Geometric Proof of Exact Quantization Rules in One Dimensional Quantum Mechanics

In terms of the construction of vector field with momentum and logarithmic derivative of wavefunction as its components, a geometric proof of an exact quantization rule in one dimensional quantum mechanics systems is given. The quantization rule arises from the SO(2) gauge transformation. In addition, the quantization rule is generalized to the case when the potential function is piecewise continuous between the two turning points. This work was supported by doctoral foundation of HPU.     

Functional Algebras and Dimensional Reduction in the LPDEs Integration Problem

Abstract

The paper is devoted to application of the noncommutative integration method for linear partial differential equations. This method is based on the noncommutative integration theory for finite-dimensional Hamiltonian systems and is generalized for so-called functional algebras.     

Exponential Clogging Time for a One Dimensional DLA

In this paper a simple DLA type model is analyzed. In (Benjamini and Yadin in Commun. Math. Phys. 279:187–223, [2008]) the standard DLA model from (Witten and Sander in Phys. Rev. B 27:5686–5697, [1983]) was considered on a cylinder and the arm growing phenomena was established, provided that the section of the cylinder has sufficiently fast mixing rate. When considering DLA on a cylinder it is natural to ask how many particles it takes to clog the cylinder, e.g. modeling clogging of arteries. In this note we formulate a very simple DLA clogging model and establish an exponential lower bound on the number of particles arriving before clogging appears. In particular we possibly shed some light on why it takes so long to reach the bypass operation.     

Exact Results for Fully Directed Flights is s-Dimensions

The critical behaviour of s-dimensional fully directed flights (FDFs) is treated by a generating function method and an exact calculation method. Our results show that the exponents v, v_|| and v_⊥ of FDFs are independent of the spatial dimensionality and the concrete form of the probability distribution of step lengths. They are in agreement with the Laplacian transformation method and the Monte Carlo simulation study for fully directed Levy flights.     

Applications of Lie Symmetries to Higher Dimensional Gravitating Fluids

We consider a radiating shear-free spherically symmetric metric in higher dimensions. Several new solutions to the Einstein’s equations are found systematically using the method of Lie analysis of differential equations. Using the five Lie point symmetries of the fundamental field equation, we obtain either an implicit solution or we can reduce the governing equations to a Riccati equation. We show that known solutions of the Einstein equations can produce infinite families of new solutions. Earlier results in four dimensions are shown to be special cases of our generalised results.     

Comparison of Exact and Perturbative Results for Two Metrics

We compare the exact and perturbative results in two metrics and show that the spurious effects due to the perturbation method do not survive for physically relevant quantities such as the vacuum expectation value of the stress-energy tensor.     

Some Exact Results for a Two-Dimensional System of Particles

The Laughlin variational wave function of a quantum liquid used in studying the fractional quantum Hall effect may be interpreted as a two-dimensional system of particles interacting via a logarithmic interaction, with a centripetal force proportional to the square of the distance from the origin. We present exact calculations of the partition function, radial distribution function, and particle density for systems of up to six particles. Received April 25, 1994; revised August 5, 1994; accepted for publication August 30, 1994     

Some Exact Results on Bond Percolation

We present some exact results on bond percolation. We derive a relation that specifies the consequences for bond percolation quantities of replacing each bond of a lattice ?? by ? bonds connecting the same adjacent vertices, thereby yielding the lattice ?? _? . This relation is used to calculate the bond percolation threshold on ?? _? . We show that this bond inflation leaves the universality class of the percolation transition invariant on a lattice of dimensionality d??2 but changes it on a one-dimensional lattice and quasi-one-dimensional infinite-length strips. We also present analytic expressions for the average cluster number per vertex and correlation length for the bond percolation problem on the N???? limits of several families of N-vertex graphs. Finally, we explore the effect of bond vacancies on families of graphs with the property of bounded diameter as N????.     

On Exact Solutions for a Luttinger Liquid with One Impurity

JETP Letters - Reasons for the existence of exact solutions of the Luttinger model have been discussed. It has been shown that scattering by impurities at certain electron-electron coupling...     

