Possible test of the thermodynamic approach to granular media

We study the steady state distribution of the energy of the Sherrington-Kirkpatrick model driven by a tapping mechanism which mimics the mechanically driven dynamics of granular media. The dynamics consists of two phases: a zero temperature relaxation phase which leads the system to a metastable state, then a tapping which excites the system thus reactivating the relaxational dynamics. Numerically, we investigate whether the distribution of the energies of the blocked states obtained agrees with a simple canonical form of the Edwards measure. It is found that this canonical measure is in good agreement with the dynamically measured energy distribution. A possible experimental test of the Edwards measure based on the study here is proposed.     

Testing the Edwards hypothesis in spin systems under tapping dynamics

The Edwards hypothesis of ergodicity of blocked configurations for gently tapped granular materials is tested for aaabstract models of spin systems on random graphs and spin chains with kinetic constraints. The tapping dynamics is modeled by considering two distinct mechanisms of energy injection: thermal and random tapping. We find that ergodicity depends upon the tapping procedure (i.e. the way the blocked configurations are dynamically accessed): for thermal tapping ergodicity is a good approximation, while it fails to describe the asymptotic stationary state reached by the random tapping dynamics. Received 30 November 2001     

纳米多晶金属样本构建的分子动力学模拟研究

研究了分子动力学模拟中纳米多晶金属样本的构建过程.首先采用Voronoi几何方法生成初始的纳米多晶铝和铜样本,然后用快速冷凝(或共轭梯度)法得到样本的局域最低能态,最后在恒温零应力周围环境下(常温常压NPT系综)退火得到最低能态样本.使用样本的残余内应力来衡量纳米多晶样本是否与实验制备的一致.通过监测这两步弛豫过程中晶界结构的变化形态、体系平均内应力和能量下降过程及具体的局域分布和不同弛豫条件下最终样本的弹性常数,发现样本的能量和残余内应力都接近实验制备的纳米多晶金属.对Voronoi几何法生成的晶界而言     

Dynamics of learning and generalization in perceptrons with constraints

Depending on the kind of constraints imposed on the weights of a perceptron, learning can be a combinatorially hard problem. As an example of this type, I discuss a perception with binary weights comparing results obtained from replica theory, dynamic mean field theory and simulated annealing. Contrary to the replica calculation, dynamics yields information about the performance of a polynomial algorithm in a situation where the best solution cannot be found in polynomial time. I also discuss improved learning algorithms and results for finite size perceptrons.     

A particle in a box in the presence of an electric field and applications to disordered systems

The Green's function and energy eigenvalues of an electron under the influence of a uniform electric field in a box with infinitely high sides is investigated. The second order correction to the energy eigenvalues is calculated by finding zeros of the wronskian and comparing with the value obtained from second order perturbation theory. Comparison is made with the limiting conditions in which the size of the box tends to infinity and the electric field tends towards zero. The results of the investigation suggest a possible criterion for localisation. The value obtained for the ground state energy is used to extend a model of Edwards to study the tail of the density of states of a disordered system in the presence of an electric field.     

Optimal control theory in adaptive simulated annealing technique: optimisation of laser pulse for selective vibrational excitations and photo-dissociation of HBr+

An optimisation method using optimal control theory based adaptive simulated annealing technique has been explored to get optimised laser pulses for selective vibrational excitations and photo-dissociation of the HBr⁺ in its ground electronic state. Potential energy curve of the system has been obtained by coupled cluster singles and doubles (CCSD) level calculation, using aug-cc-pVTZ as basis set. To have a simple pulse, a limited number of parameters is chosen as variables and the technique so developed works well. The study is extended with chirping field frequency to explore the effect of chirping in dynamics.     

