10,150 research outputs found

### 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

### 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

### 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

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