Showing papers on "Configuration space published in 1971"

Free energy in a Markovian model of a lattice spin system

Abstract: A Markov process which may be thought of as a classical lattice spin system is considered. States of the system are probability measures on the configuration space, and we study the evolution of the free energy of these states with time. It is proved that for all initial states the free energy is nonincreasing and that it strictly decreases from any initial state which is shift invariant but not an equilibrium state. Finally we show that the state of the system converges weakly to the set of Gibbsian Distributions for the given interaction, and that all shift invariant equilibrium states are Gibbsian Distributions.

Calculation of Upper and Lower Bounds to Oscillator Strengths

Abstract: A procedure is described for calculating rigorous upper and lower bounds to dipole oscillator strengths and is illustrated numerically with various simple applications to the hydrogen molecular ion. The procedure appears to give a good account of the actual errors which may arise in the conventional method based on energy minimization of the two states. In addition, specific regions of configuration space which are important for the oscillator strength, but perhaps not for the energy, are singled out and emphasized automatically.

Configuration Space Theory of "Truly Three-Body" Scattering Rates

Abstract: Configuration space theory of nonrelativistic three body scattering covering transition amplitudes of three-three chemical reaction rates

On analytic regularization in quantum field theory

Abstract: The singularities on the complex plane ofλ’s of the distributions [(ξ1 −ξ2)2 −i0+)]λ12· [(ξ1 −ξ3)2 −i0+]λ13· … · [(ξn−1 −ξn)2 −i0+]λn − 1n are investigated in the framework of the method of analytic regularization in configuration space.

Shadow channels in potential theory.

Abstract: The effect of coupling a shadow channel to a real channel is studied in the framework of nonrelativistic potential-scattering theory. For simplicity, $s$-wave scattering with energy-independent $\ensuremath{\delta}$-function potentials is considered. This model has the virtue of being exactly solvable in configuration space. The main features of the solution which are analogous to those expected in a relativistic field theory whose divergences have been removed using Sudarshan's shadow states, are as follows. The coupled problem reduces in the real channel to scattering by an effective energy-dependent pseudopotential. The physical scattering amplitude still satisfies elastic unitarity at all energies, but is piecewise analytic, with a point of nonanalyticity occurring at the threshold for the shadow channel.

Relativistic Trajectories from a Configuration-Space δ-Shell Interaction

Abstract: The Regge spectrum generated by a four-dimensional δ -shell interaction V(r)=λδ(r−a) , where r is the four-dimensional radius, is investigated by means of exact solutions of the Wick-rotated Bethe-Salpeter equation. In this model only the leading trajectory can generate resonances. It is infinitely rising with ImαReα<1 . Odd daughter trajectories either develop negative imaginary parts or do not rise. Even daughter trajectories turn over above the elastic threshold. This spectrum is contrasted with that obtained from a δ -shell interaction in potential theory. The potential-theory model is characterized by an infinite set of parallel, infinitely rising trajectories. The equivalence between the partial-wave Bethe-Salpeter equation and the continuous-dimensional formalism used here is explicitly developed. Suggestions are made for extending the method to Bethe-Salpeter equations involving spin or multichannel effects.

Quasiparticle description for indium

Abstract: Quasiparticle model has been applied for the description of the nuclear properties of the low-lying states of In isotopes. The Hamiltonian is diagonalized in the space obtained by coupling zero-and two-quasineutron configurations with the proton-hole states inN=Z=50 core, using renormalized Tabakin interaction. The inclusion of two-hole one-particle proton configurations, consistent with the experimental findings in48114Cd(3He, d)49115In reaction, in a weak coupling approximation in which the quasineutron excitation modes are first generated independently, and then coupled to the proton hole excitations to obtain the configuration space for the diagonalization work, is also studied quantitatively. The energy spectrum of the115In nucleus is calculated and discussed.