The stability of magnetobipolarons in low-dimensional systems

We investigate the stability condition of large bipolarons confined in a parabolic potential containing certain parameters and a uniform magnetic field. The variational wave function is constructed as a product form of electronic parts, consisting of center of mass and internal motion, and a part of coherent phonons generated by Lee-Low-Pines transformation from the vacuum. An analytical expression for the bipolaron energy is found, from which the ground and excited-state energies are obtained numerically by minimization procedure. The bipolaron stability region is determined by comparing the bipolaron energy with those of two separate polarons, which is already calculated within the same approximation. It is shown that the results obtained for the ground state energy of bipolarons reduce to the existing works in zero magnetic field. In the presence of a magnetic field, the stability of bipolarons is examined, for three types of low-dimensional system, as function of certain parameters, such as the magnetic-field, the electron-phonon coupling constant, Coulomb repulsion and the confinement strength. Numerical solutions for the energy levels of the ground and first excited states are examined as functions of the same parameters. Received 7 March 2002 and Received in final form 22 April 2002 Published online 25 June 2002     

Low-temperature solution of the Sherrington-Kirkpatrick model

I propose a simple scaling ansatz for the full replica symmetry breaking solution of the Sherrington-Kirkpatrick model in the low energy sector. This solution is shown to become exact in the limit x --> 0, Bx --> infinity of the Parisi replica symmetry breaking scheme parameter . The distribution function of the frozen fields has been known to develop a linear gap at zero temperature. The scaling equations are integrated to find an exact numerical value for the slope of the gap thetaP(x,y)/delta|(y --> 0) = 0.301 046.... I also use the scaling solution to devise an inexpensive numerical procedure for computing finite time scale (x =1) quantities. The entropy, the zero field cooled susceptibility, and the local field distribution function are computed in the low-temperature limit with high precision, barely achievable by currently available methods.     

Numerical results for ground states of spin glasses on Bethe lattices

The average ground state energy and entropy for ±J spin glasses on Bethe lattices of connectivities k + 1 = 3..., 26 at T = 0 are approximated numerically. To obtain sufficient accuracy for large system sizes (up to n = 2¹²), the Extremal Optimization heuristic is employed which provides high-quality results not only for the ground state energies per spin e_k+1 but also for their entropies s_k+1. The results indicate sizable differences between lattices of even and odd connectivities. The extrapolated ground state energies compare very well with recent one-step replica symmetry breaking calculations. These energies can be scaled for all even connectivities k + 1 to within a fraction of a percent onto a simple functional form, e _{k + 1} = E _SK - (2E _SK + )/, where E _SK = - 0.7633 is the ground state energy for the broken replica symmetry in the Sherrington-Kirkpatrick model. But this form is in conflict with perturbative calculations at large k + 1, which do not distinguish between even and odd connectivities. We also find non-zero entropies per spin s_k+1 at small connectivities. While s_k+1 seems to vanish asymptotically with 1/(k + 1) for even connectivities, it is numerically indistinguishable from zero already for odd k + 1 ≥ 9. Received 9 August 2002 Published online 27 January 2003 RID="a" ID="a"e-mail: sboettc@emory.edu www.physics.emory.edu/faculty/boettcher     

Isospin effect of the in-medium nucleon-nucleon cross section in excited nuclear reactions

Using relativistic mean field theory, the neutron and the proton density distribution of ⁵⁶Ni nuclei could be obtained in the ground state and the excited state. Based on the framework of the quantum molecular dynamics model, the ⁵⁶Ni nuclei have been simulated in ground state and in the neutron or proton excited state. We then used the three different states of ⁵⁶Ni to collide with the ⁵⁶Ni in the ground state. To discuss the evolution of the nuclear stopping in different reactions, two kinds of different excited nuclear reactions were studied at different reaction energies and at different impact parameters. Studies have shown that the nuclear stopping of an excited nuclear reaction is sensitive to the isospin-dependent in-medium nucleon-nucleon cross section, compared with the response value of the ground state nuclear reaction. So, it is better for the excited nuclei to extract the isospin dependence of nucleon-nucleon cross section information.     

