548 research outputs found

### Dirichlet-to-Neumann maps on bounded Lipschitz domains

The Dirichlet-to-Neumann map associated to an elliptic partial differential
equation becomes multivalued when the underlying Dirichlet problem is not
uniquely solvable. The main objective of this paper is to present a systematic
study of the Dirichlet-to-Neumann map and its inverse, the Neumann-to-Dirichlet
map, in the framework of linear relations in Hilbert spaces. Our treatment is
inspired by abstract methods from extension theory of symmetric operators,
utilizes the general theory of linear relations and makes use of some deep
results on the regularity of the solutions of boundary value problems on
bounded Lipschitz domains

### Scattering Theory for Open Quantum Systems

Quantum systems which interact with their environment are often modeled by
maximal dissipative operators or so-called Pseudo-Hamiltonians. In this paper
the scattering theory for such open systems is considered. First it is assumed
that a single maximal dissipative operator $A_D$ in a Hilbert space \sH is
used to describe an open quantum system. In this case the minimal self-adjoint
dilation $\widetilde K$ of $A_D$ can be regarded as the Hamiltonian of a closed
system which contains the open system \{A_D,\sH\}, but since $\widetilde K$
is necessarily not semibounded from below, this model is difficult to interpret
from a physical point of view. In the second part of the paper an open quantum
system is modeled with a family $\{A(\mu)\}$ of maximal dissipative operators
depending on energy $\mu$, and it is shown that the open system can be embedded
into a closed system where the Hamiltonian is semibounded. Surprisingly it
turns out that the corresponding scattering matrix can be completely recovered
from scattering matrices of single Pseudo-Hamiltonians as in the first part of
the paper. The general results are applied to a class of Sturm-Liouville
operators arising in dissipative and quantum transmitting
Schr\"{o}dinger-Poisson systems

### Entropy of N=2 black holes and their M-brane description

In this paper we discuss the M-brane description for a N=2 black hole. This
solution is a result of the compactification of M-5-brane configurations over a
Calabi-Yau threefold with arbitrary intersection numbers $C_{ABC}$. In analogy
to the D-brane description where one counts open string states we count here
open 2-branes which end on the M-5-brane.Comment: 12 pages, (hyper) LaTeX, (minor changes and refs. added

### Superpotentials from flux compactifications of M-theory

In flux compactifications of M-theory a superpotential is generated whose
explicit form depends on the structure group of the 7-dimensional internal
manifold. In this note, we discuss superpotentials for the structure groups:
G_2, SU(3) or SU(2). For the G_2 case all internal fluxes have to vanish. For
SU(3) structures, the non-zero flux components entering the superpotential
describe an effective 1-dimensional model and a Chern-Simons model if there are
SU(2) structures.Comment: 10 page

### Bent BPS domain walls of D=5 N=2 gauged supergravity coupled to hypermultiplets

Within D=5 N=2 gauged supergravity coupled to hypermultiplets we derive
consistency conditions for BPS domain walls with constant negative curvature on
the wall. For such wall solutions to exist, the covariant derivative of the
projector, governing the constraint on the Killing spinor, has to be non-zero
and proportional to the cosmological constant on the domain walls. We also
prove that in this case solutions of the Killing spinor equations are solutions
of the equations of motion. We present explicit, analytically solved examples
of such domain walls, employing the universal hypermultiplet fields. These
examples involve the running of two scalar fields and the space-time in the
transverse direction that is cut off at a critical distance, governed by the
magnitude of the negative cosmological constant on the wall.Comment: 18 pages, Late

### Time-dependent backgrounds from supergravity with gauged non-compact R-symmetry

We obtain a general class of time-dependent, asymptotically de Sitter
backgrounds which solve the first order bosonic equations that extremize the
action for supergravity with gauged non-compact $R$-symmetry. These backgrounds
correspond only to neutral fields with the correct sign of kinetic energy.
Within N=2 five-dimensional supergravity with vector-superfields we provide
examples of multi-centered charged black holes in asymptotic de Sitter space,
whose spatial part is given by a time-dependent hyper-K\"ahler space. Reducing
these backgrounds to four dimensions yields asymptotically de Sitter
multi-centered charged black hole backgrounds and we show that they are related
to an instanton configuration by a massive T-duality over time. Within N=2
gauged supergravity in four (and five)-dimensions with hyper-multiplets there
could also be neutral cosmological backgrounds that are regular and correspond
to the different de Sitter spaces at early and late times.Comment: 28 pages, Latex; minor changes and add reference

### Towards Quantum Cosmology without Singularities

In this paper we investigate the vanishing of cosmological singularities by
quantization. Starting from a 5d Kaluza--Klein approach we quantize, as a first
step, the non--spherical metric part and the dilaton field. These fields which
are classically singular become smooth after quantization. In addition, we
argue that the incorporation of non perturbative quantum corrections form a
dilaton potential. Technically, the procedure corresponds to the quantization
of 2d dilaton gravity and we discuss several models. From the 4d point of view
this procedure is a semiclassical approach where only the dilaton and moduli
matter fields are quantized.Comment: 9 pages, 2 figures, Latex, epsfig.sty, epsf.te

### BPS equations in N=2, D=5 supergravity with hypermultiplets

With the general aim to classify BPS solutions in N=2, D=5 supergravities
interacting with an arbitrary number of vector, tensor and hypermultiplets,
here we begin considering the most general electrostatic, spherical-symmetric
BPS solutions in the presence of hypermultiplet couplings. We discuss the
properties of the BPS equations and the restrictions imposed by their
integrability conditions. We exhibit explicit solutions for the case of static
BPS black-holes coupled to one (the so called universal) hypermultiplet.Comment: 20 pages, v3 some corrections performed; we thank A.Van Proeyen for
the pointing ou

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