3,174 research outputs found
Discrete quantum modes of the Dirac field in backgrounds
It is shown that the free Dirac equation in spherically symmetric static
backgrounds of any dimensions can be put in a simple form using a special
version of Cartesian gauge in Cartesian coordinates. This is manifestly
covariant under the transformations of the isometry group so that the
generalized spherical coordinates can be separated in terms of angular spinors
like in the flat case, obtaining a pair of radial equations. In this approach
the equation of the free field Dirac in backgrounds is analytically
solved obtaining the formula of the energy levels and the corresponding
normalized eigenspinors.Comment: 18 pages, Latex. Submitted to Phys.Rev.
Approximative analytical solutions of the Dirac equation in Schwarzschild spacetime
Approximative analytic solutions of the Dirac equation in the geometry of
Schwarzschild black holes are derived obtaining information about the discrete
energy levels and the asymptotic behavior of the energy eigenspinors.Comment: 8 page
On the convergence of second order spectra and multiplicity
Let A be a self-adjoint operator acting on a Hilbert space. The notion of
second order spectrum of A relative to a given finite-dimensional subspace L
has been studied recently in connection with the phenomenon of spectral
pollution in the Galerkin method. We establish in this paper a general
framework allowing us to determine how the second order spectrum encodes
precise information about the multiplicity of the isolated eigenvalues of A.
Our theoretical findings are supported by various numerical experiments on the
computation of inclusions for eigenvalues of benchmark differential operators
via finite element bases.Comment: 22 pages, 2 figures, 4 tables, research paper
Maximal extension of the Schwarzschild spacetime inspired by noncommutative geometry
We derive a transformation of the noncommutative geometry inspired
Schwarzschild solution into new coordinates such that the apparent unphysical
singularities of the metric are removed. Moreover, we give the maximal
singularity-free atlas for the manifold with the metric under consideration.
This atlas reveals many new features e.g. it turns out to describe an infinite
lattice of asymptotically flat universes connected by black hole tunnels.Comment: 17 pages LaTex, 2 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
like for parallel planes. For the electromagnetic field it is of order .
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
Birefringent Gravitational Waves and the Consistency Check of Inflation
In this work we show that the gravitational Chern-Simons term, aside from
being a key ingredient in inflationary baryogenesis, modifies super-horizon
gravitational waves produced during inflation. We compute the super-Hubble
gravitational power spectrum in the slow-roll approximation and show that its
overall amplitude is modified while its spectral index remains unchanged (at
leading order in the slow-roll parameters). Then, we calculate the correction
to the tensor to scalar ratio, T/S. We find a correction of T/S which is
dependent on (more precisely quadratic in ), the parameter
characterizing the amplitude of the Chern-Simons terms. In a stringy embedding
of the leptogenesis mechanism, is the ratio between the Planck scale
and the fundamental string scale. Thus, in principle, we provide a direct probe
of leptogenesis due to stringy dynamics in the Cosmic Microwave Background
(CMB). However, we demonstrate that the corresponding correction of T/S is in
fact very small and not observable in the regime where our calculations are
valid. To obtain a sizable effect, we argue that a non-linear calculation is
necessary.Comment: 9 pages, 1 figure, RevTe
Position and Momentum Uncertainties of the Normal and Inverted Harmonic Oscillators under the Minimal Length Uncertainty Relation
We analyze the position and momentum uncertainties of the energy eigenstates
of the harmonic oscillator in the context of a deformed quantum mechanics,
namely, that in which the commutator between the position and momentum
operators is given by [x,p]=i\hbar(1+\beta p^2). This deformed commutation
relation leads to the minimal length uncertainty relation \Delta x >
(\hbar/2)(1/\Delta p +\beta\Delta p), which implies that \Delta x ~ 1/\Delta p
at small \Delta p while \Delta x ~ \Delta p at large \Delta p. We find that the
uncertainties of the energy eigenstates of the normal harmonic oscillator
(m>0), derived in Ref. [1], only populate the \Delta x ~ 1/\Delta p branch. The
other branch, \Delta x ~ \Delta p, is found to be populated by the energy
eigenstates of the `inverted' harmonic oscillator (m<0). The Hilbert space in
the 'inverted' case admits an infinite ladder of positive energy eigenstates
provided that \Delta x_{min} = \hbar\sqrt{\beta} > \sqrt{2}
[\hbar^2/k|m|]^{1/4}. Correspondence with the classical limit is also
discussed.Comment: 16 pages, 31 eps figure
Quasi-Ferromagnet Spintronics in Graphene Nanodisk-Lead System
A zigzag graphene nanodisk can be interpreted as a quantum dot with an
internal degree of freedom. It is well described by the infinite-range
Heisenberg model. We have investigated its thermodynamical properties. 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. We have also analyzed how thermodynamical properties are
affected when two leads are attached to the nanodisk. It is shown that lead
effects are described by the many-spin Kondo Hamiltonian. There appears a new
peak in the specific heat, and the multiplicity of the ground state becomes
just one half of the system without leads. Another lead effect is to enhance
the ferromagnetic order. Being a ferromagnet, a nanodisk can be used as a spin
filter. Furthermore, since the relaxation time is finite, it is possible to
control the spin of the nanodisk by an external spin current. We then propose a
rich variety of spintronic devices made of nanodisks and leads, such as spin
memory, spin amplifier, spin valve, spin-field-effect transistor, spin diode
and spin logic gates such as spin-XNOR gate and spin-XOR gate. Graphene
nanodisks could well be basic components of future nanoelectronic and
spintronic devices.Comment: 12 pages, 13 figures, invited paper to "focus on graphene
Theory of 4e versus 2e supercurrent in frustrated Josepshon-junction rhombi chain
We consider a chain of Josepshon-junction rhombi (proposed originally in
\cite{Doucot}) in quantum regime, and in the realistic case when charging
effects are determined by junction capacitances. In the maximally frustrated
case when magnetic flux through each rhombi is equal to one half of
superconductive flux quantum , Josepshon current is due to correlated
transport of {\em pairs of Cooper pairs}, i.e. charge is quantized in units of
. Sufficiently strong deviation from the maximally frustrated point brings the system back to
usual -quantized supercurrent. We present detailed analysis of Josepshon
current in the fluctuation-dominated regime (sufficiently long chains) as
function of the chain length, ratio and flux deviation .
We provide estimates for the set of parameters optimized for the observation of
-supercurrent.Comment: 23 pages, 9 figure
Approximate solutions of the Dirac equation for the Rosen-Morse potential including the spin-orbit centrifugal term
We give the approximate analytic solutions of the Dirac equations for the
Rosen-Morse potential including the spin-orbit centrifugal term. In the
framework of the spin and pseudospin symmetry concept, we obtain the analytic
bound state energy spectra and corresponding two-component upper- and
lower-spinors of the two Dirac particles, in closed form, by means of the
Nikiforov-Uvarov method. The special cases of the s-wave kappa=1,-1 (l=l bar=0)
Rosen-Morse potential, the Eckart-type potential, the PT-symmetric Rosen-Morse
potential and non-relativistic limits are briefly studied.Comment: 23 page
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