Directed Dominating Set Problem Studied by Cavity Method: Warning Propagation and Population Dynamics

The minimal dominating set for a digraph (directed graph) is a prototypical hard combinatorial optimization problem. In a previous paper, we studied this problem using the cavity method. Although we found a solution for a given graph that gives very good estimate of the minimal dominating size, we further developed the one step replica symmetry breaking theory to determine the ground state energy of the undirected minimal dominating set problem. The solution space for the undirected minimal dominating set problem exhibits both condensation transition and cluster transition on regular random graphs. We also developed the zero temperature survey propagation algorithm on undirected Erdös-Rényi graphs to find the ground state energy. In this paper we continue to develope the one step replica symmetry breaking theory to find the ground state energy for the directed minimal dominating set problem. We find the following. (i) The warning propagation equation can not converge when the connectivity is greater than the core percolation threshold value of 3.704. Positive edges have two types warning, but the negative edges have one. (ii) We determine the ground state energy and the transition point of the Erdös-Rényi random graph. (iii) The survey propagation decimation algorithm has good results comparable with the belief propagation decimation algorithm.     

Exact ground states of Ising spin glasses: New experimental results with a branch-and-cut algorithm

In this paper we study two-dimensional Ising spin glasses on a grid with nearest neighbor and periodic boundary interactions, based on a Gaussian bond distribution, and an exterior magnetic field. We show how using a technique called branch and cut, the exact ground states of grids of sizes up to 100×100 can be determined in a moderate amount of computation time, and we report on extensive computational tests. With our method we produce results based on more than 20,000 experiments on the properties of spin glasses whose errors depend only on the assumptions on the model and not on the computational process. This feature is a clear advantage of the method over other, more popular ways to compute the ground state, like Monte Carlo simulation including simulated annealing, evolutionary, and genetic algorithms, that provide only approximate ground states with a degree of accuracy that cannot be determineda priori. Our ground-state energy estimation at zero field is –1.317.     

Storage of electromagnetic field energy in matter

The partitioning, uniqueness and form of field energy stored in matter, and its properties as a state function, is established. Consequently, the first and second laws apply to the nonfield and field parts of the internal energy as separate entities. This provides a bridge between thermodynamics and the classical theory of electromagnetism. Presentation of the temperature as the sum of nonfield and field contributions is used to establish field dependent barriers to temperature decrease toward the absolute zero, and the existence of field induced temperature jumps. These temperature jumps appear at the instant the field is switched on, or turned off. The partitioning of field and nonfield energies is illustrated for a specific case of an ideal gas, and the heat absorbed by the field is derived in terms of difference in adiabatic magnetization. Finally, the current, restrictive, form of electromagnetic field energy density is redefined with respect to the effect of field energy stored outside the system boundaries. Received 6 June 2000 / Received in final form 26 March 2002 Published online 24 September 2002 RID="a" ID="a"e-mail: zimmels@tx.technion.ac.il     

Squeezed magnetobipolarons in two-dimensional quantum dot

In this Letter, a different method was given for calculating the energies of the magnetobipolarons confined in a parabolic QD (quantum dot). We introduced single-mode squeezed states transformation, which are based on the Lee-Low-Pines and Huybrechts (LLP-H) canonical transformations. This method can provide results not only for the ground state energy but also for the excited states energies. Moreover, it can be applied to the entire range of the electron-phonon coupling strength. Comparing with the results of the LLP-H transformations, we have obtained more accurate results for the ground state energy, excited states energies and binding energy of the bipolarons. It shows that the magnetic field and the quantum dot can facilitate the formation of the bipolarons when η is smaller than some value.     

