arXiv subjects

Arnab Das

Publications and source records attributed to Arnab Das.

61 records · Page 4Linked to original sources

arXiv2006

Analysis of the long-range random field quantum antiferromagnetic Ising model

We introduce a solvable quantum antiferromagnetic model. The model, with Ising spins in a transverse field, has infinite range antiferromagnetic interactions with random fields on each site, following an arbitrary distribution. As is well-known, frustration in the random field Ising model gives rise to a many-valley structure in the spin-configuration space. In addition, the antiferromagnetism also induces a regular frustration even for the ground state. In this paper, we investigate analytically the critical phenomena in the model, having both randomness and frustration and we report some analytical results for it.

cond-mat.dis-nn↗

arXiv2005

Many-Polaron Effects in the Holstein Model

We derive an effective polaronic interaction Hamiltonian, {\it exact to second order in perturbation}, for the spinless one-dimensional Holstein model. The small parameter is given by the ratio of the hopping term ($t$) to the polaronic energy ($g^2 ω_0$) in all the region of validity for our perturbation; however, the exception being the regime of extreme anti-adiabaticity ($t/ω_0 \le 0.1$) and small electron-phonon coupling ($g < 1$) where the small parameter is $t/ω_0$. We map our polaronic Hamiltonian onto a next-to-nearest-neighbor interaction anisotropic Heisenberg spin model. By studying the mass gap and the power-law exponent of the spin-spin correlation function for our Heisenberg spin model, we analyze the Luttinger liquid to charge-density-wave transition at half-filling in the effective polaronic Hamiltonian. We calculate the structure factor at all fillings and find that the spin-spin correlation length decreases as one deviates from half-filling. We also extend our derivation of polaronic Hamiltonian to $d$-dimensions.

cond-mat.str-el↗

arXiv2005

An analytic treatment of the Gibbs-Pareto behavior in wealth distribution

We develop a general framework, based on Boltzmann transport theory, to analyze the distribution of wealth in societies. Within this framework we derive the distribution function of wealth by using a two-party trading model for the poor people while for the rich people a new model is proposed where interaction with wealthy entities (huge reservoir) is relevant. At equilibrium, the interaction with wealthy entities gives a power-law (Pareto-like) behavior in the wealth distribution while the two-party interaction gives a Boltzmann-Gibbs distribution.

cond-mat.stat-mech↗

arXiv2005

Quantum Annealing in a Kinetically Constrained System

Classical and quantum annealing is discussed for a kinetically constrained chain of $N$ non-interacting asymmetric double wells, represented by Ising spins in a longitudinal field $h$. It is shown that in certain cases, where the kinetic constraints may arise from infinitely high but vanishingly narrow barriers appearing in the relaxation path of the system, quantum annealing exploiting the quantum-mechanical penetration of sufficiently narrow barriers may be far more efficient than its thermal counterpart. We have used a semiclassical picture of scattering dynamics to do our simulation for the quantum system.

cond-mat.stat-mech↗

arXiv2003

Quantum Spin Glass Phase Boundary in (+/-)J Transverse Field Ising Systems

Here we study zero temperature quantum phase transition driven by the transverse field for random $\pm J$ Ising model on chain and square lattice. We present some analytical results for one dimension and some numerical results for very small square lattice under periodic boundary condition. The numerical results are obtained employing exact diagonalization technique following Lanczos method.

cond-mat.stat-mech↗

arXiv2003

A distribution function analysis of wealth distribution

We develop a general framework to analyze the distribution functions of wealth and income. Within this framework we study wealth distribution in a society by using a model which turns on two-party trading for poor people while for rich people interaction with wealthy entities (huge reservoir) is relevant. At equilibrium, the interaction with wealthy entities gives a power law (Pareto-like) behavior in the wealth distribution while the two party interaction gives a distribution similar to that reported earlier.

cond-mat.stat-mech↗

arXiv2003

Analytic treatment of a trading market model

We mathematically analyze a simple market model where trading at each point in time involves only two agents with the sum of their money being conserved and with neither parties resulting with negative money after the interaction process. The exchange involves random re-distribution among the two players of a fixed fraction of their total money. We obtain a simple integral nonlinear equation for the money distribution. We find that the zero savings and finite savings cases belong to different universality classes. While the zero savings case can be solved analytically, the finite savings solution is obtained by numerically solving the integral equation. We find remarkable agreement with results obtained by other researchers using sophisticated numerical techniques.

cond-mat.stat-mech↗