Four-Boson Systems Close to a Universal Regime

Universal properties of weakly-bound four-boson systems near the scaling limit are discussed by considering recent results obtained from the solution of Faddeev-Yakubovsky (FY) equations, which confirm a previous conjecture on a four-body scale dependence. In the present contribution, within a discussion on our numerical results obtained for the binding energies of two consecutive tetramer states, we are analyzing the relative relevance of the two possible configurations of the four-body system.     

Limiting Velocity and Dispersion Law of Domain Walls in Ferrimagnets Close to the Spin Compensation Point

JETP Letters - The motion of domain walls in GdFeCo-type ferrimagnets near the point of compensation of sublattice spins s1 and s2, when the effects of the exchange increase in the limiting wall...     

The Lyapunov Exponent of Products of Random 2×2 Matrices Close to the Identity

We study products of arbitrary random real 2×2 matrices that are close to the identity matrix. Using the Iwasawa decomposition of SL(2,?), we identify a continuum regime where the mean values and the covariances of the three Iwasawa parameters are simultaneously small. In this regime, the Lyapunov exponent of the product is shown to assume a scaling form. In the general case, the corresponding scaling function is expressed in terms of Gauss’ hypergeometric function. A number of particular cases are also considered, where the scaling function of the Lyapunov exponent involves other special functions (Airy, Bessel, Whittaker, elliptic). The general solution thus obtained allows us, among other things, to recover in a unified framework many results known previously from exactly solvable models of one-dimensional disordered systems.     

Universal solutions to the simplex equations

We construct a class of solutions to the p-simplex equation in terms of solutions to the Yang-Baxter equation, for every p ≥ slant 3. This may make the construction of solvable p-dimensional lattice models possible.     

研究物理课堂关注学生发展

课程改革的攻坚环节是课程实施，而课程实施的基本途径是课堂教学．课堂教学要注重启发学生思维，张扬学生个性，以兴趣为先导，将信息技术等多媒体融于教学，化难为易，使学生爱学、乐学。课堂教学是教师有目的、有计划地组织学生实现有效学习的活动过程，要突出有思想的教学，把形式和目的有机结合，如果把“研究物理课堂、关注学生发展”作为高中物理教研价值取向的话，我们就可以通过教师专业化水平的提高来适应学生多样化的需求，促进学生个性全面和谐发展．     

Singular Harmonic Maps and Applications to General Relativity

The study of axially symmetric stationary multi-black-hole configurations and the force between co-axially rotating black holes involves, as a first step, an analysis on the “boundary regularity” of the so-called reduced singular harmonic maps. We carry out this analysis by considering those harmonic maps as solutions to some homogeneous divergence systems of partial differential equations with singular coefficients. Our results extend previous works by Weinstein (Comm Pure Appl Math 43:903–948, 1990; Comm Pure Appl Math 45:1183–1203, 1992) and by Li and Tian (Manu Math 73(1):83–89, 1991; Commun Math Phys 149:1–30, 1992; Differential geometry: PDE on manifolds, vol 54, pp. 317–326, 1993). This paper is based on the Ph.D. thesis of the author (Singular harmonic maps into hyperbolic spaces and applications to general relativity, PhD thesis, The State University of New Jersey, Rutgers, 2009).     

SRB States and Nonequilibrium Statistical Mechanics Close to Equilibrium

Nonequilibrium statistical mechanics close to equilibrium is studied using SRB states and a formula [10] for their derivatives with respect to parameters. We write general expressions for the thermodynamic fluxes (or currents) and the transport coefficients, generalizing the results of [4, 5]. In this framework we give a general proof of the Onsager reciprocity relations. Received: 2 December 1996 / Accepted: 13 March 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.     

Maps of Matrices and Portrait Maps of the Density Operators of Composite and Noncomposite Systems

We obtain a new inequality for arbitrary Hermitian matrices. We describe particular linear maps called the matrix portrait of arbitrary N × N matrices. The maps are obtained as analogs of partial tracing of density matrices of multipartite qudit systems. The structure of the maps is inspired by “portrait” map of the probability vectors corresponding to the action on the vectors by stochastic matrices containing either unity or zero matrix elements. We obtain new entropic inequalities for arbitrary qudit states including a single qudit and discuss entangled single qudit state. We consider in detail the examples of N = 3 and 4. Also we point out the possible use of entangled states of systems without subsystems (e.g., a single qudit) as a resource for quantum computations.     

