16,760 research outputs found
Constraint-preserving boundary treatment for a harmonic formulation of the Einstein equations
We present a set of well-posed constraint-preserving boundary conditions for
a first-order in time, second-order in space, harmonic formulation of the
Einstein equations. The boundary conditions are tested using robust stability,
linear and nonlinear waves, and are found to be both less reflective and
constraint preserving than standard Sommerfeld-type boundary conditions.Comment: 18 pages, 7 figures, accepted in CQ
Casimir densities for a spherical boundary in de Sitter spacetime
Two-point functions, mean-squared fluctuations, and the vacuum expectation
value of the energy-momentum tensor operator are investigated for a massive
scalar field with an arbitrary curvature coupling parameter, subject to a
spherical boundary in the background of de Sitter spacetime. The field is
prepared in the Bunch-Davies vacuum state and is constrained to satisfy Robin
boundary conditions on the sphere. Both the interior and exterior regions are
considered. For the calculation in the interior region, a mode-summation method
is employed, supplemented with a variant of the generalized Abel-Plana formula.
This allows us to explicitly extract the contributions to the expectation
values which come from de Sitter spacetime without boundaries. We show that the
vacuum energy-momentum tensor is non-diagonal with the off-diagonal component
corresponding to the energy flux along the radial direction. With dependence on
the boundary condition and the mass of the field, this flux can be either
positive or negative. Several limiting cases of interest are then studied. In
terms of the curvature coupling parameter and the mass of the field, two very
different regimes are realized, which exhibit monotonic and oscillatory
behavior of the vacuum expectation values, respectively, far from the sphere.
The decay of the boundary induced expectation values at large distances from
the sphere is shown to be power-law (monotonic or oscillating), independent of
the value of the field mass.Comment: 32 pages, 4 figures, new paragraph about generalizations, discussion
and references added, accepted for publication in Phys. Rev.
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
Tagged particle in single-file diffusion
Single-file diffusion is a one-dimensional interacting infinite-particle
system in which the order of particles never changes. An intriguing feature of
single-file diffusion is that the mean-square displacement of a tagged particle
exhibits an anomalously slow sub-diffusive growth. We study the full statistics
of the displacement using a macroscopic fluctuation theory. For the simplest
single-file system of impenetrable Brownian particles we compute the large
deviation function and provide an independent verification using an exact
solution based on the microscopic dynamics. For an arbitrary single-file
system, we apply perturbation techniques and derive an explicit formula for the
variance in terms of the transport coefficients. The same method also allows us
to compute the fourth cumulant of the tagged particle displacement for the
symmetric exclusion process.Comment: 34 pages, to appear in Journal of Statistical Physics (2015
Strongly localised molecular orbitals for -quartz
A previously proposed computational procedure for constructing a set of
nonorthogonal strongly localised one-electron molecular orbitals (O. Danyliv,
L. Kantorovich - physics/0401107) is applied to a perfect -quartz
crystal characterised by an intermediate type of chemical bonding. The orbitals
are constructed by applying various localisation methods to canonical
Hartree-Fock orbitals calculated for a succession of finite molecular clusters
of increased size with appropriate boundary conditions. The calculated orbitals
span the same occupied Fock space as the canonical HF solutions, but have an
advantage of reflecting the true chemical nature of the bonding in the system.
The applicability of several localisation techniques as well as of a number of
possible choices of localisation regions (structure elements) are discussed for
this system in detail
Fine structures in the spectrum of the open-boundary Heisenberg chain at large anisotropies
At large anisotropies, the spectrum of the Heisenberg XXZ spin chain
separates into `bands' with energies largely determined by the number of domain
walls. The band structure is richer with open boundary conditions: there are
more bands and the bands develop intricate fine structures. We characterize and
explain these structures and substructures in the open-boundary chain. The fine
structures are explained using degenerate perturbation theory. We also present
some dynamical consequences of these sub-band structures, through explicit time
evolution of the wavefunction from initial states motivated by the fine
structure analysis
Massless black holes and black rings as effective geometries of the D1-D5 system
We compute correlation functions in the AdS/CFT correspondence to study the
emergence of effective spacetime geometries describing complex underlying
microstates. The basic argument is that almost all microstates of fixed charges
lie close to certain "typical" configurations. These give a universal response
to generic probes, which is captured by an emergent geometry. The details of
the microstates can only be observed by atypical probes. We compute two point
functions in typical ground states of the Ramond sector of the D1-D5 CFT, and
compare with bulk two-point functions computed in asymptotically AdS_3
geometries. For large central charge (which leads to a good semiclassical
limit), and sufficiently small time separation, a typical Ramond ground state
of vanishing R-charge has the M=0 BTZ black hole as its effective description.
At large time separation this effective description breaks down. The CFT
correlators we compute take over, and give a response whose details depend on
the microstate. We also discuss typical states with nonzero R-charge, and argue
that the effective geometry should be a singular black ring. Our results
support the argument that a black hole geometry should be understood as an
effective coarse-grained description that accurately describes the results of
certain typical measurements, but breaks down in general.Comment: 47 pages, 4 figures. v2: references added. v3: minor corrections to
Appendix A, references adde
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