Metal-insulator transition in two-dimensional systems with long-range correlated disorder

We study the localization properties of electrons in a two-dimensional model with on-site energies exhibiting long-range correlated disorder. The localization length and conductance of the system are calculated by using the finite size scaling method combined with transfer matrix technique. In the presence of long-range correlations, we find that there is a continuous line of fixed points indicating that the system undergoes a disorder driven Kosterlitz-Thouless-type metal-insulator transition. Received 6 March 2003 Published online 20 June 2003 RID="a" ID="a"e-mail: wsliu@sjtu.edu.cn     

Quantum phase transitions in matrix product states of one-dimensional spin-1 chains

We present a new model of quantum phase transitions in matrix product systems of one-dimensional spin-1 chains and study the phases coexistence phenomenon. We find that in the thermodynamic limit the proposed system has three different quantum phases and by adjusting the control parameters we are able to realize any phase, any two phases equal coexistence and the three phases equM coexistence. At every critical point the physical quantities including the entanglement are not discontinuous and the matrix product system has long-range correlation and N-spin maximal entanglement. We believe that our work is helpful for having a comprehensive understanding of quantum phase transitions in matrix product states of one-dimensional spin chains and of certain directive significance to the preparation and control of one-dimensional spin lattice models with stable coherence and N-spin maximal entanglement.     

Quantum phase transitions in matrix product states of one-dimensional spin-1/2 chains

For the matrix product system of a one-dimensional spin-1/2 chain, we present a new model of quantum2 phase transitions and find that in the thermodynamic limit, both sides of the critical point are respectively described by phases ｜Ψa 〉=｜1··· 1 representing all particles spin up and ｜Ψb 〉=｜0··· 0 representing all particles spin down, while the phase transition point is an isolated intermediate-coupling point where√ the two phases coexist equally, which is2 described by the so-called N-qubit maximally entangled GHZ state ｜Ψpt =√2/2（｜1··· 1 ＋｜0··· 0）. At the critical point,2the physical quantities including the entanglement are not discontinuous and the matrix product system has longrange correlation and N-qubit maximal entanglement. We believe that our work is helpful for having a comprehensive understanding of quantum phase transitions in matrix product states of one-dimensional spin chains and of potential directive significance to the preparation and control of one-dimensional spin lattice models with stable coherence and N-qubit maximal entanglement.     

Effects of long-range interaction on critical and multicritical behavior of compressible disordered systems

A field-theoretic approach is applied to describe behavior of weakly disordered, isotropic elastic compressible systems with long-range interactions directly in the three-dimensional space for various values of the long-range interaction parameter a. A renormalization-group procedure is applied separately for a > 2 and a ≤ 2 directly in the three-dimensional space. Renormalization-group equations are analyzed in the two-loop approximation, and critical and tricritical points are determined. It is shown that long-range effects are not important when a ≤ 2, whereas they play a key role in the opposite case of a > 2. Critical exponents characterizing the system are obtained for various values of the long-range interaction parameter. Behavior of homogeneous and disordered systems characterized by two fluctuating order parameters is also described.     

Relativistic scattering theory for long-range potentials of the nonelectrostatic type

We define a modified free-time evolution for the Dirac equation with long-range potentials (1/|x|), where is the Dirac matrix, and prove a strong asymptotic completeness of the corresponding wave operators. Our methods also work for the magnetic fields ·A(x).     

Direct calculation of intermolecular potential energy surfaces

A variation perturbation method is presented for the direct calculation of intermolecular interaction energies. The theory is based on valence bond ideas but avoids the full evaluation of the matrix elements by expansion in powers of interchange, a procedure which is valid for small overlap between the systems. The participating excited states are regarded as polarized pseudo-states and are determined by optimizing the long-range multipole-multipole part of the interaction energy. The validity of these ideas is illustrated by a calculation of the He-He interaction. A remarkable simplification is pointed out, in which the interaction energy is given almost exactly by the sum of the repulsive term, calculated as zero + single interchange, plus the long-range interaction.     