Exact Solitary Wave Solutions of Surface Waves in a Convecting Fluids

In the standard Painlevé analysis, the singular manifold can be extended to many different forms because of its arbitrariness. Using some kinds of standard and nonstandard truncation approaches for the extended singular manifolds to a convecting fluid, we can obtain abundant solitary wave structures.     

One Dimensional Behavior of Singular N Dimensional Solutions of Semilinear Heat Equations

We consider u(x,t) a solution of u _t =Δu+|u| ^{p − 1} u that blows up at time T, where u:ℝ ^N ×[0, T)→ℝ, p>1, (N−2)p<N+2 and either u(0)≥ 0 or (3N−4)p<3N+8. We are concerned with the behavior of the solution near a non isolated blow-up point, as T−t→ 0. Under a non-degeneracy condition and assuming that the blow-up set is locally continuous and N−1 dimensional, we escape logarithmic scales of the variable T−t and give a sharper expansion of the solution with the much smaller error term (T−t)^{1, 1/2−η} for any η>0. In particular, if in addition p>3, then the solution is very close to a superposition of one dimensional solutions as functions of the distance to the blow-up set. Finally, we prove that the mere hypothesis that the blow-up set is continuous implies that it is C ^{1, 1/2−η} for any η>0. Received: 20 June 2001 / Accepted: 6 October 2001     

Coherent Stochastic Resonance in One Dimensional Diffusion with One Reflecting and One Absorbing Boundaries

It is shown that the single-step periodic signal (periodic telegraph signal) can not produce coherent stochastic resonance for diffusion on a segment with one absorbing and one reflecting end points while the multi-step periodic signal does. The general features of this process are exihibited. The resonant frequency is found to decrease and the mean first passage time at resonant frequency increases linearly, as we increase the length of the medium. The cycle variable is shown to be the proper argument to express the first passage probability at resonance. A formula for first passage probability at resonance is derived in terms of two universal functions, which clearly isolates its dependence on the length of the medium.     

Growth Diversity in One Dimensional Fluctuating Interfaces

A set of one dimensional interfaces involving attachment and detachment of k-particle neighbors is studied numerically using both large scale simulations and finite size scaling analysis. A labeling algorithm introduced by Barma and Dhar in related spin Hamiltonians enables to characterize the asymptotic behavior of the interface width according to the initial state of the substrate. For equal deposition-evaporation probability rates it is found that in most cases the initial conditions induce regimes of saturated width. In turn, scaling exponents obtained for initially flat interfaces indicate power law growths which depend on k. In contrast, for unequal probability rates the interface width exhibits a logarithmic growth for all k>1 regardless of the initial state of the substrate.     

非完整超晶格中电子透射问题的计算机模拟

采用转移矩阵方法,模拟研究了垒高无序和阱宽无序非完整超晶格的电子态问题.计算了垒高无序有限超晶格的透射谱和其局域态波函数以及阱宽无序有限超晶格的透射谱和本征值,直观地给出了垒高无序和阱宽无序非完整有限超晶格其电子态行为的物理图像.模拟结果表明:垒高无序和阱宽无序这两种常见非完整一维有限超晶格的子带带隙间均存在强烈的电子运动定域化,且电子波的布喇格散射对周期性势场更敏感;这两种非完整性引起的局域,通过计算电子局域态波函数和有限系统的本征值得到了证实;对本文讨论的这种类型和周期的超晶格,如果控制阱宽在9.1～10.9nm间随机变化,即阱宽的值最大相差1.8岫时,计算机模拟的结果是,阱宽的这种非周期性开始使子带的带隙消失.     

Limit Properties of One Dimensional Periodic Hopping Model

在细致平衡的基础上,通过形式运算得到了平均速度及有效扩散常数在模型的内部状态数量趋向无穷大时的极限显示表达式．这一结果将有助于进一步了解一维跳跃模型的性质.     

基于飞秒激光的一维速度场测量方法

飞秒激光诱导氰基化学发光利用飞秒光丝标记流场中的气体分子,通过观测被标记分子在固定时间内的位移可获得流场的速度信息.一维的光丝在实验结果中包含了一维的速度场信息,但由于无法将光丝移动前后的位置信息精确关联,因此只能给出中心一点的速度.针对此问题,我们提出了一种一维速度场反演算法,可根据移动后光丝的位置及其线型反演出整条...