67 research outputs found
Analytic Approximation of the Tavis-Cummings Ground State via Projected States
We show that an excellent approximation to the exact quantum solution of the
ground state of the Tavis-Cummings model is obtained by means of a
semi-classical projected state. This state has an analytical form in terms of
the model parameters and, in contrast to the exact quantum state, it allows for
an analytical calculation of the expectation values of field and matter
observables, entanglement entropy between field and matter, squeezing
parameter, and population probability distributions. The fidelity between this
projected state and the exact quantum ground state is very close to 1, except
for the region of classical phase transitions. We compare the analytical
results with those of the exact solution obtained through the direct
Hamiltonian diagonalization as a function of the atomic separation energy and
the matter-field coupling.Comment: 22 pages, 13 figures, accepted for publication in Physics Script
Mass and Spin of Poincare Gauge Theory
We discuss two expressions for the conserved quantities (energy momentum and
angular momentum) of the Poincar\'e Gauge Theory. We show, that the variations
of the Hamiltonians, of which the expressions are the respective boundary
terms, are well defined, if we choose an appropriate phase space for asymptotic
flat gravitating systems. Furthermore, we compare the expressions with others,
known from the literature.Comment: 16 pages, plain-tex; to be published in Gen. Rel. Gra
On the Spectrum of Field Quadratures for a Finite Number of Photons
The spectrum and eigenstates of any field quadrature operator restricted to a
finite number of photons are studied, in terms of the Hermite polynomials.
By (naturally) defining \textit{approximate} eigenstates, which represent
highly localized wavefunctions with up to photons, one can arrive at an
appropriate notion of limit for the spectrum of the quadrature as goes to
infinity, in the sense that the limit coincides with the spectrum of the
infinite-dimensional quadrature operator. In particular, this notion allows the
spectra of truncated phase operators to tend to the complete unit circle, as
one would expect. A regular structure for the zeros of the Christoffel-Darboux
kernel is also shown.Comment: 16 pages, 11 figure
Energy extremality in the presence of a black hole
We derive the so-called first law of black hole mechanics for variations
about stationary black hole solutions to the Einstein--Maxwell equations in the
absence of sources. That is, we prove that where the black hole parameters and denote mass, surface gravity, horizon area, angular velocity of the
horizon, angular momentum, electric potential of the horizon and charge
respectively. The unvaried fields are those of a stationary, charged, rotating
black hole and the variation is to an arbitrary `nearby' black hole which is
not necessarily stationary. Our approach is 4-dimensional in spirit and uses
techniques involving Action variations and Noether operators. We show that the
above formula holds on any asymptotically flat spatial 3-slice which extends
from an arbitrary cross-section of the (future) horizon to spatial
infinity.(Thus, the existence of a bifurcation surface is irrelevant to our
demonstration. On the other hand, the derivation assumes without proof that the
horizon possesses at least one of the following two (related)properties: ()
it cannot be destroyed by arbitrarily small perturbations of the metric and
other fields which may be present, () the expansion of the null geodesic
generators of the perturbed horizon goes to zero in the distant future.)Comment: 30 pages, latex fil
Isotropization of Bianchi type models and a new FRW solution in Brans-Dicke theory
Using scaled variables we are able to integrate an equation valid for
isotropic and anisotropic Bianchi type I, V, IX models in Brans-Dicke (BD)
theory. We analyze known and new solutions for these models in relation with
the possibility that anisotropic models asymptotically isotropize, and/or
possess inflationary properties. In particular, a new solution of curve
() Friedmann-Robertson-Walker (FRW) cosmologies in Brans-Dicke theory
is analyzed.Comment: 15 pages, 4 postscript figures, to appear in Gen. Rel. Grav., special
issue dedicated in honour of Prof. H. Dehne
Kerr-Schild Symmetries
We study continuous groups of generalized Kerr-Schild transformations and the
vector fields that generate them in any n-dimensional manifold with a
Lorentzian metric. We prove that all these vector fields can be intrinsically
characterized and that they constitute a Lie algebra if the null deformation
direction is fixed. The properties of these Lie algebras are briefly analyzed
and we show that they are generically finite-dimensional but that they may have
infinite dimension in some relevant situations. The most general vector fields
of the above type are explicitly constructed for the following cases: any
two-dimensional metric, the general spherically symmetric metric and
deformation direction, and the flat metric with parallel or cylindrical
deformation directions.Comment: 15 pages, no figures, LaTe
Dynamic Interpretation of Hedgehog Signaling in the Drosophila Wing Disc
Morphogens are classically defined as molecules that control patterning by acting at a distance to regulate gene expression in a concentration-dependent manner. In the Drosophila wing imaginal disc, secreted Hedgehog (Hh) forms an extracellular gradient that organizes patterning along the anterior–posterior axis and specifies at least three different domains of gene expression. Although the prevailing view is that Hh functions in the Drosophila wing disc as a classical morphogen, a direct correspondence between the borders of these patterns and Hh concentration thresholds has not been demonstrated. Here, we provide evidence that the interpretation of Hh signaling depends on the history of exposure to Hh and propose that a single concentration threshold is sufficient to support multiple outputs. Using mathematical modeling, we predict that at steady state, only two domains can be defined in response to Hh, suggesting that the boundaries of two or more gene expression patterns cannot be specified by a static Hh gradient. Computer simulations suggest that a spatial “overshoot” of the Hh gradient occurs, i.e., a transient state in which the Hh profile is expanded compared to the Hh steady-state gradient. Through a temporal examination of Hh target gene expression, we observe that the patterns initially expand anteriorly and then refine, providing in vivo evidence for the overshoot. The Hh gene network architecture suggests this overshoot results from the Hh-dependent up-regulation of the receptor, Patched (Ptc). In fact, when the network structure was altered such that the ptc gene is no longer up-regulated in response to Hh-signaling activation, we found that the patterns of gene expression, which have distinct borders in wild-type discs, now overlap. Our results support a model in which Hh gradient dynamics, resulting from Ptc up-regulation, play an instructional role in the establishment of patterns of gene expression
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