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V. Karimipour

Publications and source records attributed to V. Karimipour.

44 records · Page 3Linked to original sources
arXiv1998

A Modified Quantum Renormalization Group for xxz Spin Chain

A simple modification of the standard Renormalization Group (RG) technique for the study of quantum spin systems is introduced. Our method which takes into account the effect of boundary conditions by employing the concept of superblock, may be regarded as a simple way for obtaining first estimates of many properties of spin systems. By applying this method to the xxz spin 1/2 Heisenberg chain, we obtain the ground state energy with much higher accuracy than the standard RG. We have also obtained the staggered magnetization and the z-component of spin-spin correlation function which confirms the absence of long-range order in the massless region of the 1D xxz model.

cond-mat.stat-mech↗
arXiv1998

Exact solution of a one-parameter family of asymmetric exclusion processes

We define a family of asymmetric processes for particles on a one-dimensional lattice, depending on a continuous parameter $λ\in [0,1] $, interpolating between the completely asymmetric processes [1] (for $λ=1$) and the n=1 drop-push models [2] (for $ λ=0$). For arbitrary $\la$, the model describes an exclusion process, in which a particle pushes its right neighbouring particles to the right, with rates depending on the number of these particles. Using the Bethe ansatz, we obtain the exact solution of the master equation .

cond-mat↗
arXiv1997

Global Conformal Invariance in D-dimensions and Logarithmic Correlation Functions

We define transformation of multiplets of fields (Jordan cells) under the D-dimensional conformal group, and calculate two and three point functions of fields, which show logarithmic behaviour. We also show how by a formal differentiation procedure, one can obtain n-point function of logarithmic field theory from those of ordinary conformal field theory.

hep-th↗
arXiv1996

"A Solvable Hamiltonian System" Integrability and Action-Angle Variables

We prove that the dynamical system charaterized by the Hamiltonian $ H = λN \sum_{j}^{N} p_j + μ\sum_{j,k}^{N} {{(p_j p_k)}^{1\over 2}} \{ cos [ ν( q_j - q_k)] \} $ proposed and studied by Calogero [1,2] is equivalent to a system of {\it non-interacting} harmonic oscillators. We find the explicit form of the conserved currents which are in involution. We also find the action-angle variables and solve the initial value problem in simple form.

hep-th↗
arXiv1996

Analysis of Poisson Networks and Their Relation with Random Cellular Structures

We perform a detailed analysis of the statistical properties of Poisson networks and show that the metric and topological properties of random cellular structures, can not be derived from simple models of random networks based on a poisson point distribution [1]. In particular we show that Lewis and Aboav-Wieare laws are not obeyed in these network.

cond-mat↗
arXiv1996

Relation of The New Calogero Models and xxz Spin Chains

We extend our previous analysis of the classical integrable models of Calogero in several respects. Firstly we provide the algebraic resaons of their quantum integrability.Secondly we show why these systems allow their initial value problem to be solved in closed form . Furthermore we show that due to their similarity with the above models the classical and quantum Heisenberg magnets with long rang interactions in a magnetic field are also intergrable. Explicit expressions are given for the integrals of motion in involution in the classical case and for the commuting operators in the quantum case.

hep-th↗
arXiv1996

Algebraic and Geometric Structure of the Integrable Models recently Proposed by Calogero

We show that the integrability of the dynamical system recently proposed by Calogero and characterized by the Hamiltonian $ H = \sum_{j,k}^{N} p_j p_k \{λ+ μcos [ ν( q_j - q_k)] \} $ is due to a simple algebraic structure . It is shown that the integrals of motion are related to the Casimiar invariants of of the $su(1,1)$ algebra. Our method shows clearly how these types of systems can be generalized .

hep-th↗