On a Boltzmann equation for Haldane statistics

The study of quantum quasi-particles at low temperatures including their statistics, is a frontier area in modern physics. In a seminal paper F.D. Haldane proposed a definition based on a generalization of the Pauli exclusion principle for fractional quantum statistics. The present paper is a study of quantum quasi-particles obeying Haldane statistics in a fully non-linear kinetic Boltzmann equation model with large initial data on a torus. Strong L1 solutions are obtained for the Cauchy problem. The main results concern existence, uniqueness and stability. Depending on the space dimension and the collision kernel, the results obtained are local or global in time.Comment: 24 pages. arXiv admin note: text overlap with arXiv:1406.0265 This is the published version of the paper. The condition (2.3) on the collision kernel is strengthened, as required for the result to hol

Directional Relays for Multi-Hop Cooperative Cognitive Radio Networks

In this paper, we investigate power allocation and beamforming in a relay assisted cognitive radio (CR) network. Our objective is to maximize the performance of the CR network while limiting interference in the direction of the primary users (PUs). In order to achieve these goals, we first consider joint power allocation and beamforming for cognitive nodes in direct links. Then, we propose an optimal power allocation strategy for relay nodes in indirect transmissions. Unlike the conventional cooperative relaying networks, the applied relays are equipped with directional antennas to further reduce the interference to PUs and meet the CR network requirements. The proposed approach employs genetic algorithm (GA) to solve the optimization problems. Numerical simulation results illustrate the quality of service (QoS) satisfaction in both primary and secondary networks. These results also show that notable improvements are achieved in the system performance if the conventional omni-directional relays are replaced with directional ones

Well-posedness of the Cauchy problem for a space-dependent anyon Boltzmann equation

A fully non-linear kinetic Boltzmann equation for anyons and large initial data is studied in a periodic 1d setting. Strong L1 solutions are obtained for the Cauchy problem. The main results concern global existence, uniqueness, and stability.Comment: 22 pages. In this version an earlier error has been corrected, and with it a study of the time asymptotics moved to a future paper. arXiv admin note: text overlap with arXiv:1207.059