Revised Iterative Solution for Groundstate of Schrodinger Equation

A revised iterative method based on Green function defined by quadratures along a single trajectory is proposed to solve the low-lying quantum wave function for Schrodinger equation. Specially a new expression of the perturbed energy is obtained, which is much simpler than the traditional one. The method is applied to solve the unharmonic oscillator potential. The revised iteration procedure gives exactly the same result as those based on the single trajectory quadrature method. A comparison of the revised iteration method to the old one is made using the example of Stark effect. The obtained results are consistent to each other after making power expansion.     

Groundstate properties of the Coqblin-Schrieffer model in a crystalline field: Universality ofj=5/2 in cubic symmetry

The Bethe-ansatz equations for the Coqblin-Schrieffer model are discussed assuming an arbitary splitting of the ionic multiplet, e.g. by magnetic and axial and cubic crystal fields. Explicit expressions for the populations of thef-levels and the static spin susceptibility are obtained for the casej=5/2(Ce³⁺) in a cubic environment. The universality of this solution is discussed.     

The Groundstate of 2-Dimensional Infinite-U Hubbard Model with a Single Hole

The groundstate energies of 1 - and 2-D infinite-U Hubbard models with a single hole are obtained by a simple method. It is found that the groundstates for an arbitrary finite system are multiple degenerate states with S_z = S, S - 1, …, -S (S = (N - 1)/2, N = even is the number of sites). Based on these results, it is shown that the hole and the spin-ffip(s) can not form a bound state, then it provides an alternate proof of Nagaoka's theorem.     

Revised Iterative Solution for Groundstate of Schrodinger Equation

A revised iterative method based on Green function defined by quadratures along a single trajectory is proposed to solve the low-lying quantum wave function for Schro^edinger equation. Specially a new expression of the perturbed energy is obtained, which is much simpler than the traditional one. The method is applied to solve the unharmonic oscillator potential. The revised iteration procedure gives exactly the same result as those based on the single trajectory quadrature method. A comparison of the revised iteration method to the old one is made using the example of Stark effect. The obtained results are consistent to each other after making power expansion.     

New properties of a class of generalized kinetic equations

We give some properties of a new class of hard-sphere kinetic equations of great generality, introduced earlier by Polewczak. The assumptions used to obtain the general class are very weak, and the equations include not only the standard and revised Enskog equations, but also generalizations thereof that can be expected to yield essentially exact transport coefficients. In particular, there is a natural two-particle realization that is obtained from maximizing the information entropy subject to prescribed two-particle and one-particle probability distribution functions;k-particle analogs fork > 2 also naturally follow. We obtain Liapunov functionals for the whole class of equations under consideration and discuss the question of which of these functionals can be expected to play the role ofH-functions. We also obtain several more special results that include new lower bounds on the potential part of theH-function for the revised Enskog equation. The bounds are instrumental in obtaining global existence theorems and also imply that the necessary condition for invertibility of the nonequilibrium extension of local activity as a functional of local density is satisfied.     

Quantization and conformal properties of a generalized Calogero model

We analyze a generalization of the quantum Calogero model with the underlying conformal symmetry, paying special attention to the two-body model deformation. Owing to the underlying SU(1,1) symmetry, we find that the analytic solutions of this model can be described within the scope of the Bargmann representation analysis, and we investigate its dynamical structure by constructing the corresponding Fock space realization. The analysis from the standpoint of supersymmetric quantum mechanics (SUSYQM), when applied to this problem, reveals that the model is also shape invariant. For a certain range of the system parameters, the two-body generalization of the Calogero model is shown to admit a one-parameter family of self-adjoint extensions, leading to inequivalent quantizations of the system. PACS 02.30.Ik; 03.65.Fd; 03.65.-w     

Groundstate proton radioactivity of nuclei in the tin region

Proton radioactivities with decay energies of (0.98±0.08) MeV and (0.83±0.08) MeV were produced by the fusion reactions⁵⁸Ni+⁵⁸Ni→¹¹⁶Ba ? and⁵⁸Ni+⁵⁴Fe→¹¹²Xe ?, and their halflives were measured to be (33±7) μs and (109±17) μs, respectively. The intensities of the lines correspond to production cross sections of about 30 μb and 40 μb. The two activities are assigned to the direct proton decay of¹¹³Cs and¹⁰⁹I. The measured halflives are compared with values calculated ford _5/2 andg _7/2 groundstates of¹⁰⁹I and¹¹³Cs and spectroscopic factors are deduced for the decays. An extensive search for the proton decay of¹⁰⁵Sb, produced in the reaction⁵⁰Cr(⁵⁸Ni,p2 n)¹⁰⁵Sb, had a negative result, excluding decay energies between 0.5 MeV and 1.5 MeV for halflives between 10 ns and 5 s.     

