Colossal Magnetoresistance using the Small Polaron Picture with Finite Bandwidth Effects

We present a small polaron picture and show that finite bandwidth effects are important to understand colossal magnetoresistance. Besides the polaron size parameter, we show that there is another parameter (adiabaticity parameter) that is relevant to studying magnetoresistance. We find that for fixed values of the polaron size parameter an increase in the adiabaticity parameter increases the magnetoresistance. The magnetic transition is studied within a mean field approach. We point out important oversights in the literature. We find that for the reported values of the bandwidth (based on band structure calculations) and for experimentally determined values of activation energy and Debye frequency, the calculated values of the magnetoresistance compare favorably with experimental ones. We calculate the optical conductivity too and find that there is reasonable agreement with experiment.Comment: 11 pages, 4 figures, Accepted in Physical Review

Mixed Charge-Spin Response Functions of an Arbitrarily Polarized Electron Gas

In this paper, using different approaches we demonstrate the equality of the two mixed charge-spin response functions of a spin-polarized electron gas when orbital effects are negligible. Within a generalized STLS approximation we show that the two mixed responses are equal. We also present arguments for the equality of the two dynamic responses by considering a symmetry of the effective screened interaction between two opposite spin electrons. Furthermore, using the reflection symmetry of the system and the fact that the hamiltonian is real we prove rigorously that the two responses coincide identically.Comment: 4 page

Many-player entangled state solutions in game theory problems

We propose a non-classical multi-player entangled state which eliminates the need for communication, yet can solve problems (that require coordination) better than classical approaches. For the entangled state, we propose a slater determinant of all allowed states of a filled band in a condensed matter system -- the integer quantum Hall state at filling factor 1. Such a state gives the best solution (i.e., best Nash equilibrium) for some classical stochastic problems where classical solutions are far from ideal

Small Magnetic Polaron Picture of Colossal Magnetoresistance in Manganites

We present a small-but-sizeable magnetic polaron picture where transport at high temperatures is activated while at low temperatures it is band-like. We show that both double exchange and finite bandwidth effects are important to understand colossal magnetoresistance as well as the coincidence of the metal-insulator and the ferromagnetic transitions in manganites. The magnetic transition is explained using band-like motion of the polarons.Comment: 4 pages, 2 figures, corrected forma

Coexistence of long-range orders in a Bose-Holstein model

Exploring supersolidity in naturally occurring and artificially designed systems has been and will continue to be an area of immense interest. Here, we study how superfluid and charge-density-wave (CDW) states cooperate or compete in a minimal model for hard-core-bosons (HCBs) coupled locally to optical phonons: a two-dimensional Bose-Holstein model. Our study is restricted to the parameter regimes of strong HCB-phonon coupling and non-adiabaticity. We use Quantum Monte Carlo simulation (involving stochastic-series-expansion technique) to study phase transitions and to investigate whether we have homogeneous or phase-separated coexistence. The effective Hamiltonian involves, besides a nearest-neighbor hopping and a nearest-neighbor repulsion, sizeable double-hopping terms (obtained from second-order perturbation). At densities not far from half-filling, in the parameter regime where the double-hopping terms are non-negligible (negligible) compared to the nearest-neighbor hopping, we get checkerboard-supersolidity (phase separation) with CDW being characterized by ordering wavevector $\vec{Q}=(\pi,\pi)$.Comment: Revised versio

Supersolidity in a Bose-Holstein model

We derive an effective d-dimensional Hamiltonian for a system of hard-core-bosons coupled to optical phonons in a lattice. At non-half-fillings, a superfluid-supersolid transition occurs at intermediate boson-phonon couplings, while at strong-couplings the system phase separates. We demonstrate explicitly that the presence of next-nearest-neighbor hopping and nearest-neighbor repulsion leads to supersolidity. Thus we present a microscopic mechanism for the homogeneous coexistence of charge-density-wave and superfluid orders

Quantum phase transition in Bose-Holstein model in two dimensions

We derive an effective d-dimensional Hamiltonian for a system of hard-core-bosons coupled to optical phonons in a lattice. Away from half-filling, we show that the presence of next-nearest-neighbor hopping in the effective Hamiltonian leads to a superfluid-to-supersolid transition at intermediate boson-phonon (b-p) couplings, while at strong-couplings the system phase separates. However, at half-filling and at a critical b-p coupling (as in the xxz-model), the system undergoes a superfluid-to-charge-density-wave transition without any signature of supersolidity. Our analyses is based on extensive calculations of the structure factor, the superfluid fraction, the Bose-Einstein condensate fraction, and the system energy at various fillings. We present a phase diagram for this system and compare it to that of the xxz-model. We also demonstrate explicitly that the next-nearest-neighbor hopping (in the absence of nearest-neighbor hopping) in the effective Hamiltonian leads only to a single transition, i.e., a first-order superfluid-to-supersolid transition

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.Comment: 2 pages, RevTeX4, 1 ps figure, to be published in Physica Scripta T: Proc. Vol. `Unconventional Applications of Statistical Physics', March, 200

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.Comment: 6 pages and 5 PS figure

Study of the ferromagnetic-insulator phase in manganites

Understanding the coexistence of ferromagnetism and insulating behavior in manganites is an unsolved problem. We propose a localized-band model involving effective intermediate-range electron-electron (electron-hole) repulsion (attraction) generated by cooperative electron-phonon interaction. Double exchange mechanism, involving holes virtually hopping to nearest neighbors and back, produces magnetic polarons in an antiferromagnetic environment; when these magnetic polarons coalesce and percolate the system, we get a ferromagnetic insulator. Ferromagnetism gets more pronounced when the holes (doping) increases or when the ratio hopping/polaronic-energy dominates over superexchange-coupling/hopping.Comment: 11 figure