Simple analytic solution of fireball hydrodynamics

A new family of simple analytic solutions of hydrodynamics is found for slowly expanding, rotationally symmetric fireballs assuming an ideal gas equation of state. The temperature profile is position-independent only in the collisionless gas limit. The Zimányi-Bondorf-Garpman solution and the Buda-Lund parameterization of expanding hydrodynamic particle sources are recovered as special cases. The results are applied to predict new features of proton correlations and spectra for 1.93 AGeV Ni+Ni collisions.     

The equations of Wilson's renormalization group in dimension 4 and analytic renormalization

Wilson's renormalization group equations are introduced and investigated in the framework of perturbation theory with respect to the deviation of the renormalization exponent from its bifurcation value. We consider the case when the dimension is equal to 4. An exact solution of these equations is constructed using analytic renormalization of the projection Hamiltonians.     

Covering group and graph of discretized volumes

We consider a discretized volume V consisting of finite, congruent and attached copies of a tile t. We find a group L _V the orbit of which, when applied to t, is just V. We show the connection between the structural matrixQ in the formal solution of a boundary value problem formulated for volume V and the so called auxiliary matrix of the graph Γ _v associated with V. We show boundary value problems to be isomorphic if the graphs associated with the volumes are isomorphic, or, if the covering groups are Sunada pairs.     

Lectures on the functional renormalization group method

These introductory notes are about functional renormalization group equations and some of their applications. It is emphasised that the applicability of this method extends well beyond critical systems, it actually provides us a general purpose algorithm to solve strongly coupled quantum field theories. The renormalization group equation of F. Wegner and A. Houghton is shown to resum the loop-expansion. Another version, due to J. Polchinski, is obtained by the method of collective coordinates and can be used for the resummation of the perturbation series. The genuinely non-perturbative evolution equation is obtained by a manner reminiscent of the Schwinger-Dyson equations. Two variants of this scheme are presented where the scale which determines the order of the successive elimination of the modes is extracted from external and internal spaces. The renormalization of composite operators is discussed briefly as an alternative way to arrive at the renormalization group equation. The scaling laws and fixed points are considered from local and global points of view. Instability induced renormalization and new scaling laws are shown to occur in the symmetry broken phase of the scaler theory. The flattening of the effective potential of a compact variable is demonstrated in case of the sine-Gordon model. Finally, a manifestly gauge invariant evolution equation is given for QED.     

Superconducting states of the cylinder with a single vortex in magnetic field according to the Ginzburg-Landau theory

Self-consistent solutions of the nonlinear Ginzburg-Landau (GL) equations are investigated numerically for a superconducting (SC) cylinder, placed in an axial magnetic field, with a single vortex on the axis (m=1). Two modes, which show the original state of the cylinder, SC or normal (s ₀ andn ₀), are studied. The field increase (FI) and the field decrease (FD) regimes are studied. The critical fields destroying the SC state withm=1 are found in both regimes. It is shown that in a cylinder of radiusR and GL-parameter ϰ, there exist a number of solutions depending only on the radial co-ordinater corresponding to different states such as M,e, d, p,i, n, ,n ^*, and the state diagram on the plane of the variables (ϰ,R) is described. The critical fields corresponding to intrastate transitions and the onset of hysteresis are obtained. The critical fieldH ₀(R) dividing the paramagnetic and diamagnetic states of the cylinder withm=1 is determined. The limiting fields of supercooling or superheating of the normal state at which the restoration of the SC state occurs are established. It is shown, that (in both casesm=1,0) there exist two critical parameters, and , which divide bulk SC into three groups (with and ), in accordance with the behavior in a magnetic field. The parameters and mark the boundary for the existence of a supercooled normal -state in FD-regime and a superheated SC M-state in FI-regime respectively. It is shown, that the value , which was claimed in a number of papers as related to type-I superconductors, is illusory. We regret to inform that Professor Gely Zharkov passed away on 9th July 2004.     

Photosensitized formation of singlet oxygen by vitamins of the B group

Presented at the XV IUPAC Symposium on Photochemistry, Prague, July 17–22, 1994.     

An introduction to physical theory of molecular evolution

This work is a tutorial in Molecular Evolution from the point of view of Physics. We discuss Eigen's model, a link between evolutionary theory and physics. We will begin by assuming the existence of (marco) molecules or replicators with the template property, that is, the capacity to self-replicate. According to this assumption, information will be randomly generated and destroyed by mutations in the code (i.e., errors in the copying process) and new bits of information will be fixed (made stable) by the existence of an external pressure on the system (i.e., selection), and the ability of the molecules to replicate themselves. Our aim is to build a model in order to describe molecular evolution from as general a standpoint as possible. As we will see, even very simple models from the theoretical point of view will have surprisingly deep consequences.     

Kinematic and electrooptical anharmonicity in the semiempirical intensity theory of IR and raman spectra of polyatomic molecules

Saratov State University, 83 Astrakhanskaya Str., Saratov, 410601, Russia. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 62, No. 6, pp. 49–57, November–December, 1995.     

B and collider physics: Working group report

This report summarises the work done during WHEPP-6 (Institute of Mathematical Sciences, Chennai, India, Jan 3–15, 2000) in Working group on ‘B and collider physics’.     

| m | Partial wave treatment for two-dimensional Coulomb-scattering and Regge pole

The symmetry and |m| partial-wave analysis for two-dimensional (2D) Coulomb-scattering is investigated. As a function of energyE, the |m| partial-wave scattering amplitudef _|m|(θ) is analytically continuated to the, negativeE (complexk) plane, and it is found that the bound state energy eigenvalues (E<0) are just located at the poles off _|m|(θ) on the positive imaginaryk axis as is expected. In addition, as a function of |m|,f _|m|(θ) is analytically continuated to the complex |m| plane, the bound state energy eigenvalues are just located at the poles off _|m|(θ) on the positive real |m| axis.     

Supersymmetric solution of gauge hierarchy problem

Some recent developments with respect to the resolution of the gauge hierarchy problem in grand unified theories by supersymmetry are presented. A general argument is developed to show how global supersymmetry maintains the stability of the different mass-scales under perturbative effects.     

Momentum dependence of pseudogap and superconducting gap in variation theory

To consider the origin of a pseudogap and a superconducting (SC) gap found in the high-T_c cuprates, we evaluated the momentum dependence of the singlet gap corresponding to the pseudogap and the SC gap in the t–J model, using an optimization variational Monte Carlo (VMC) method. In the underdoped regime, the singlet gap is significantly modified from the simple d_x²-y²(d)-wave gap (∝ cos k_x − cos k_y) by the contribution of long-range pairings. Its angular dependence at the quasi Fermi surface is qualitatively consistent with those experimentally observed in both hole and electron-doped cuprates. On the other hand, a SC gap is almost unchanged, preserving the original simple d-wave form. Thus, it seems that the incoherent part of the singlet gap mainly influences the forms of observed gaps.