Phase behavior of the Lattice Restricted Primitive Model with nearest-neighbor exclusion

The global phase behavior of the lattice restricted primitive model with nearest neighbor exclusion has been studied by grand canonical Monte Carlo simulations. The phase diagram is dominated by a fluid (or charge-disordered solid) to charge-ordered solid transition that terminates at the maximum density, $\rho^*_{max}=\sqrt2$ and reduced temperature $T^*\approx0.29$. At that point, there is a first-order phase transition between two phases of the same density, one charge-ordered and the other charge-disordered. The liquid-vapor transition for the model is metastable, lying entirely within the fluid-solid phase envelope.Comment: 6 pages, color. submitted to J. Chem. Phy

Phase diagrams in the lattice RPM model: from order-disorder to gas-liquid phase transition

The phase behavior of the lattice restricted primitive model (RPM) for ionic systems with additional short-range nearest neighbor (nn) repulsive interactions has been studied by grand canonical Monte Carlo simulations. We obtain a rich phase behavior as the nn strength is varied. In particular, the phase diagram is very similar to the continuum RPM model for high nn strength. Specifically, we have found both gas-liquid phase separation, with associated Ising critical point, and first-order liquid-solid transition. We discuss how the line of continuous order-disorder transitions present for the low nn strength changes into the continuum-space behavior as one increases the nn strength and compare our findings with recent theoretical results by Ciach and Stell [Phys. Rev. Lett. {\bf 91}, 060601 (2003)].Comment: 7 pages, 10 figure

Simplified solutions of the Cox-Thompson inverse scattering method at fixed energy

Simplified solutions of the Cox-Thompson inverse quantum scattering method at fixed energy are derived if a finite number of partial waves with only even or odd angular momenta contribute to the scattering process. Based on new formulae various approximate methods are introduced which also prove applicable to the generic scattering events.Comment: 9 pages, 3 figure

Numerical studies of the fractional quantum Hall effect in systems with tunable interactions

The discovery of the fractional quantum Hall effect in GaAs-based semiconductor devices has lead to new advances in condensed matter physics, in particular the possibility for exotic, topological phases of matter that possess fractional, and even non-Abelian, statistics of quasiparticles. One of the main limitations of the experimental systems based on GaAs has been the lack of tunability of the effective interactions between two-dimensional electrons, which made it difficult to stabilize some of the more fragile states, or induce phase transitions in a controlled manner. Here we review the recent studies that have explored the effects of tunability of the interactions offered by alternative two-dimensional systems, characterized by non-trivial Berry phases and including graphene, bilayer graphene and topological insulators. The tunability in these systems is achieved via external fields that change the mass gap, or by screening via dielectric plate in the vicinity of the device. Our study points to a number of different ways to manipulate the effective interactions, and engineer phase transitions between quantum Hall liquids and compressible states in a controlled manner.Comment: 9 pages, 4 figures, updated references; review for the CCP2011 conference, to appear in "Journal of Physics: Conference Series

Diffusive transport in networks built of containers and tubes

We developed analytical and numerical methods to study a transport of non-interacting particles in large networks consisting of M d-dimensional containers C_1,...,C_M with radii R_i linked together by tubes of length l_{ij} and radii a_{ij} where i,j=1,2,...,M. Tubes may join directly with each other forming junctions. It is possible that some links are absent. Instead of solving the diffusion equation for the full problem we formulated an approach that is computationally more efficient. We derived a set of rate equations that govern the time dependence of the number of particles in each container N_1(t),N_2(t),...,N_M(t). In such a way the complicated transport problem is reduced to a set of M first order integro-differential equations in time, which can be solved efficiently by the algorithm presented here. The workings of the method have been demonstrated on a couple of examples: networks involving three, four and seven containers, and one network with a three-point junction. Already simple networks with relatively few containers exhibit interesting transport behavior. For example, we showed that it is possible to adjust the geometry of the networks so that the particle concentration varies in time in a wave-like manner. Such behavior deviates from simple exponential growth and decay occurring in the two container system.Comment: 21 pages, 18 figures, REVTEX4; new figure added, reduced emphasis on graph theory, additional discussion added (computational cost, one dimensional tubes