Universal transition to inactivity in global mixed coupling

The collective dynamics of a network of nonlinear oscillators can be represented in terms of activity level of the network. We have studied a universal transition from activity to inactivity in a globally coupled network of identical oscillators. We consider mixed coupling, where some of the network elements interact through the similar variables while others with dissimilar variables. The coupling strength at which the network become inactive is inversely proportional to the fraction of oscillators coupled through dissimilar variables. Results are presented for the network of various globally coupled limit-cycle oscillators such as Stuart-Landau oscillators, MacArthur prey-predator model as well as for the chaotic Rössller oscillators. The analytical condition for the onset of inactivity in the system is calculated using linear stability analysis which is found to be in good agreement with the numerical results.     

Universal attosecond response to the removal of an electron

When an electron is suddenly removed, a universal response of the system is shown to occur on an attosecond (10(-18) s) time scale. During this response time, which lasts about 50 attoseconds, the density of the created hole changes in a characteristic way. Explicit examples are shown. The results are analyzed in terms of the eigenstates of the residual ion and related to the filling of the exchange-correlation hole associated with the electron in the ground state of the system by the remaining electrons.     

Universal properties of the transition from quasi-periodicity to chaos in dissipative systems

An exact renormalization group transformation is developed for dissipative systems which describes how the transition to chaos may occur in a continuous and universal manner if the frequency ratio in the quasi-periodic regime is held at a fixed irrational value. Our approach is a natural extension of K.A.M. theory to strong coupling. Most of our analysis is for analytic circle maps. We have found a strong coupling fixed point where invertibility is lost, which describes the universal features of the transition to chaos. We find numerically that any two such critical maps with the same winding number are C¹ conjugate. It follows that the low frequency peaks in an experimental spectrum are universal and we determine how their envelope scales with frequency.When the winding number has a periodic continued fraction, our renormalization transform has a fixed point and spectra are self similar in addition. For a set of non-periodic winding numbers with full measure our renormalization transformation yields an ergodic trajectory in a sub-space of all critical maps. Physically one finds singular and universal spectra that do not scale.     

Universal approach to optimal photon storage in atomic media

We present a universal physical picture for describing storage and retrieval of photon wave packets in a Lambda-type atomic medium. This physical picture encompasses a variety of different approaches to pulse storage ranging from adiabatic reduction of the photon group velocity and pulse-propagation control via off-resonant Raman fields to photon-echo-based techniques. Furthermore, we derive an optimal control strategy for storage and retrieval of a photon wave packet of any given shape. All these approaches, when optimized, yield identical maximum efficiencies, which only depend on the optical depth of the medium.     

Universal multifractal approach to intermittency in high energy physics

A new stochastic approach to intermittency in high energy physics is proposed. It yields to intermittency exponents defined independently of phase-space dimensions; their role in the calculation of generalized moments is discussed. A straightforward application of universal multifractals is suggested and a new parametric technique for phase-space analysis is provided.     

Kinetic Theory of Area-Preserving Maps. Application to the Standard Map in the Diffusive Regime

The evolution of the distribution function of a dynamical system governed by a general two-dimensional area-preserving iterative map is studied by the methods of nonequilibrium statistical mechanics. A closed, non-Markovian master equation determines the angle-averaged distribution function (the density profile). The complementary, angle-dependent part (the fluctuations) is expressed as a non-Markovian functional of the density profile. Whenever there exist two widely separated intrinsic time scales, the master equation can be markovianized, yielding an asymptotic kinetic equation. The general theory is applied to the standard map in the diffusive regime, i.e., for large stochasticity parameter and large scale length. The non-Markovian master equation can be written and solved analytically in this approximation. The two characteristic time scales are exhibited. This permits the thorough study of the evolution of the density profile, its tendency toward the Markovian approximation, and eventually toward a diffusive Gaussian packet. The evolution of the fluctuations is also described in detail. The various relaxation processes are governed asymptotically by a single diffusion coefficient, which is calculated analytically. This model appears as a testing bench for the study of kinetic equations. The various previous approaches to this problem are reviewed and critically discussed.