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| 折扣與優(yōu)惠：團(tuán)購最低可5折優(yōu)惠 - 了解詳情 | 論文格式：Word格式(*.doc) |  |
摘要:隨機(jī)行走在很多領(lǐng)域里都有重要的應(yīng)用，因此受到越來越多人的關(guān)注。特別是一維最近鄰的無規(guī)行走過程，由于它的理論表述上的簡單性和數(shù)學(xué)上易處理性以及它對(duì)眾多物理模型的代表性，而引起了人們的注意。本文主要研究的是存在有次近鄰跳躍的隨機(jī)行走問題，在次近鄰跳躍的結(jié)果上取一些特殊值推導(dǎo)出最近鄰跳躍的情況。 在這篇文章當(dāng)中主要采用的研究方法是近年來量子行走中用到的方法。首先將主方程運(yùn)用到簡單一維復(fù)式格子中得到描寫演化過程的矩陣，接著將描寫演化的矩陣對(duì)角化再在K空間求解隨機(jī)行走的演化問題，然后通過Fourier變換后回到坐標(biāo)空間求解位移的平均和位移平方的平均值，最終得到在復(fù)式晶格上的隨機(jī)行走中有次近鄰跳躍的有意思的結(jié)果。 通過本文的計(jì)算和研究，當(dāng)i無限大時(shí)得出了i步的隨機(jī)行走，每一步的平均步長，其表達(dá)式為。它與i的奇偶性和L、S都無關(guān)，只與間距有關(guān)。并且知道在隨機(jī)行走中的次近鄰跳躍起到增加步長的作用。 關(guān)鍵詞：一維復(fù)式晶格；次近鄰跳躍；平均步長
Abstract:Random walk has important applications in many areas, and has been receiving more and more attention. Especially the random walk on one-dimensional lattice with nearest neighbor hopping, because of its mathematical simplicity and wide applications in many physical systems, has attracted much attention. In this paper we study the random walk on a one-dimensional non-Bravais lattice with next-nearest neighbor jumps. In this article we utilize methods used in the study of quantum walk in recent years. First, the master equation is applied to one-dimensional non-Bravais lattice and the evolution is described by a matrix. Then the evolution matrix is diagonalized in the K space and then Fourier transformed back to coordinate space. The probability is used to solve the average displacement and the average squared displacement, and eventually we get the exact results on the random walk in the non-Bravais lattice with next-nearest neighbor jumps. Through this calculation and study, we can see that when i is large, the behavior is the same with that of a simple random walk, each step of the average step size, with expression. It is independent of the parity of i nor the length of L 、S, only related to a and p. And the next-nearest neighbor jumps play the role of increasing the average step length. Keywords: One-dimensional non-Bravais lattice; Next-nearest neighbor hopping; Average step length |
