrons above a drop of He near a metal electrode, a drop of colloid liquid etc. Two kinds of ordering are in competition in the clusters: a triangular lattice and a shell structure. The ground-state configurations corresponding to the local and global minima of the potential energy for clusters with N = 1 – 40 “particles” are calculated. The structure, the potential energy and the radial and angular r.m.s. displacements as functions of temperature are also calculated. Analysing these quantities the melting of clusters is studied. One- or two-stage melting occurs depending on the number of particles in the cluster. In the case of clusters consisting of two shells melting has two stages: at lower temperature reorientation of neighbouring shells (“orientational melting”) arises; at much higher temperatures the radial shell order disappears. In clusters consisting of more than two shells total melting occurs as a first-order one-stage transition (analogously to a dipole crystal). This is connected with the barrier of rotation being less than the barrier of interchange of particles between shells for small microclusters while the barriers are of equal order for clusters with a greater number of particles.     

The structural instabilities in ferronematic based on liquid crystal with negative diamagnetic susceptibility anisotropy

The studied ferronematic is a nematic liquid crystal (ZLI1695) of low negative anisotropy of the diamagnetic susceptibility (χ_a<0) doped with the magnetic particles Fe₃O₄. Structural instabilities are interpreted within Burylov and Raikher's theory. The high magnetic fields were oriented perpendicular (Freedericksz transition) or parallel to the initial director. Using capacitance measurements the Freedericksz threshold magnetic field of the ferronematic B_FN, and the critical magnetic field B_max, at which the initial parallel orientation between the director and the magnetic moment of magnetic particles breaks down, have been determined. The values of these quantities have been used to estimate the surface density of the anchoring energy W of liquid crystal molecules on the surface of the magnetic particles. The obtained values indicate a soft anchoring of the liquid crystal on the magnetic particles with a preferred parallel orientation of the magnetic moment of magnetic particles and the director.     

Covariantized Nœther identities and conservation laws for perturbations in metric theories of gravity

A construction of conservation laws and conserved quantities for perturbations in arbitrary metric theories of gravity is developed. In an arbitrary field theory, with the use of incorporating an auxiliary metric into the initial Lagrangian covariantized N?ther identities are carried out. Identically conserved currents with corresponding superpotentials are united into a family. Such a generalized formalism of the covariantized identities gives a natural basis for constructing conserved quantities for perturbations. A new family of conserved currents and correspondent superpotentials for perturbations on arbitrary curved backgrounds in metric theories is suggested. The conserved quantities are both of pure canonical N?ther and of Belinfante corrected types. To test the results each of the superpotentials of the family is applied to calculate the mass of the Schwarzschild-anti-de Sitter black hole in the Einstein–Gauss–Bonnet gravity. Using all the superpotentials of the family gives the standard accepted mass.