Useful Bases for Problems in Nuclear and Particle Physics

A set of exactly computable orthonormal basis functions that are useful in computations involving constituent quarks is presented. These basis functions are distinguished by the property that they fall off algebraically in momentum space and can be exactly Fourier-Bessel transformed. The configuration space functions are associated Laguerre polynomials multiplied by an exponential weight, and their Fourier-Bessel transforms can be expressed in terms of Jacobi polynomials in $\Lambda^2/(k^2 + \Lambda^2)$. A simple model of a meson containing a confined quark-antiquark pair shows that this basis is much better at describing the high-momentum properties of the wave function than the harmonic-oscillator basis.Comment: 12 pages LaTeX/revtex, plus 2 postscript figure

The two-level atom laser: analytical results and the laser transition

The problem of the two-level atom laser is studied analytically. The steady-state solution is expressed as a continued fraction, and allows for accurate approximation by rational functions. Moreover, we show that the abrupt change observed in the pump dependence of the steady-state population is directly connected with the transition to the lasing regime. The condition for a sharp transition to Poissonian statistics is expressed as a scaling limit of vanishing cavity loss and light-matter coupling, $\kappa \to 0$, $g \to 0$, such that $g^2/\kappa$ stays finite and $g^2/\kappa > 2 \gamma$, where $\gamma$ is the rate of atomic losses. The same scaling procedure is also shown to describe a similar change to Poisson distribution in the Scully-Lamb laser model too, suggesting that the low-$\kappa$, low-$g$ asymptotics is of a more general significance for the laser transition.Comment: 23 pages, 3 figures. Extended discussion of the paper aim (in the Introduction) and of the results (Conclusions and Discussion). Results unchange

Non mean-field behavior of the contact process on scale-free networks

We present an analysis of the classical contact process on scale-free networks. A mean-field study, both for finite and infinite network sizes, yields an absorbing-state phase transition at a finite critical value of the control parameter, characterized by a set of exponents depending on the network structure. Since finite size effects are large and the infinite network limit cannot be reached in practice, a numerical study of the transition requires the application of finite size scaling theory. Contrary to other critical phenomena studied previously, the contact process in scale-free networks exhibits a non-trivial critical behavior that cannot be quantitatively accounted for by mean-field theory.Comment: 5 pages, 4 figures, published versio

Critical behavior of Born Infeld AdS black holes in higher dimensions

Based on a canonical framework, we investigate the critical behavior of Born-Infeld AdS black holes in higher dimensions. As a special case, considering the appropriate limit, we also analyze the critical phenomena for Reissner Nordstrom AdS black holes. The critical points are marked by the divergences in the heat capacity at constant charge. The static critical exponents associated with various thermodynamic entities are computed and shown to satisfy the thermodynamic scaling laws. These scaling laws have also been found to be compatible with the static scaling hypothesis. Furthermore, we show that the values of these exponents are universal and do not depend on the spatial dimensionality of the AdS space. We also provide a suggestive way to calculate the critical exponents associated with the spatial correlation which satisfy the scaling laws of second kind.Comment: LaTex, 22 pages, 12 figures, minor modifications in text, To appear in Phys. Rev.