几何结构对Na8团簇熔化过程的影响

运用距离相关紧密结合的分子动力学模型,对金属原子团簇Na8的两种不同的异构体进行了数值模拟.根据零温下基态结构中不同原子到质心的不同距离,把Na8的两种异构体分为多个子系统.分别提取各个子系统在不同温度下的围绕质心的径向分布、无单位键长涨落、平均位移、扩散系数,发现尽管两个异构体的基态能量很接近,但他们的稳定性、熔化过程的热力学性质等有着很大的差别,这也反映了它们在几何结构上的差别.     

I–V characterization of a quantum well infrared photodetector with stepped and graded barriers

I–V characterization of an n-type quantum well infrared photodetector which consists of stepped and graded barriers has been done under dark at temperatures between 20–300 K. Different current transport mechanisms and transition between them have been observed at temperature around 47 K. Activation energies of the electrons at various bias voltages have been obtained from the temperature dependent I–V measurements. Activation energy at zero bias has been calculated by extrapolating the bias dependence of the activation energies. Ground state energies and barrier heights of the four different quantum wells have been calculated by using an iterative technique, which depends on experimentally obtained activation energy. Ground state energies also have been calculated with transfer matrix technique and compared with iteration results. Incorporating the effect of high electron density induced electron exchange interaction on ground state energies; more consistent results with theoretical transfer matrix calculations have been obtained.     

Jamming, freezing and metastability in one-dimensional spin systems

We consider in parallel three one-dimensional spin models with kinetic constraints: the paramagnetic constrained Ising chain, the ferromagnetic Ising chain with constrained Glauber dynamics, and the same chain with constrained Kawasaki dynamics. At zero temperature the dynamics of these models is fully irreversible, leading to an exponentially large number of blocked states. Using a mapping of these spin systems onto sequential adsorption models of, respectively, monomers, dimers, and hollow trimers, we present exact results on the statistics of blocked states. We determine the distribution of their energy or magnetization, and in particular the large-deviation function describing its exponentially small tails. The spin and energy correlation functions are also determined. The comparison with an approach based on a priori statistics reveals systematic discrepancies with the Edwards hypothesis, concerning in particular the fall-off of correlations. Received 26 February 2002 Published online 6 June 2002     

Zero field isotropic Muonium Kubo — Toyabe relaxation functions

Static zero field Gaussian Kubo — Toyabe relaxation functions for muons in isotropic muonium atoms are presented. That is, as with diamagnetic muons, an average of the spin dynamics of a muon in an isolated isotropic ground state muonium atom is taken over an isotropic Gaussian continuous classical local random magnetic field distribution. This motion approximates the exact quantal spin dynamics generated by the dipole-dipole interactions between the muonium atom and the surrounding nuclear spins associated with the site at which the muonium atom has stopped. Expressions are derived for triplet muonium only since, in general, singlet muonium is not observed. For normal nuclear spins and ground state muonium, the resulting relaxation functions are identical to the standard diamagnetic function (except for a shift in the time scale).     

Tapping spin glasses and ferromagnets on random graphs.

We consider a tapping dynamics, analogous to that in experiments on granular media, on spin glasses and ferromagnets on random thin graphs. Between taps, zero temperature single spin flip dynamics takes the system to a metastable state. Tapping corresponds to flipping simultaneously any spin with probability p. This dynamics leads to a stationary regime with a steady state energy E(p). We analytically solve this dynamics for the one-dimensional ferromagnet and +/-J spin glass. Numerical simulations for spin glasses and ferromagnets of higher connectivity are carried out; in particular, we find a novel first order transition for the ferromagnetic systems.     

Theory of the Stark effect for P donors in Si

We develop an effective mass theory for substitutional donors in silicon in an inhomogeneous environment. Valley-orbit coupling is included perturbatively. We specifically consider the Stark effect in Si:P. In this case, the theory becomes more accurate at high fields, while it is designed to give correct experimental binding energies at zero field. Unexpectedly, the ground state energy for the donor electron is found to increase with electric field as a consequence of spectrum narrowing of the 1s manifold. Our results are of particular importance for the Kane quantum computer.