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

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

Perturbation hydrogen-atom spectrum in deformed space with minimal length

We study energy spectrum for hydrogen atom with deformed Heisenberg algebra leading to minimal length. We develop correct perturbation theory free of divergences. It gives a possibility to calculate analytically in the 3D case the corrections to $s$-levels of hydrogen atom caused by the minimal length. Comparing our result with experimental data from precision hydrogen spectroscopy an upper bound for the minimal length is obtained.Comment: 9 pages, 3 figure

Vacuum energy between a sphere and a plane at finite temperature

We consider the Casimir effect for a sphere in front of a plane at finite temperature for scalar and electromagnetic fields and calculate the limiting cases. For small separation we compare the exact results with the corresponding ones obtained in proximity force approximation. For the scalar field with Dirichlet boundary conditions, the low temperature correction is of order $T^2$ like for parallel planes. For the electromagnetic field it is of order $T^4$. For high temperature we observe the usual picture that the leading order is given by the zeroth Matsubara frequency. The non-zero frequencies are exponentially suppressed except for the case of close separation.Comment: 14 pages, 3 figures, revised version with several improvement

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

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

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

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

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