Bethe-Ansatz solution of a model for a mixed valent impurity with two magnetic configurations: Groundstate and thermodynamics

We consider a mixed valence impurity with two magnetic configurations of spinJ ₂ andJ ₁=J ₂±1/2, respectively, coupled bys-wave conduction electrons via a hybridization matrix element. The model contains theU limit of the non-degenerate Anderson model and the Kondo exchange Hamiltonian for arbitrary spin as special cases. The model is solved by Bethe's ansatz and the groundstate and the thermodynamic properties are discussed. The Kondo limit and the highT perturbation expansion are extracted from the thermodynamic Bethe-ansatz equations. The ground state is magnetic if neitherJ ₁ norJ ₂ is a singlet.Heisenberg fellow of the Deutsche Forschungsgemeinschaft     

Majorization properties of generalized thermal distributions

We examine the majorization properties of general thermal-like mixed states depending on a set of parameters. Sufficient conditions which ensure the increase in mixedness, and hence of any associated entropic form, when these parameters are varied, are identified. We then discuss those exhibiting a power law distribution, showing that they can be characterized by two distinct mixing parameters, one associated with temperature and the other with the non-extensivity index q. Illustrative numerical results are also provided.     

Operator properties of generalized coherent state systems

The main properties of standard quantum mechanical coherent states and the two generalizations of Klauder and of Perelomov are reviewed. For a system of generalized coherent states in the latter sense, necessary and sufficient conditions for existence of a diagonal coherent stable representation for all Hilbert-Schmidt operators are obtained. The main ingredients are Clebsch-Gordan theory and induced representation theory.     

Groundstate with Zero Eigenvalue for Generalized Sombrero-Shaped Potential in N-Dimensional Space

Based on an iterative method for solving the groundstate of Schrödinger equation, it is found that a kind of generalized Sombrero-shaped potentials in N-dimensional space has groundstates with zero eigenvalue. The restrictions on the parameters in the potential are discussed.     

Groundstate with Zero Eigenvalue for Generalized Sombrero-Shaped Potential in N-Dimensional Space

Based on an iterative method for solving the groundstate of Schrodinger equation, it is found that a kind of generalized Sombrero-shaped potentials in N-dimensional space has groundstates with zero eigenvalue. The restrictions on the parameters in the potential are discussed.     

The generalized Yablonskii-Vorob'ev polynomials and their properties

Rational solutions of the generalized second Painlevé hierarchy are classified. Representation of the rational solutions in terms of special polynomials, the generalized Yablonskii-Vorob'ev polynomials, is introduced. Differential-difference relations satisfied by the polynomials are found. Hierarchies of differential equations related to the generalized second Painlevé hierarchy are derived. One of these hierarchies is a sequence of differential equations satisfied by the generalized Yablonskii-Vorob'ev polynomials.     

Statistical properties of 2-D generalized hyperbolic attractors

Recently Pesin introduced a large class of hyperbolic attractors, and for those attractors he established the Smale spectral decomposition. In this paper our main results are a stretched exponential bound on the decay of correlations and the central limit theorem. Also we will obtain conditions under which two well known attractors-those of Belykh and Lozi-are subject to our main results. (c) 1995 American Institute of Physics.     

A path-sampling scheme for computing thermodynamic properties of a many-body system in a generalized ensemble

We propose to compute the thermodynamic properties of many-body systems using a path-sampling Monte Carlo scheme implemented in a generalized path ensemble. Trial paths are generated through an expanded ensemble using a reversible discretization of Langevins equation of motion. We also show how the systematic errors resulting from the use of a finite time step can rigorously be taken into account in the path-sampling scheme. We find that the degree of convergence of the estimated thermodynamic quantity towards the exact value correlates with the mean acceptance rates of the path-sampling scheme. An application of the path method for simulating glassy systems is finally suggested.Received: 28 January 2004, Published online: 8 June 2004PACS: 82.60.Lf Thermodynamics of solutions - 07.05.Tp Computer modeling and simulation - 64.70.Pf Glass transitions     

Basic properties of the generalized Boltzmann-Gibbs- Shannon entropy

We consider the most general expression, S(v∣m), for the entropy of an m-continuous probability measure v relative to a σ-finite reference measure m,both defined on an otherwise arbitrary measurable space. The functional v ?:S(v∣m) is examined with regard to range, continuity and behaviour to coarse-graining v, and we study how S(v∣m) changes if both measures are transfered to another measurable space. Some important entropy inequalities are generalized for the functional v ?: S(v∣m), and we show that, even in this general context, Jaynes' principle distinguishes the Gibbsian probability measures as the typical probability measures with maximum entropy.