The Nullity of Bicyclic Signed Graphs

Let \Gamma be a signed graph and let A(\Gamma) be the adjacency matrix of \Gamma. The nullity of \Gamma is the multiplicity of eigenvalue zero in the spectrum of A(\Gamma). In this paper we characterize the signed graphs of order n with nullity n-2 or n-3, and introduce a graph transformation which preserves the nullity. As an application we determine the unbalanced bicyclic signed graphs of order n with nullity n-3 or n-4, and signed bicyclic signed graphs (including simple bicyclic graphs) of order n with nullity n-5

Exciton Valley Dynamics probed by Kerr Rotation in WSe2 Monolayers

We have experimentally studied the pump-probe Kerr rotation dynamics in WSe$_2$ monolayers. This yields a direct measurement of the exciton valley depolarization time $\tau_v$. At T=4K, we find $\tau_v\approx 6$ps, a fast relaxation time resulting from the strong electron-hole Coulomb exchange interaction in bright excitons. The exciton valley depolarization time decreases significantly when the lattice temperature increases with $\tau_v$ being as short as 1.5ps at 125K. The temperature dependence is well explained by the developed theory taking into account the exchange interaction and a fast exciton scattering time on short-range potentials.Comment: 5 pages, 3 figure

Entanglement in a two-identical-particle system

The definition of entanglement in identical-particle system is introduced. The separability criterion in two-identical particle system is given. The physical meaning of the definition is analysed. Applications to two-boson and two-fermion systems are made. It is found new entanglement and correlation phenomena in identical-boson systems exist, and they may have applications in the field of quantum information.Comment: 4 page

Optimal Dividend Payments for the Piecewise-Deterministic Poisson Risk Model

This paper considers the optimal dividend payment problem in piecewise-deterministic compound Poisson risk models. The objective is to maximize the expected discounted dividend payout up to the time of ruin. We provide a comparative study in this general framework of both restricted and unrestricted payment schemes, which were only previously treated separately in certain special cases of risk models in the literature. In the case of restricted payment scheme, the value function is shown to be a classical solution of the corresponding HJB equation, which in turn leads to an optimal restricted payment policy known as the threshold strategy. In the case of unrestricted payment scheme, by solving the associated integro-differential quasi-variational inequality, we obtain the value function as well as an optimal unrestricted dividend payment scheme known as the barrier strategy. When claim sizes are exponentially distributed, we provide easily verifiable conditions under which the threshold and barrier strategies are optimal restricted and unrestricted dividend payment policies, respectively. The main results are illustrated with several examples, including a new example concerning regressive growth rates.Comment: Key Words: Piecewise-deterministic compound Poisson model, optimal stochastic control, HJB equation, quasi-variational inequality, threshold strategy, barrier strateg

Casimir effect for the massless Dirac field in two-dimensional Reissner-Nordstr\"{o}m spacetime

In this paper, the two-dimensional Reissner-Nordstr\"{o}m black hole is considered as a system of the Casimir type. In this background the Casimir effect for the massless Dirac field is discussed. The massless Dirac field is confined between two ``parallel plates'' separated by a distance $L$ and there is no particle current drilling through the boundaries. The vacuum expectation values of the stress tensor of the massless Dirac field at infinity are calculated separately in the Boulware state, the Hartle-Hawking state and the Unruh state.Comment: 10 pages, no figure. Accepted for publication in IJMP