1,980 research outputs found
Statistical Entropy of Schwarzschild Black Holes
The entropy of a seven dimensional Schwarzschild black hole of arbitrary
large radius is obtained by a mapping onto a near extremal self-dual
three-brane whose partition function can be evaluated. The three-brane arises
from duality after submitting a neutral blackbrane, from which the
Schwarzschild black hole can be obtained by compactification, to an infinite
boost in non compact eleven dimensional space-time and then to a Kaluza-Klein
compactification. This limit can be defined in precise terms and yields the
Bekenstein-Hawking value up to a factor of order one which can be set to be
exactly one with the extra assumption of keeping only transverse brane
excitations. The method can be generalized to five and four dimensional black
holes.Comment: 11 pages, LaTex, no figures, corrected typ
A simple minimax estimator for quantum states
Quantum tomography requires repeated measurements of many copies of the
physical system, all prepared by a source in the unknown state. In the limit of
very many copies measured, the often-used maximum-likelihood (ML) method for
converting the gathered data into an estimate of the state works very well. For
smaller data sets, however, it often suffers from problems of rank deficiency
in the estimated state. For many systems of relevance for quantum information
processing, the preparation of a very large number of copies of the same
quantum state is still a technological challenge, which motivates us to look
for estimation strategies that perform well even when there is not much data.
In this article, we review the concept of minimax state estimation, and use
minimax ideas to construct a simple estimator for quantum states. We
demonstrate that, for the case of tomography of a single qubit, our estimator
significantly outperforms the ML estimator for small number of copies of the
state measured. Our estimator is always full-rank, and furthermore, has a
natural dependence on the number of copies measured, which is missing in the ML
estimator.Comment: 26 pages, 3 figures. v2 contains minor improvements to the text, and
an additional appendix on symmetric measurement
On Visibility in the Afshar Two-Slit Experiment
A modified version of Young's experiment by Shahriar Afshar indirectly
reveals the presence of a fully articulated interference pattern prior to the
post-selection of a particle in a "which-slit" basis. While this experiment
does not constitute a violation of Bohr's Complementarity Principle as claimed
by Afshar, both he and many of his critics incorrectly assume that a commonly
used relationship between visibility parameter V and "which-way" parameter K
has crucial relevance to his experiment. It is argued here that this
relationship does not apply to this experimental situation and that it is wrong
to make any use of it in support of claims for or against the bearing of this
experiment on Complementarity.Comment: Final version; to appear in Foundations of Physic
G+++ Invariant Formulation of Gravity and M-Theories: Exact BPS Solutions
We present a tentative formulation of theories of gravity with suitable
matter content, including in particular pure gravity in D dimensions, the
bosonic effective actions of M-theory and of the bosonic string, in terms of
actions invariant under very-extended Kac-Moody algebras G+++. We conjecture
that they host additional degrees of freedom not contained in the conventional
theories. The actions are constructed in a recursive way from a level expansion
for all very-extended algebras G+++. They constitute non-linear realisations on
cosets, a priori unrelated to space-time, obtained from a modified Chevalley
involution. Exact solutions are found for all G+++. They describe the algebraic
properties of BPS extremal branes, Kaluza-Klein waves and Kaluza-Klein
monopoles. They illustrate the generalisation to all G+++ invariant theories of
the well-known duality properties of string theories by expressing duality as
Weyl invariance in G+++. Space-time is expected to be generated dynamically. In
the level decomposition of E8+++ = E11, one may indeed select an A10
representation of generators Pa which appears to engender space-time
translations by inducing infinite towers of fields interpretable as field
derivatives in space and time.Comment: Latex 45 pages, 1 figure. Discussion on pages 19 and 20 altered.
Appendix B amplified. 4 footnotes added. 2 references added. Acknowledgments
updated. Additional minor correction
Kac-Moody Symmetries of Ten-dimensional Non-maximal Supergravity Theories
A description of the bosonic sector of ten-dimensional N=1 supergravity as a
non-linear realisation is given. We show that if a suitable extension of this
theory were invariant under a Kac-Moody algebra, then this algebra would have
to contain a rank eleven Kac-Moody algebra, that can be identified to be a
particular real form of very-extended D_8. We also describe the extension of
N=1 supergravity coupled to an abelian vector gauge field as a non-linear
realisation, and find the Kac-Moody algebra governing the symmetries of this
theory to be very-extended B_8. Finally, we discuss the related points for the
N=1 supergravity coupled to an arbitrary number of abelian vector gauge fields
Strong-driving-assisted multipartite entanglement in cavity QED
We propose a method of generating multipartite entanglement by considering
the interaction of a system of N two-level atoms in a cavity of high quality
factor with a strong classical driving field. It is shown that, with a
judicious choice of the cavity detuning and the applied coherent field
detuning, vacuum Rabi coupling produces a large number of important
multipartite entangled states. It is even possible to produce entangled states
involving different cavity modes. Tuning of parameters also permits us to
switch from Jaynes-Cummings to anti-Jaynes-Cummings like interaction.Comment: Last version with minor changes and added references. Accepted for
publication in Phys. Rev. Letter
An E9 multiplet of BPS states
We construct an infinite E9 multiplet of BPS states for 11D supergravity. For
each positive real root of E9 we obtain a BPS solution of 11D supergravity, or
of its exotic counterparts, depending on two non-compact transverse space
variables. All these solutions are related by U-dualities realised via E9 Weyl
transformations in the regular embedding of E9 in E10, E10 in E11. In this way
we recover the basic BPS solutions, namely the KK-wave, the M2 brane, the M5
brane and the KK6-monopole, as well as other solutions admitting eight
longitudinal space dimensions. A novel technique of combining Weyl reflexions
with compensating transformations allows the construction of many new BPS
solutions, each of which can be mapped to a solution of a dual effective action
of gravity coupled to a certain higher rank tensor field. For real roots of E10
which are not roots of E9, we obtain additional BPS solutions transcending 11D
supergravity (as exemplified by the lowest level solution corresponding to the
M9 brane). The relation between the dual formulation and the one in terms of
the original 11D supergravity fields has significance beyond the realm of BPS
solutions. We establish the link with the Geroch group of general relativity,
and explain how the E9 duality transformations generalize the standard Hodge
dualities to an infinite set of `non-closing dualities'.Comment: 76 pages, 6 figure
Ionization potentials in the limit of large atomic number
By extrapolating the energies of non-relativistic atoms and their ions with
up to 3000 electrons within Kohn-Sham density functional theory, we find that
the ionization potential remains finite and increases across a row, even as
. The local density approximation becomes chemically
accurate (and possibly exact) in some cases. Extended Thomas-Fermi theory
matches the shell-average of both the ionization potential and density change.
Exact results are given in the limit of weak electron-electron repulsion.Comment: 4 pages, 5 figure
Average transmission probability of a random stack
The transmission through a stack of identical slabs that are separated by
gaps with random widths is usually treated by calculating the average of the
logarithm of the transmission probability. We show how to calculate the average
of the transmission probability itself with the aid of a recurrence relation
and derive analytical upper and lower bounds. The upper bound, when used as an
approximation for the transmission probability, is unreasonably good and we
conjecture that it is asymptotically exact.Comment: 10 pages, 6 figure
- …