Quantum field theory of phase transitions in Fermi systems

The theory of fermion phase transitions is reviewed from a unified field theoretic standpoint, based on the diagrammatic perturbation expansion of a generalized matrix propagator. Transitions from a normal to a condensed phase are characterized by the spontaneous appearance of long-range order and (in the presence of a suitable infinitesimal external field) broken symmetry. This is illustrated by the ferromagnetic, solid, superconducting and spindensity wave ground states. The phenomenon is explained qualitatively as caused by the creation of a long-range internal field, F, due to the interactions between particles. This field establishes long-range order in the system, and is in turn itself established by the long-range order, in a self-consistent fashion. The mechanism here is expressed quantitatively in terms of a self-consistent Dyson equation relating a generalized matrix propagator, G, to a proper self-energy matrix, Σ. The off-diagonal elements of G describe ‘anomalous’ propagation processes which are characteristic for the condensed phase, and they yield directly the long-range order parameters. The Σ-matrix is just the potential of the internal field. The method is illustrated by applying it to the ferromagnetic phase of a system with δ-function interaction between particles. Finally, the technique is used to derive the vertex part equation for the transition point.     

The long-range correlations of various Ising lattices

The object of this paper is to determine the long-range order parameter for any Ising lattice whose partition function can be evaluated by existing methods. The partition function of a general class of two-dimensional lattices is evaluated by a technique found byGreek andHurst, and this technique is extended to determine correlation coefficients. In this way the determination of the long-range correlation coefficients is reduced to an eigenvalue problem, which can be solved by algebraic methods. A simple formula is found for the long-range order parameter, which contains, but is considerably more general than the known result for the rectangular lattice.     

Measurements of viscosity in pure-electron plasmas

Measurements of the viscosity in quiescent magnetized pure-electron plasmas are up to 10(8) times larger than predicted by classical collisional theory. This strong viscosity is due to long-range " E x B drift collisions" between electrons separated by up to a Debye length. Recent theories of long-range collisions show order-of-magnitude agreement with the measurements, but do not give the observed dependence on the plasma column length. A simple empirical scaling law fits the length and magnetic field dependence surprisingly well.     

Evidence for an emission source of large space-time extent in Au+Au collisions at RHIC

The source imaging technique of Brown and Danielewicz has been used to extract two-pion emission source functions over a broad range of k _T and centralities in Au+Au collisions at $\sqrt s = 200$ GeV. The source functions reflect the combined contributions of a short-range Gaussian-like component and a long-range exponential-like component. A parametrization of the source function gives a RMS radius for the long-range source which is approximately three times that for the short-range source. The centrality dependence of the extracted source parameters for the short- and long-range sources indicate similar patterns.     

Behaviour of adiabatic potentials in the scattering of three particles

We examine, anddiscuss, the basic procedure (the trick needed in 1, 2 pr 3 dimensions) to calculate 3 to 3 scattering using hypersherical harmonics. To illustrate this, we look at three particles in a plane, subject to finite repulsive core interactions, and obtain, numerically, long-range adiabatic effective potentials. Their asymptotic behaviour is such as to provide the correct (nonanalytic) low-energy dependence of the three-body phase shifts. We note that the expansion is not uniform in the number of harmonics needed as the hyperadius changes. and that the asymptotic behaviour of the converged effective potentials differs from that of the matrix elements.     

Spin wave propagation in the domain state of a random field magnet

Inelastic neutron scattering with high wave-vector resolution has characterized the propagation of transverse spin wave modes near the antiferromagnetic zone center in the metastable domain state of a random field Ising magnet. A well-defined, long wavelength excitation is observed despite the absence of long-range magnetic order. Direct comparisons with the spin wave dispersion in the long-range ordered antiferromagnetic state reveal no measurable effects from the domain structure. This result recalls analogous behavior in thermally disordered anisotropic spin chains but contrasts sharply with that of the phonon modes in relaxor ferroelectrics. Received 2 November 2002 / Received in final form 4 February 2003 Published online 11 April 2003 RID="a" ID="a"leheny@pha.jhu.edu     

强场中NO分子回归谱的长程散射矩阵的理论研究

采用半经典散射矩阵方法研究外磁场中高里德伯态双原子分子在能量范围为77010—77050cm^-1的回归谱.通过引进模型势简化强磁场中NO分子的高里德伯电子的势函数,找出其在核转动量子数分别为N=1,3,5的三个通道中的闭合轨道,重点分析了强磁场中NO分子的长程散射矩阵元实部的傅里叶变换谱与闭合轨道之间的一一对应关系.     

Statistical mechanics in biology: how ubiquitous are long-range correlations?

