Quasi-Phase Transition and Many-Spin Kondo Effects in Graphene Nanodisk

The trigonal zigzag nanodisk with size $N$ has $N$ localized spins. We investigate its thermodynamical properties with and without external leads. Leads are made of zigzag graphene nanoribbons or ordinary metallic wires. There exists a quasi-phase transition between the quasi-ferromagnet and quasi-paramagnet states, as signaled by a sharp peak in the specific heat and in the susceptability. Lead effects are described by the many-spin Kondo Hamiltonian. A new peak emerges in the specific heat. Furthermore, the band width of free electrons in metallic leads becomes narrower. By investigating the spin-spin correlation it is argued that free electrons in the lead form spin-singlets with electrons in the nanodisk. They are indications of many-spin Kondo effects.Comment: 5 pages, 5 figure

Quasinormal modes of Unruh's Acoustic Black Hole

We have studied the sound perturbation of Unruh's acoustic geometry and we present an exact expression for the quasinormal modes of this geometry. We are obtain that the quasinormal frequencies are pure-imaginary, that give a purely damped modes.Comment: 5 Page

A two-stage approach to relaxation in billiard systems of locally confined hard spheres

We consider the three-dimensional dynamics of systems of many interacting hard spheres, each individually confined to a dispersive environment, and show that the macroscopic limit of such systems is characterized by a coefficient of heat conduction whose value reduces to a dimensional formula in the limit of vanishingly small rate of interaction. It is argued that this limit arises from an effective loss of memory. Similarities with the diffusion of a tagged particle in binary mixtures are emphasized.Comment: Submitted to Chaos, special issue "Statistical Mechanics and Billiard-Type Dynamical Systems

Dispersion relation of the non-linear Klein-Gordon equation through a variational method

We derive approximate expressions for the dispersion relation of the nonlinear Klein-Gordon equation in the case of strong nonlinearities using a method based on the Linear Delta Expansion. All the results obtained in this article are fully analytical, never involve the use of special functions, and can be used to obtain systematic approximations to the exact results to any desired degree of accuracy. We compare our findings with similar results in the literature and show that our approach leads to better and simpler results.Comment: 10 pages, 3 figures, matches published versio

Explicit Solutions for N-Dimensional Schrodinger Equations with Position-Dependent Mass

With the consideration of spherical symmetry for the potential and mass function, one-dimensional solutions of non-relativistic Schrodinger equations with spatially varying effective mass are successfully extended to arbitrary dimensions within the frame of recently developed elegant non-perturbative technique, where the BenDaniel-Duke effective Hamiltonian in one-dimension is assumed like the unperturbed piece, leading to well-known solutions, whereas the modification term due to possible use of other effective Hamiltonians in one-dimension and, together with, the corrections coming from the treatments in higher dimensions are considered as an additional term like the perturbation. Application of the model and its generalization for the completeness are discussed.Comment: 8 pages, no figure

Exact results for spatial decay of the one-body density matrix in low-dimensional insulators

We provide a tight-binding model of insulator, for which we derive an exact analytic form of the one-body density matrix and its large-distance asymptotics in dimensions $D=1,2$. The system is built out of a band of single-particle orbitals in a periodic potential. Breaking of the translational symmetry of the system results in two bands, separated by a direct gap whose width is proportional to the unique energy parameter of the model. The form of the decay is a power law times an exponential. We determine the power in the power law and the correlation length in the exponential, versus the lattice direction, the direct-gap width, and the lattice dimension. In particular, the obtained exact formulae imply that in the diagonal direction of the square lattice the inverse correlation length vanishes linearly with the vanishing gap, while in non-diagonal directions, the linear scaling is replaced by the square root one. Independently of direction, for sufficiently large gaps the inverse correlation length grows logarithmically with the gap width.Comment: 4 pages, 2 figure

Lagrange mesh, relativistic flux tube, and rotating string

The Lagrange mesh method is a very accurate and simple procedure to compute eigenvalues and eigenfunctions of nonrelativistic and semirelativistic Hamiltonians. We show here that it can be used successfully to solve the equations of both the relativistic flux tube model and the rotating string model, in the symmetric case. Verifications of the convergence of the method are given.Comment: 2 figure

Upper limit on the critical strength of central potentials in relativistic quantum mechanics

In the context of relativistic quantum mechanics, where the Schr\"odinger equation is replaced by the spinless Salpeter equation, we show how to construct a large class of upper limits on the critical value, $g_{\rm{c}}^{(\ell)}$, of the coupling constant, $g$, of the central potential, $V(r)=-g v(r)$. This critical value is the value of $g$ for which a first $\ell$-wave bound state appears.Comment: 8 page

Municipal Solid Waste Flow Control in the Post-Carbone World

Garbage will always ultimately be the government\u27s problem. Evolving environmental standards and state and federal policies will continue to require reasoned responses from local governments and municipal solid waste flow control is a vital cog in many jurisdictions\u27 solid waste management solutions. Without flow control of some form, governments\u27 ability to plan and provide for the most environmentally sound and economically acceptable solutions will wane, leaving the public vulnerable to the vagaries of a private market that does not have a duty to protect the public health and safety. The Carbone decision has blunted one of the local governments chief weapons-legislative flow control-and it appears Congress will not supply an adequate answer for many solid waste systems. More than ever, alternatives to legislative flow control will be needed to enable municipalities to fulfill their solid waste duties, to comply with federal and state mandates, and to provide workable, environmentally-sound, long-term solid waste programs serving the interests of the public health and safety. Local governments must act soon by examining these options and deciding which will best serve the public

Global boundary conditions for a Dirac operator on the solid torus

We study a Dirac operator subject to Atiayh-Patodi-Singer like boundary conditions on the solid torus and show that the corresponding boundary value problem is elliptic, in the sense that the Dirac operator has a compact parametrix