Two component spin-fermion model for high-TcT_c cuprates: Applications to neutron scattering and ARPES experiments

Motivated by neutron scattering experiments in the high-$T_c$ cuprates, we propose the two-component spin-fermion model as a minimal phenomenological model which has both local spins and itinerant fermions as independent degrees of freedom. Our calculations of the dynamic spin correlation function provide a successful description of the puzzling neutron experiment data and show that: (1) the upward dispersion branch of magnetic excitations is mostly due to the local spin excitations; (2) the downward dispersion branch is from collective particle-hole excitations of fermions; and (3) the resonance mode is a mixture of both degrees of freedom. Using the same model with the same set of parameters we calculated the renormalized quasiparticle dispersion and successfully reproduced one of the key features of the angle resolved photoemission spectroscopy (ARPES) experiments, i.e., the high energy kink structure in the fermion quasiparticle dispersion, hence further support the two component spin-fermion phenomenology.Comment: 7 figures, 12 pages. arXiv admin note: substantial text overlap with arXiv:0706.138

Resonant impurity scattering in the ±\pms-gap state of the Fe-based superconductors

We study the impurity scattering on the $\pm$s-wave superconductor, with realistic parameters for the Fe-pnictide superconductors. Using $\mathcal{T}$-matrix method, generalized for the two bands, we found that impurity scattering of the unitary limit forms off-centered bound states inside of the superconducting gap, which modifies, surprisingly, the density of states (DOS) of a fully opened gap to a V-shaped one as in the case of a d-wave superconductor. This behavior provides coherent explanations to the several conflicting experimental issues of the Fe-pnictide superconductors: the V-shaped DOS but with an isotropic gap observed in the photoemission and tunneling experiments; the power law behavior of the nuclear spin-lattice relaxation rate ($1/T_1 \approx T^{\alpha}$ ; $\alpha \approx 3$), down to very low temperatures.Comment: 5 pages, 3 figures, Revisions of Figures and their captions; references update

Embedded Solitons in Lagrangian and Semi-Lagrangian Systems

We develop the technique of the variational approximation for solitons in two directions. First, one may have a physical model which does not admit the usual Lagrangian representation, as some terms can be discarded for various reasons. For instance, the second-harmonic-generation (SHG) model considered here, which includes the Kerr nonlinearity, lacks the usual Lagrangian representation if one ignores the Kerr nonlinearity of the second harmonic, as compared to that of the fundamental. However, we show that, with a natural modification, one may still apply the variational approximation (VA) to those seemingly flawed systems as efficiently as it applies to their fully Lagrangian counterparts. We call such models, that do not admit the usual Lagrangian representation, \textit{semi-Lagrangian} systems. Second, we show that, upon adding an infinitesimal tail that does not vanish at infinity, to a usual soliton ansatz, one can obtain an analytical criterion which (within the framework of VA) gives a condition for finding \textit{embedded solitons}, i.e., isolated truly localized solutions existing inside the continuous spectrum of the radiation modes. The criterion takes a form of orthogonality of the radiation mode in the infinite tail to the soliton core. To test the criterion, we have applied it to both the semi-Lagrangian truncated version of the SHG model and to the same model in its full form. In the former case, the criterion (combined with VA for the soliton proper) yields an \emph{exact} solution for the embedded soliton. In the latter case, the criterion selects the embedded soliton with a relative error $\approx 1$.Comment: 10 pages, 1 figur

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

Possible Pairing Mechanisms of PuCoGa5_5 Superconductor

We examine possible pairing mechanisms of superconductivity in PuCoGa$_5$ based on spin-fluctuations or phonons as mediating bosons. We consider experimental data of specific heat C(T) and resistivity $\rho(T)$ as input to determine a consistent scattering boson with the superconducting transition temperature of 18.5K in PuCoGa$_5$. Irrespective to the type of boson, the characteristic boson frequency is found to be $\sim 150 K$ from the resistivity fitting. The spin fluctuation model is most consistent with the experimental resistivity, successfully explaining the anomalous temperature dependence ($\sim \frac{T^2}{150 K +T}$) at low temperatures as well as the saturation behavior at high temperatures. Assuming that the pairing state is non s-wave, the large residual resistivity $\rho_{imp} \sim 20 \mu \Omega cm \sim 120 K$ suggests that an ideally pure sample of PuCoGa$_5$ would have a maximum T$_c$ of 39 K.Comment: 6 pages, 5 figure

Optimal trajectory planning meets network-level routing: Integrated control framework for emerging mobility systems

In this paper, we introduce a hierarchical decision-making framework for emerging mobility systems. Despite numerous studies focusing on optimizing vehicle flow, practical feasibility has often been overlooked. To address this gap, we present a route-recovery method and energy-optimal trajectory planning tailored for connected and automated vehicles (CAVs) to ensure the realization of optimal flow. Our approach identifies the optimal vehicle flow to minimize total travel time while considering consistent mobility demands in urban settings. We deploy a heuristic route-recovery algorithm that assigns routes to CAVs and departure/arrival time at each road segment. Furthermore, we propose an efficient coordination method that rapidly solves constrained optimization problems by flexibly piecing together unconstrained energy-optimal trajectories. The proposed method has the potential to effectively generate optimal vehicle flow, contributing to the reduction of travel time and energy consumption in urban areas.Comment: 17 pages, 11 figure

A Hierarchical Approach to Optimal Flow-Based Routing and Coordination of Connected and Automated Vehicles

This paper addresses the challenge of generating optimal vehicle flow at the macroscopic level. Although several studies have focused on optimizing vehicle flow, little attention has been given to ensuring it can be practically achieved. To overcome this issue, we propose a route-recovery and eco-driving strategy for connected and automated vehicles (CAVs) that guarantees optimal flow generation. Our approach involves identifying the optimal vehicle flow that minimizes total travel time, given the constant travel demands in urban areas. We then develop a heuristic route-recovery algorithm to assign routes to CAVs that satisfy all travel demands while maintaining the optimal flow. Our method lets CAVs arrive at each road segment at their desired arrival time based on their assigned route and desired flow. In addition, we present an efficient coordination framework to minimize the energy consumption of CAVs and prevent collisions while crossing intersections. The proposed method can effectively generate optimal vehicle flow and potentially reduce travel time and energy consumption in urban areas.Comment: 7 pages, 7 figure

Nuclear spin-lattice relaxation rate in the D+iD superconducting state: implications for CoO superconductor

We calculated the nuclear spin-lattice relaxation rate $1/T_1$ for the D+iD superconducting state with impurities. We found that small amount of unitary impurities quickly produces the residual density of states inside the gap. As a result, the T-linear behavior in 1/T$_1$ is observed at low temperatures. Our results show that the D+iD pairing symmetry of the superconducting state of Na$_{0.35}$CoO$_{2} \cdot y$H$_2$ O is compatible with recent $^{59}$Co 1/T$_1$ experiments of several groups.Comment: 5 pages, 4 figures, minor change