The purpose of this opening talk is to describe examples of recent progress in applying statistical mechanics to biological systems. We first briefly review several biological systems, and then focus on the fractal features characterized by the long-range correlations found recently in DNA sequences containing non-coding material. We discuss the evidence supporting the finding that for sequences containing only coding regions, there are no long-range correlations. We also discuss the recent finding that the exponent alpha characterizing the long-range correlations increases with evolution, and we discuss two related models, the insertion model and the insertion-deletion model, that may account for the presence of long-range correlations. Finally, we summarize the analysis of long-term data on human heartbeats (up to 10(4) heart beats) that supports the possibility that the successive increments in the cardiac beat-to-beat intervals of healthy subjects display scale-invariant, long-range "anti-correlations" (a tendency to beat faster is balanced by a tendency to beat slower later on). In contrast, for a group of subjects with severe heart disease, long-range correlations vanish. This finding suggests that the classical theory of homeostasis, according to which stable physiological processes seek to maintain "constancy," should be extended to account for this type of dynamical, far from equilibrium, behavior.     

The spherical hierarchical model

The spherical version of Dyson's hierarchical model is analyzed. A particular case which is designed to simulate the long-range Ising problem is dealt with in detail. A phase transition is found with critical temperature $$\beta _c = \tfrac{1}{2}(2^\alpha - 2)(4 - 2^\alpha )^{ - 1} $$ wheren ^th neighbor spins interact with a strength ofn ^?α. Critical exponents are calculated for this particular case and are found to be identical with the critical exponents of the long-range spherical Ising model.     

A mechanism of long-range order induced by random fields: Effective anisotropy created by defects

A microscopic mechanism of the long-range order in two-dimensional space induced by random local fields of crystal defects has been found. The impurity-induced effective anisotropy has been shown to arise in the system due to anisotropic distribution of impurity-induced random local field directions in the n-dimensional space of vector order parameter with the O(n) symmetry. The expression for the effective anisotropy constant has been obtained. A weak anisotropy of the “easy axis” type transforms the X–Y model and the Heisenberg model to the class of Ising models, and brings into long-range order existence in the system.     

Matrix order indices in statistical mechanics

A new notion of matrix order indices which relates the matrix norm and its trace is introduced. These indices can be defined for any given matrix. They are especially important for matrices describing many-body systems, equilibrium as well as nonequilibrium, for which the indices present a quantitative measure of the level of ordering. They characterize not only the long-range order, but also mid-range order. In the latter case, when order parameters do not exist, the matrix indices are well defined, providing an explicit classification of various mid-range orders. The matrix order indices are suitable for describing phase transitions with both off-diagonal and diagonal orders. Contrary to order parameters whose correct definition requires the thermodynamic limit, the matrix indices do not necessarily need the latter. Because of this, such indices can distinguish between different phases of finite systems, thus, allowing for the classification of crossover phase transitions.     

Deformation-Induced Destruction of the Long-Range Order in Single Crystals of Ni3Fe Alloy

In the present work, x-ray diffraction and electron microscopy are used to investigate the state of a Ni₃Fe single crystal during plastic deformation. It is demonstrated that the observed destruction of long-range atomic order is accompanied with splitting of superdislocations and generation of single dislocations. The change of the long-range order parameter for single crystals deformed in the [001] direction estimated from the degree of splitting of superdislocations is in good agreement with x-ray measurements of this parameter. The destruction of long-range order for intermediate deformations < 40% is well described by the model of mechanical mixing of the alloy, the main role in which is played by the mechanisms of plane defect generation by shears along slip planes.     

Improved performance accordion heteronuclear multiple-bond correlation spectroscopy-IMPEACH-MBC.

A modification of the recently reported ACCORD-HMBC long-range heteronuclear shift correlation experiment is described. The new experiment, IMPEACH-MBC (improved performance accordion heteronuclear multiple-bond correlation), introduces a new pulse sequence element, a constant time variable delay. The incorporation of the constant time variable delay into the IMPEACH-MBC sequence suppresses (1)H-(1)H coupling modulation inherent to the utilization of the accordion principle to sample a broad range of potential long-range heteronuclear couplings. (1)H-(1)H coupling modulation, which introduces an F(1) modulation or a "skew" of responses in the second frequency domain of the ACCORD-HMBC experiment, is suppressed in the IMPEACH-MBC experiment. Results of identically optimized IMPEACH-MBC and ACCORD-HMBC experiments performed on a sample of strychnine are compared.