Quantitative analysis of Sr2RuO4 ARPES spectra: Many-body interactions in a model Fermi liquid

ARPES spectra hold a wealth of information about the many-body interactions in a correlated material. However, the quantitative analysis of ARPES spectra to extract the various coupling parameters in a consistent manner is extremely challenging, even for a model Fermi liquid system. We propose a fitting procedure which allows quantitative access to the intrinsic lineshape, deconvolved of energy and momentum resolution effects, of the correlated 2-dimensional material Sr2RuO4. For the first time in correlated 2-dimensional materials, we find an ARPES linewidth that is narrower than its binding energy, a key property of quasiparticles within Fermi liquid theory. We also find that when the electron-electron scattering component is separated from the electron-phonon and impurity scattering terms it decreases with a functional form compatible with Fermi liquid theory as the Fermi energy is approached. In combination with the previously determined Fermi surface, these results give the first complete picture of a Fermi liquid system via ARPES. Furthermore, we show that the magnitude of the extracted imaginary part of the self-energy is in remarkable agreement with DC transport measurements.Comment: 10 pages, 5 figure

Formation of shock waves in a Bose-Einstein condensate

We consider propagation of density wave packets in a Bose-Einstein condensate. We show that the shape of initially broad, laser-induced, density perturbation changes in the course of free time evolution so that a shock wave front finally forms. Our results are well beyond predictions of commonly used zero-amplitude approach, so they can be useful in extraction of a speed of sound from experimental data. We discuss a simple experimental setup for shock propagation and point out possible limitations of the mean-field approach for description of shock phenomena in a BEC.Comment: 8 pages & 6 figures, minor changes, more references, to appear in Phys. Rev.

Heun Functions and the energy spectrum of a charged particle on a sphere under magnetic field and Coulomb force

We study the competitive action of magnetic field, Coulomb repulsion and space curvature on the motion of a charged particle. The three types of interaction are characterized by three basic lengths: l_{B} the magnetic length, l_{0} the Bohr radius and R the radius of the sphere. The energy spectrum of the particle is found by solving a Schr\"odinger equation of the Heun type, using the technique of continued fractions. It displays a rich set of functioning regimes where ratios \frac{R}{l_{B}} and \frac{R}{l_{0}} take definite values.Comment: 12 pages, 5 figures, accepted to JOPA, november 200

Dynamics of Phase Transitions: The 3D 3-state Potts model

In studies of the QCD deconfining phase transition or cross-over by means of heavy ion experiments, one ought to be concerned about non-equilibrium effects due to heating and cooling of the system. In this paper we extend our previous study of Glauber dynamics of 2D Potts models to the 3D 3-state Potts model, which serves as an effective model for some QCD properties. We investigate the linear theory of spinodal decomposition in some detail. It describes the early time evolution of the 3D model under a quench from the disordered into the ordered phase well, but fails in 2D. Further, the quench leads to competing vacuum domains, which are difficult to equilibrate, even in the presence of a small external magnetic field. From our hysteresis study we find, as before, a dynamics dominated by spinodal decomposition. There is evidence that some effects survive in the case of a cross-over. But the infinite volume extrapolation is difficult to control, even with lattices as large as $120^3$.Comment: 12 pages; added references, corrected typo

Simple and Robust Solver for the Poisson-Boltzmann Equation

A variational approach is used to develop a robust numerical procedure for solving the nonlinear Poisson-Boltzmann equation. Following Maggs et al., we construct an appropriate constrained free energy functional, such that its Euler-Lagrange equations are equivalent to the Poisson-Boltzmann equation. We then develop, implement, and test an algorithm for its numerical minimization, which is quite simple and unconditionally stable. The analytic solution for planar geometry is used for validation. Furthermore, some results are presented for a charged colloidal sphere surrounded by counterions.Comment: 11 pages, 5 figures, 2 table