Universality in Four-Boson Systems

We report recent advances on the study of universal weakly bound four-boson states from the solutions of the Faddeev-Yakubovsky equations with zero-range two-body interactions. In particular, we present the correlation between the energies of successive tetramers between two neighbor Efimov trimers and compare it to recent finite range potential model calculations. We provide further results on the large momentum structure of the tetramer wave function, where the four-body scale, introduced in the regularization procedure of the bound state equations in momentum space, is clearly manifested. The results we are presenting confirm a previous conjecture on a four-body scaling behavior, which is independent of the three-body one. We show that the correlation between the positions of two successive resonant four-boson recombination peaks are consistent with recent data, as well as with recent calculations close to the unitary limit. Systematic deviations suggest the relevance of range corrections.     

Universal Properties of the Four-Boson System in Two Dimensions

We consider the nonrelativistic four-boson system in two dimensions interacting via a short-range attractive potential. For a weakly attractive potential with one shallow two-body bound state with binding energy B₂, the binding energies B_N of shallow N-body bound states are universal and thus do not depend on the details of the interaction potential. We compute the four-body binding energies in an effective quantum mechanics approach. There are exactly two bound states: the ground state with B₄⁽⁰⁾=197.3(1)B₂ and one excited state with B₄⁽¹⁾=25.5(1)B₂. We compare our results to recent predictions for N-body bound states with large N1.On leave from FZ Jülich, Institut für Kernphysik (Theorie), D-52425 Jülich and HISKP (Theorie), Universität Bonn, Nußallee 14–16, D-53115 Bonn, Germany     

Universal Four-Boson System: Dimer-Atom-Atom Efimov Effect and Recombination Reactions

Recent theoretical developments in the four-boson system with resonant interactions are described. Momentum-space scattering equations for the four-particle transition operators are used. The properties of unstable tetramers with approximate dimer-atom-atom structure are determined. In addition, the three- and four-cluster recombination processes in the four-boson system are studied.     

Low-Lying States of Four-Boson Systems with a Repulsive Core and an Attractive Tail in the Interaction

 The Schr?dinger equation of a four-boson model system is solved via a variational procedure. The pairwise interaction contains a repulsive core and an attractive tail. The features of the low-lying states are extracted via an analysis of the wave functions. The decisive effect of symmetry is demonstrated. A classification of states based on the inherent nodal structures of the internal wave functions is proposed. Received May 10, 1999; revised June 20, 2000; accepted for publication August 16, 2000     

Analysis of the Structure of Low-Lying States of Four-Boson Systems Based on Symmetry

The structure of inherent nodal surfaces of four-boson systems has been investigated. The most probable structures for each low-lying state have been found. A number of predictions on the structures of individual states and on the systematics of the spectra have been found. Received July 18, 1996; revised March 15, 1997; accepted in final form September 30, 1997     

From Dinuclear Systems to Close Binary Stars and Galaxies

The evolution of close binary cosmic objects in the mass-asymmetry coordinate is considered. Conditions for the formation of stable symmetric binary stars and galaxies are analyzed. The role of symmetrization of an asymmetric binary system in the transformation of the potential energy into the internal energy and in the release of a large amount of energy is explained.     

Close to Close Packing

For various lattice gas models with nearest neighbor exclusion (and, in one case, second-nearest neighbor exclusion as well), we obtain lower bounds on m, the average number of particles on the nonexcluded lattice sites closest to a given particle. They are all of the form m/m _cp 1–const·(N _cp /N–1), where N is the number of occupied sites, m _cp is the value of m at close packing, and N _cp is the value of N at close packing. An analogous result exists for hard disks in the plane.     

Universal Algorithm of the Nonequilibrium Dynamics of Chaotic Systems

Scenarios of transition of nonlinear dynamical systems to chaos are considered based on the study of the behavior of nonlinear dynamical systems represented as feedback systems and analysis of universality and scale invariance (fractal) properties of threshold dynamical structures at points of unstable equilibrium of these systems.     