Anisotropic evolution of 5D Friedmann-Robertson-Walker spacetime

We examine the time evolution of the five-dimensional Einstein field equations subjected to a flat, anisotropic Robertson-Walker metric, where the 3D and higher-dimensional scale factors are allowed to dynamically evolve at different rates. By adopting equations of state relating the 3D and higher-dimensional pressures to the density, we obtain an exact expression relating the higher-dimensional scale factor to a function of the 3D scale factor. This relation allows us to write the Friedmann-Robertson-Walker field equations exclusively in terms of the 3D scale factor, thus yielding a set of 4D effective Friedmann-Robertson-Walker field equations. We examine the effective field equations in the general case and obtain an exact expression relating a function of the 3D scale factor to the time. This expression involves a hypergeometric function and cannot, in general, be inverted to yield an analytical expression for the 3D scale factor as a function of time. When the hypergeometric function is expanded for small and large arguments, we obtain a generalized treatment of the dynamical compactification scenario of Mohammedi [Phys.Rev.D 65, 104018 (2002)] and the 5D vacuum solution of Chodos and Detweiler [Phys.Rev.D 21, 2167 (1980)], respectively. By expanding the hypergeometric function near a branch point, we obtain the perturbative solution for the 3D scale factor in the small time regime. This solution exhibits accelerated expansion, which, remarkably, is independent of the value of the 4D equation of state parameter w. This early-time epoch of accelerated expansion arises naturally out of the anisotropic evolution of 5D spacetime when the pressure in the extra dimension is negative and offers a possible alternative to scalar field inflationary theory.Comment: 20 pages, 4 figures, paper format streamlined with main results emphasized and details pushed to appendixes, current version matches that of published versio

Distribution of Oscillator Strengths for Recombination of Localised Excitons in Two Dimensions

We investigate the distribution of oscillator strengths for the recombination of excitons in a two dimensional sample, trapped in local minima of the confinement potential: the results are derived from a statistical topographic model of the potential. The predicted distribution of oscillator strengths is very different from the Porter-Thomas disribution which usually characterises disordered systems, and is notable for the fact that small oscillator strengths are extremely rare.Comment: Plain TeX, 11 pages, 2 of 3 Postscript figures, to appear in "Chaos, Solitons and Fractals" special issue on Mesoscopic Physics, July 199

Topological phase transition in a RNA model in the de Gennes regime

We study a simplified model of the RNA molecule proposed by G. Vernizzi, H. Orland and A. Zee in the regime of strong concentration of positive ions in solution. The model considers a flexible chain of equal bases that can pairwise interact with any other one along the chain, while preserving the property of saturation of the interactions. In the regime considered, we observe the emergence of a critical temperature T_c separating two phases that can be characterized by the topology of the predominant configurations: in the large temperature regime, the dominant configurations of the molecule have very large genera (of the order of the size of the molecule), corresponding to a complex topology, whereas in the opposite regime of low temperatures, the dominant configurations are simple and have the topology of a sphere. We determine that this topological phase transition is of first order and provide an analytic expression for T_c. The regime studied for this model exhibits analogies with that for the dense polymer systems studied by de GennesComment: 15 pages, 4 figure

A Coupled-Cluster Formulation of Hamiltonian Lattice Field Theory: The Non-Linear Sigma Model

We apply the coupled cluster method (CCM) to the Hamiltonian version of the latticised O(4) non-linear sigma model. The method, which was initially developed for the accurate description of quantum many-body systems, gives rise to two distinct approximation schemes. These approaches are compared with each other as well as with some other Hamiltonian approaches. Our study of both the ground state and collective excitations leads to indications of a possible chiral phase transition as the lattice spacing is varied.Comment: 44 Pages, 14 figures. Uses Latex2e, graphicx, amstex and geometry package

Asymptotic behavior of permutation records

We study the asymptotic behavior of two statistics defined on the symmetric group S_n when n tends to infinity: the number of elements of S_n having k records, and the number of elements of S_n for which the sum of the positions of their records is k. We use a probabilistic argument to show that the scaled asymptotic behavior of these statistics can be described by remarkably simple functions.Comment: 15 pages, 3 figures. v3: final version, to appear in Journal of Combinatorial Theory, Series

Thermodynamics of a finite system of classical particles with short and long range interactions and nuclear fragmentation

We describe a finite inhomogeneous three dimensional system of classical particles which interact through short and (or) long range interactions by means of a simple analytic spin model. The thermodynamic properties of the system are worked out in the framework of the grand canonical ensemble. It is shown that the system experiences a phase transition at fixed average density in the thermodynamic limit. The phase diagram and the caloric curve are constructed and compared with numerical simulations. The implications of our results concerning the caloric curve are discussed in connection with the interpretation of corresponding experimental data.Comment: 11pages, LaTeX, 6 figures. Major change : A new section dealing with numerical simulations in the framework of a cellular model has been adde