235 research outputs found
Evaporation induced traversability of the Einstein--Rosen wormhole
Suppose, the Universe comes into existence (as classical spacetime) already
with an empty spherically symmetric macroscopic wormhole present in it.
Classically the wormhole would evolve into a part of the Schwarzschild space
and thus would not allow any signal to traverse it. I consider semiclassical
corrections to that picture and build a model of an evaporating wormhole. The
model is based on the assumption that the vacuum polarization and its
backreaction on the geometry of the wormhole are weak. The lack of information
about the era preceding the emergence of the wormhole results in appearance of
three parameters which -- along with the initial mass -- determine the
evolution of the wormhole. For some values of these parameters the wormhole
turns out to be long-lived enough to be traversed and to transform into a time
machine.Comment: v.2 A bit of discussion has been added and a few references v.3
Insignificant changes to match the published versio
Landau-Zener problem for energies close to potential crossing points
We examine one overlooked in previous investigations aspect of well - known
Landau - Zener (LZ) problem, namely, the behavior in the intermediate, i.e.
close to a crossing point, energy region, when all four LZ states are coupled
and should be taken into account. We calculate the 4 x 4 connection matrix in
this intermediate energy region, possessing the same block structure as the
known connection matrices for the tunneling and in the over-barrier regions of
the energy, and continously matching those in the corresponding energy regions.Comment: 5 pages, 1 figur
Analytic approach to bifurcation cascades in a class of generalized H\'enon-Heiles potentials
We derive stability traces of bifurcating orbits in H\'enon-Heiles potentials
near their saddlesComment: LaTeX revtex4, 38 pages, 7 PostScript figures, 2 table
A generalized virial theorem and the balance of kinetic and potential energies in the semiclassical limit
We obtain two-sided bounds on kinetic and potential energies of a bound state
of a quantum particle in the semiclassical limit, as the Planck constant
\hbar\ri 0.
Proofs of these results rely on the generalized virial theorem obtained in
the paper as well as on a decay of eigenfunctions in the classically forbidden
region
Effective action and heat kernel in a toy model of brane-induced gravity
We apply a recently suggested technique of the Neumann-Dirichlet reduction to
a toy model of brane-induced gravity for the calculation of its quantum
one-loop effective action. This model is represented by a massive scalar field
in the -dimensional flat bulk supplied with the -dimensional kinetic
term localized on a flat brane and mimicking the brane Einstein term of the
Dvali-Gabadadze-Porrati (DGP) model. We obtain the inverse mass expansion of
the effective action and its ultraviolet divergences which turn out to be
non-vanishing for both even and odd spacetime dimensionality . For the
massless case, which corresponds to a limit of the toy DGP model, we obtain the
Coleman-Weinberg type effective potential of the system. We also obtain the
proper time expansion of the heat kernel in this model associated with the
generalized Neumann boundary conditions containing second order tangential
derivatives. We show that in addition to the usual integer and half-integer
powers of the proper time this expansion exhibits, depending on the dimension
, either logarithmic terms or powers multiple of one quarter. This property
is considered in the context of strong ellipticity of the boundary value
problem, which can be violated when the Euclidean action of the theory is not
positive definite.Comment: LaTeX, 20 pages, new references added, typos correcte
Asymptotic Expansion for the Wave Function in a one-dimensional Model of Inelastic Interaction
We consider a two-body quantum system in dimension one composed by a test
particle interacting with an harmonic oscillator placed at the position .
At time zero the test particle is concentrated around the position with
average velocity while the oscillator is in its ground state. In a
suitable scaling limit, corresponding for the test particle to a semi-classical
regime with small energy exchange with the oscillator, we give a complete
asymptotic expansion of the wave function of the system in both cases
and .Comment: 23 page
Nonlinear modes for the Gross-Pitaevskii equation -- demonstrative computation approach
A method for the study of steady-state nonlinear modes for Gross-Pitaevskii
equation (GPE) is described. It is based on exact statement about coding of the
steady-state solutions of GPE which vanish as by reals. This
allows to fulfill {\it demonstrative computation} of nonlinear modes of GPE
i.e. the computation which allows to guarantee that {\it all} nonlinear modes
within a given range of parameters have been found. The method has been applied
to GPE with quadratic and double-well potential, for both, repulsive and
attractive nonlinearities. The bifurcation diagrams of nonlinear modes in these
cases are represented. The stability of these modes has been discussed.Comment: 21 pages, 6 figure
A large time asymptotics for transparent potentials for the Novikov-Veselov equation at positive energy
In the present paper we begin studies on the large time asymptotic behavior
for solutions of the Cauchy problem for the Novikov--Veselov equation (an
analog of KdV in 2 + 1 dimensions) at positive energy. In addition, we are
focused on a family of reflectionless (transparent) potentials parameterized by
a function of two variables. In particular, we show that there are no isolated
soliton type waves in the large time asymptotics for these solutions in
contrast with well-known large time asymptotics for solutions of the KdV
equation with reflectionless initial data
Mean Field Model of Coagulation and Annihilation Reactions in a Medium of Quenched Traps: Subdiffusion
We present a mean field model for coagulation () and annihilation
() reactions on lattices of traps with a distribution of depths
reflected in a distribution of mean escape times. The escape time from each
trap is exponentially distributed about the mean for that trap, and the
distribution of mean escape times is a power law. Even in the absence of
reactions, the distribution of particles over sites changes with time as
particles are caught in ever deeper traps, that is, the distribution exhibits
aging. Our main goal is to explore whether the reactions lead to further (time
dependent) changes in this distribution.Comment: 9 pages, 3 figure
Asymptotic estimation of some multiple integrals and the electromagnetic deuteron form factors at high momentum transfer
A theorem about asymptotic estimation of multiple integral of a special type
is proved for the case when the integrand peaks at the integration domain
bound, but not at a point of extremum. Using this theorem the asymptotic
expansion of the electromagnetic deuteron form factors at high momentum
transfers is obtained in the framework of two-nucleon model in both
nonrelativistic and relativistic impulse approximations. It is found that
relativistic effects slow down the decrease of deuteron form factors and result
in agreement between the relativistic asymptotics and experimental data at high
momentum transfers.Comment: 16 pages, 1 figur
- …