Random walk and SU(2) Clebsch–Gordon coefficients

1979 ◽  
Vol 57 (11) ◽  
pp. 2050-2051
Author(s):  
F. Lemire ◽  
J. Patera
Keyword(s):  
Random Walk ◽  
Generating Function ◽  
Transition Function ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
New Interpretation ◽  
Source Of Information

This article contains a new interpretation of the values of the SU(2) Clebsch–Gordon coefficients (CGC). It is shown that a given CGC C(l1,l2,l;m1,m2,m) can be understood as a transition function for a random walk on a two dimensional lattice between the origin and the point (m1,m2) in l1 + l2 + l steps. This interpretation is based on the generating function for the CGC which has previously been shown to be a rich and concise source of information on the CGC.

scholarly journals Quantum walks and elliptic integrals

2010 ◽  
Vol 20 (6) ◽  
pp. 1091-1098 ◽  
Author(s):  
NORIO KONNO
Keyword(s):  
Random Walk ◽  
Generating Function ◽  
Elliptic Integral ◽  
Quantum Walk ◽  
Quantum Walks ◽  
Elliptic Integrals ◽  
Two Dimensional ◽  
One Dimensional ◽  
Similar Expression ◽  
Return Probability

Pólya showed in his 1921 paper that the generating function of the return probability for a two-dimensional random walk can be written in terms of an elliptic integral. In this paper we present a similar expression for a one-dimensional quantum walk.

Correlated random walk

1955 ◽  
Vol 51 (4) ◽  
pp. 639-651 ◽  
Author(s):  
J. Gillis
Keyword(s):  
Random Walk ◽  
Generating Function ◽  
Correlated Random Walk ◽  
Dimensional Lattice ◽  
General Properties ◽  
Special Cases ◽  
Previous Step

ABSTRACTRandom walk on a d-dimensional lattice is investigated such that, at any stage, the probabilities of the step being in the various possible directions depend upon the direction of the previous step. The motion may be characterized by a generating function which is here derived. The generating function is then used to obtain some general properties of the walk. Certain special cases are considered in greater detail. The existence of recurrent points is investigated in particular, and the probability of returning to the origin after 2n steps. This latter function is evaluated asymptotically for the cases d = 1 and d = an even integer.

Small Angle Electron Scattering From Vacuum Condensed Metallic Films

1968 ◽  
Vol 26 ◽  
pp. 380-381
Author(s):  
J. Silcox ◽  
R. H. Wade
Keyword(s):  
Electron Scattering ◽  
Small Angle ◽  
Ring Structure ◽  
Two Dimensional ◽  
Metallic Films ◽  
Micro Structure ◽  
Angle Scattering ◽  
The Fourier Transform ◽  
Source Of Information ◽  
Kinematical Theory

Recent work has drawn attention to the possibilities that small angle electron scattering offers as a source of information about the micro-structure of vacuum condensed films. In particular, this serves as a good detector of discontinuities within the films. A review of a kinematical theory describing the small angle scattering from a thin film composed of discrete particles packed close together will be presented. Such a model could be represented by a set of cylinders packed side by side in a two dimensional fluid-like array, the axis of the cylinders being normal to the film and the length of the cylinders becoming the thickness of the film. The Fourier transform of such an array can be regarded as a ring structure around the central beam in the plane of the film with the usual thickness transform in a direction normal to the film. The intensity profile across the ring structure is related to the radial distribution function of the spacing between cylinders.

On the absorption probabilities and mean time for absorption for discrete Markov chains

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Nikolaos Halidias
Keyword(s):  
Markov Chain ◽  
Random Walk ◽  
Markov Chains ◽  
Generating Function ◽  
Discrete Time ◽  
Probability Generating Function ◽  
The Mean ◽  
Mean Time ◽  
Absorption Probabilities

Abstract In this note we study the probability and the mean time for absorption for discrete time Markov chains. In particular, we are interested in estimating the mean time for absorption when absorption is not certain and connect it with some other known results. Computing a suitable probability generating function, we are able to estimate the mean time for absorption when absorption is not certain giving some applications concerning the random walk. Furthermore, we investigate the probability for a Markov chain to reach a set A before reach B generalizing this result for a sequence of sets A 1 , A 2 , … , A k {A_{1},A_{2},\dots,A_{k}} .

scholarly journals DISCRETE AND CONTINUUM APPROACHES TO THREE-DIMENSIONAL QUANTUM GRAVITY

1991 ◽  
Vol 06 (39) ◽  
pp. 3591-3600 ◽  
Author(s):  
HIROSI OOGURI ◽  
NAOKI SASAKURA
Keyword(s):  
Gauge Theory ◽  
Moduli Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Analogue Model ◽  
Gauge Invariant ◽  
Invariant Functions ◽  
Dimensional Lattice ◽  
Chern Simons ◽  
Dimensional Surface

It is shown that, in the three-dimensional lattice gravity defined by Ponzano and Regge, the space of physical states is isomorphic to the space of gauge-invariant functions on the moduli space of flat SU(2) connections over a two-dimensional surface, which gives physical states in the ISO(3) Chern–Simons gauge theory. To prove this, we employ the q-analogue of this model defined by Turaev and Viro as a regularization to sum over states. A recent work by Turaev suggests that the q-analogue model itself may be related to an Euclidean gravity with a cosmological constant proportional to 1/k2, where q=e2πi/(k+2).

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