Effective potential for composite operators and for an auxiliary scalar field in a Nambu-Jona-Lasinio model

We derive the effective potentials for composite operators in a Nambu-Jona-Lasinio (NJL) model at zero and finite temperature and show that in each case they are equivalent to the corresponding effective potentials based on an auxiliary scalar field. The both effective potentials could lead to the same possible spontaneous breaking and restoration of symmetries including chiral symmetry if the momentum cutoff in the loop integrals is large enough, and can be transformed to each other when the Schwinger-Dyson (SD) equation of the dynamical fermion mass from the fermion-antifermion vacuum (or thermal) condensates is used. The results also generally indicate that two effective potentials with the same single order parameter but rather different mathematical expressions can still be considered physically equivalent if the SD equation corresponding to the extreme value conditions of the two potentials have the same form.Comment: 7 pages, no figur

A simpler and more efficient algorithm for the next-to-shortest path problem

Given an undirected graph $G=(V,E)$ with positive edge lengths and two vertices $s$ and $t$, the next-to-shortest path problem is to find an $st$-path which length is minimum amongst all $st$-paths strictly longer than the shortest path length. In this paper we show that the problem can be solved in linear time if the distances from $s$ and $t$ to all other vertices are given. Particularly our new algorithm runs in $O(|V|\log |V|+|E|)$ time for general graphs, which improves the previous result of $O(|V|^2)$ time for sparse graphs, and takes only linear time for unweighted graphs, planar graphs, and graphs with positive integer edge lengths.Comment: Partial result appeared in COCOA201

Collapse arrest and soliton stabilization in nonlocal nonlinear media

We investigate the properties of localized waves in systems governed by nonlocal nonlinear Schrodinger type equations. We prove rigorously by bounding the Hamiltonian that nonlocality of the nonlinearity prevents collapse in, e.g., Bose-Einstein condensates and optical Kerr media in all physical dimensions. The nonlocal nonlinear response must be symmetric, but can be of completely arbitrary shape. We use variational techniques to find the soliton solutions and illustrate the stabilizing effect of nonlocality.Comment: 4 pages with 3 figure

Design and Analysis of IPACT-based Bandwidth Allocation for Delay-Guarantee in OFDMA-PON

To guarantee delay performances for timesensitive services in an orthogonal frequency-division multiple access passive optical network (OFDMA-PON), we propose a two-dimension (i.e., subcarriers and time) upstream bandwidth allocation method based on interleaved polling with adaptive cycle time (IPACT). We first analyze its delay performance in terms of cycle time, i.e., the length of a polling cycle. Then, by setting the maximum polling cycle so as to guarantee timely transmissions for time-sensitive services, we identify the requirements, i.e., maximum bandwidth allocation, maximum number of allowed optical network units (ONUs), and optimum number of subcarriers, for upstream bandwidth allocation with delay guarantees. The proposed scheme is evaluated both numerically and via simulation

Infrared Hall conductivity of Na0.7_{0.7}CoO2_2

We report infrared Hall conductivity $\sigma_{xy}(\omega)$ of Na$_{0.7}$CoO$_2$ thin films determined from Faraday rotation angle $\theta_{F}$ measurements. $\sigma_{xy}(\omega)$ exhibits two types of hole conduction, Drude and incoherent carriers. The coherent Drude carrier shows a large renormalized mass and Fermi liquid-like behavior of Hall scattering rate, $\gamma_{H} \sim aT^{2}$. The spectral weight is suppressed and disappears at T = 120K. The incoherent carrier response is centered at mid-IR frequency and shifts to lower energy with increasing T. Infrared Hall constant is positive and almost independent of temperature in sharp contrast with the dc-Hall constant.Comment: 5 Pages, 5 Figures. Author list corrected in metadata only, paper is unchange

Stability of two-dimensional spatial solitons in nonlocal nonlinear media

We discuss existence and stability of two-dimensional solitons in media with spatially nonlocal nonlinear response. We show that such systems, which include thermal nonlinearity and dipolar Bose Einstein condensates, may support a variety of stationary localized structures - including rotating spatial solitons. We also demonstrate that the stability of these structures critically depends on the spatial profile of the nonlocal response function.Comment: 8 pages, 9 figure