Power Spectrum of a Noisy System Close to a Heteroclinic Orbit

We consider a two-dimensional dynamical system that possesses a heteroclinic orbit connecting four saddle points. This system is not able to show self-sustained oscillations on its own. If endowed with white Gaussian noise it displays stochastic oscillations, the frequency and quality factor of which are controlled by the noise intensity. This stochastic oscillation of a nonlinear system with noise is conveniently characterized by the power spectrum of suitable observables. In this paper we explore different analytical and semianalytical ways to compute such power spectra. Besides a number of explicit expressions for the power spectrum, we find scaling relations for the frequency, spectral width, and quality factor of the stochastic heteroclinic oscillator in the limit of weak noise. In particular, the quality factor shows a slow logarithmic increase with decreasing noise of the form \(Q\sim [\ln (1/D)]^2\). Our results are compared to numerical simulations of the respective Langevin equations.     

Universal Prohibited Zones in the Coordinate Space of Few-Body Systems

In some special zones of the high-dimensional coordinate space of few-body systems with identical particles, the operation of an element (or a product of elements) of the symmetry groups of the Hamiltonian on a quantum state might be equivalent to the operation of another element. Making use of the matrix representations of the groups, the equivalence of a pair of operations leads to a set of homogeneous linear equations imposed on the wave functions. When the matrix of these equations is non-degenerate, the wave functions will appear as nodal surfaces in these zones. In this case, these zones are prohibited. In this paper, tightly bound 4-boson systems with three types of interaction have been studied analytically and numerically. The existence of the universal prohibited zones has been revealed, and their decisive effect on the structures of the eigenstates is demonstrated.     

走近新课标——谈预习对探究式教学活动的重要影响

结合教学实际,从探究式教学的一个重要影响因素--预习,分析探究式教学中预习与否对学生科学素养的培养上存在的巨大的差异.     

Universal Dynamics,¶a Unified Theory of Complex Systems.¶Emergence, Life and Death

A universal framework is proposed, where all laws are regularities of relations between things or agents. Parts of the world at one or all times are modelled as networks called \system s with a minimum of axiomatic properties. A notion of locality is introduced by declaring some relations direct (or links). Dynamics is composed of basic constituents called mechanisms. They are conditional actions of basic local structural transformations (“enzymes”): indirect relations become direct (friend of friend becomes friend), links are removed, objects copied. This defines a kind of universal chemistry. I show how to model basic life processes in a self contained fashion as a kind of enzymatic computation. The framework also accommodates the gauge theories of fundamental physics. Emergence creates new functionality by cooperation – nonlocal phenomena arise out of local interactions. I explain how this can be understood in a reductionist way by multiscale analysis (e.g. renormalization group). Received: 20 April 2000 / Accepted: 20 April 2000     

Universal Form of Stochastic Evolution for Slow Variables in Equilibrium Systems

Nonlinear, multiplicative Langevin equations for a complete set of slow variables in equilibrium systems are generally derived on the basis of the separation of time scales. The form of the equations is universal and equivalent to that obtained by Green. An equation with a nonlinear friction term for Brownian motion turns out to be an example of the general results. A key method in our derivation is to use different discretization schemes in a path integral formulation and the corresponding Langevin equation, which also leads to a consistent understanding of apparently different expressions for the path integral in previous studies.     

Time Flow in a Noncommutative Regime

We develop an approach to dynamical and probabilistic properties of the model unifying general relativity and quantum mechanics, initiated in the paper (Heller et al. (2005) International Journal Theoretical Physics 44, 671). We construct the von Neumann algebra of random operators on a groupoid, which now is not related to a finite group G, but is the pair groupoid of the Lorentzian frame bundle E over spacetime M. We consider the time flow on depending on the state . The state defining the noncommutative dynamics is assumed to be normal and faithful. Then the pair is a noncommutative probabilistic space and can also be interpreted as an equilibrium thermal state, satisfying the Kubo-Martin-Schwinger condition. We argue that both the “time flow” and thermodynamics have their common roots in the noncommutative unification of dynamics and probability.