Interacting electrons in a two-dimensional disordered environment: Effect of a Zeeman magnetic field

The effect of a Zeeman magnetic field coupled to the spin of the electrons on the conducting properties of the disordered Hubbard model is studied. Using the Determinant Quantum Monte Carlo method, the temperature- and magnetic-field- dependent conductivity is calculated,as well as the degree of spin polarization. We find that the Zeeman magnetic field suppresses the metallic behavior present for certain values of interaction- and disorder- strength, and is able to induce a metal-insulator transition at a critical field strength. It is argued that the qualitative features of magnetoconductance in this microscopic model containing both repulsive interactions and disorder are in agreement with experimental findings in two-dimensional electron- and hole-gases in semiconductor structures.Comment: 4 pages, 4 figure

Quantum phases of mixtures of atoms and molecules on optical lattices

We investigate the phase diagram of a two-species Bose-Hubbard model including a conversion term, by which two particles from the first species can be converted into one particle of the second species, and vice-versa. The model can be related to ultra-cold atom experiments in which a Feshbach resonance produces long-lived bound states viewed as diatomic molecules. The model is solved exactly by means of Quantum Monte Carlo simulations. We show than an "inversion of population" occurs, depending on the parameters, where the second species becomes more numerous than the first species. The model also exhibits an exotic incompressible "Super-Mott" phase where the particles from both species can flow with signs of superfluidity, but without global supercurrent. We present two phase diagrams, one in the (chemical potential, conversion) plane, the other in the (chemical potential, detuning) plane.Comment: 7 pages, 10 figure

Feshbach-Einstein condensates

We investigate the phase diagram of a two-species Bose-Hubbard model describing atoms and molecules on a lattice, interacting via a Feshbach resonance. We identify a region where the system exhibits an exotic super-Mott phase and regions with phases characterized by atomic and/or molecular condensates. Our approach is based on a recently developed exact quantum Monte Carlo algorithm: the Stochastic Green Function algorithm with tunable directionality. We confirm some of the results predicted by mean-field studies, but we also find disagreement with these studies. In particular, we find a phase with an atomic but no molecular condensate, which is missing in all mean-field phase diagrams.Comment: 4 pages, 6 figure

Linearly edge-reinforced random walks

We review results on linearly edge-reinforced random walks. On finite graphs, the process has the same distribution as a mixture of reversible Markov chains. This has applications in Bayesian statistics and it has been used in studying the random walk on infinite graphs. On trees, one has a representation as a random walk in an independent random environment. We review recent results for the random walk on ladders: recurrence, a representation as a random walk in a random environment, and estimates for the position of the random walker.Comment: Published at http://dx.doi.org/10.1214/074921706000000103 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Determinant Quantum Monte Carlo Study of the Screening of the One Body Potential near a Metal-Insulator Transition

In this paper we present a determinant quantum monte carlo study of the two dimensional Hubbard model with random site disorder. We show that, as in the case of bond disorder, the system undergoes a transition from an Anderson insulating phase to a metallic phase as the onsite repulsion U is increased beyond a critical value U_c. However, there appears to be no sharp signal of this metal-insulator transition in the screened site energies. We observe that, while the system remains metallic for interaction values upto twice U_c, the conductivity is maximal in the metallic phase just beyond U_c, and decreases for larger correlation.Comment: 6 pages, 10 eps figures, Revtex

Purification of quantum trajectories

We prove that the quantum trajectory of repeated perfect measurement on a finite quantum system either asymptotically purifies, or hits upon a family of `dark' subspaces, where the time evolution is unitary.Comment: 10 page

Data Dissemination Performance in Large-Scale Sensor Networks

As the use of wireless sensor networks increases, the need for (energy-)efficient and reliable broadcasting algorithms grows. Ideally, a broadcasting algorithm should have the ability to quickly disseminate data, while keeping the number of transmissions low. In this paper we develop a model describing the message count in large-scale wireless sensor networks. We focus our attention on the popular Trickle algorithm, which has been proposed as a suitable communication protocol for code maintenance and propagation in wireless sensor networks. Besides providing a mathematical analysis of the algorithm, we propose a generalized version of Trickle, with an additional parameter defining the length of a listen-only period. This generalization proves to be useful for optimizing the design and usage of the algorithm. For single-cell networks we show how the message count increases with the size of the network and how this depends on the Trickle parameters. Furthermore, we derive distributions of inter-broadcasting times and investigate their asymptotic behavior. Our results prove conjectures made in the literature concerning the effect of a listen-only period. Additionally, we develop an approximation for the expected number of transmissions in multi-cell networks. All results are validated by simulations