1,111 research outputs found
Chern-Simons and Born-Infeld gravity theories and Maxwell algebras type
Recently was shown that standard odd and even-dimensional General Relativity
can be obtained from a -dimensional Chern-Simons Lagrangian invariant
under the algebra and from a -dimensional Born-Infeld
Lagrangian invariant under a subalgebra respectively. Very
Recently, it was shown that the generalized In\"on\"u-Wigner contraction of the
generalized AdS-Maxwell algebras provides Maxwell algebras types
which correspond to the so called Lie algebras. In this article we
report on a simple model that suggests a mechanism by which standard
odd-dimensional General Relativity may emerge as a weak coupling constant limit
of a -dimensional Chern-Simons Lagrangian invariant under the Maxwell
algebra type , if and only if . Similarly, we show
that standard even-dimensional General Relativity emerges as a weak coupling
constant limit of a -dimensional Born-Infeld type Lagrangian invariant
under a subalgebra of the Maxwell algebra type, if and
only if . It is shown that when this is not possible for a
-dimensional Chern-Simons Lagrangian invariant under the
and for a -dimensional Born-Infeld type Lagrangian
invariant under algebra.Comment: 30 pages, accepted for publication in Eur.Phys.J.C. arXiv admin note:
text overlap with arXiv:1309.006
Generalized Poincare algebras and Lovelock-Cartan gravity theory
We show that the Lagrangian for Lovelock-Cartan gravity theory can be
re-formulated as an action which leads to General Relativity in a certain
limit. In odd dimensions the Lagrangian leads to a Chern-Simons theory
invariant under the generalized Poincar\'{e} algebra
while in even dimensions the Lagrangian leads to a Born-Infeld theory invariant
under a subalgebra of the algebra. It is also shown that
torsion may occur explicitly in the Lagrangian leading to new torsional
Lagrangians, which are related to the Chern-Pontryagin character for the
group.Comment: v2: 18 pages, minor modification in the title, some clarifications in
the abstract, introduction and section 2, section 4 has been rewritten, typos
corrected, references added. Accepted for publication in Physic letters
The effect of a velocity barrier on the ballistic transport of Dirac fermions
We propose a novel way to manipulate the transport properties of massless
Dirac fermions by using velocity barriers, defining the region in which the
Fermi velocity, , has a value that differs from the one in the
surrounding background. The idea is based on the fact that when waves travel
accross different media, there are boundary conditions that must be satisfied,
giving rise to Snell's-like laws. We find that the transmission through a
velocity barrier is highly anisotropic, and that perfect transmission always
occurs at normal incidence. When in the barrier is larger that the
velocity outside the barrier, we find that a critical transmission angle
exists, a Brewster-like angle for massless Dirac electrons.Comment: 4.3 pages, 5 figure
Three-dimensional Maxwellian Carroll gravity theory and the cosmological constant
In this work, we present the three-dimensional Maxwell Carroll gravity by considering the ultra-relativistic limit of the Maxwell Chern-Simons gravity theory defined in three spacetime dimensions. We show that an extension of the Maxwellian Carroll symmetry is necessary in order for the invariant tensor of the ultra-relativistic Maxwellian algebra to be non-degenerate. Consequently, we discuss the origin of the aforementioned algebra and theory as a flat limit. We show that the theoretical setup with cosmological constant yielding the extended Maxwellian Carroll Chern-Simons gravity in the vanishing cosmological constant limit is based on a new enlarged extended version of the Carroll symmetry. Indeed, the latter exhibits a non-degenerate invariant tensor allowing the proper construction of a Chern-Simons gravity theory which reproduces the extended Maxwellian Carroll gravity in the flat limit
Wrinkling of a bilayer membrane
The buckling of elastic bodies is a common phenomenon in the mechanics of
solids. Wrinkling of membranes can often be interpreted as buckling under
constraints that prohibit large amplitude deformation. We present a combination
of analytic calculations, experiments, and simulations to understand wrinkling
patterns generated in a bilayer membrane. The model membrane is composed of a
flexible spherical shell that is under tension and that is circumscribed by a
stiff, essentially incompressible strip with bending modulus B. When the
tension is reduced sufficiently to a value \sigma, the strip forms wrinkles
with a uniform wavelength found theoretically and experimentally to be \lambda
= 2\pi(B/\sigma)^{1/3}. Defects in this pattern appear for rapid changes in
tension. Comparison between experiment and simulation further shows that, with
larger reduction of tension, a second generation of wrinkles with longer
wavelength appears only when B is sufficiently small.Comment: 9 pages, 5 color figure
Training quantum measurement devices to discriminate unknown non-orthogonal quantum states
Here, we study the problem of decoding information transmitted through
unknown quantum states. We assume that Alice encodes an alphabet into a set of
orthogonal quantum states, which are then transmitted to Bob. However, the
quantum channel that mediates the transmission maps the orthogonal states into
non-orthogonal states, possibly mixed. If an accurate model of the channel is
unavailable, then the states received by Bob are unknown. In order to decode
the transmitted information we propose to train a measurement device to achieve
the smallest possible error in the discrimination process. This is achieved by
supplementing the quantum channel with a classical one, which allows the
transmission of information required for the training, and resorting to a
noise-tolerant optimization algorithm. We demonstrate the training method in
the case of minimum-error discrimination and show that it achieves error
probabilities very close to the optimal one. In particular, in the case of two
unknown pure states our proposal approaches the Helstrom bound. A similar
result holds for a larger number of states in higher dimensions. We also show
that a reduction of the search space, which is used in the training process,
leads to a considerable reduction in the required resources. Finally, we apply
our proposal to the case of the dephasing channel reaching an accurate value of
the optimal error probability
High-Order SUSY-QM, the Quantum XP Model and zeroes of the Riemann Zeta function
Making use of the first- and second-order algorithms of supersymmetric
quantum mechanics (SUSY-QM), we construct quantum mechanical Hamiltonians whose
spectra are related to the zeroes of the Riemann Zeta function .
Inspired by the model of Das and Kalauni (DK), which corresponds to this
function in the strip , and taking the factorization energy equal to
zero, we use the wave function , , as a seed solution
for our algorithms, obtaining XP-like operators. Thus, we construct SUSY-QM
partner Hamiltonians whose zero energy mode locates exactly the nontrivial
zeroes of along the critical line in the complex plane.
We further find that unlike the DK case, where the SUSY-QM partner potentials
correspond to free particles, our partner potentials belong to the family of
inverse squared distance potentials with complex couplings
Two-sided estimates of minimum-error distinguishability of mixed quantum states via generalized Holevo-Curlander bounds
We prove a concise factor-of-2 estimate for the failure rate of optimally
distinguishing an arbitrary ensemble of mixed quantum states, generalizing work
of Holevo [Theor. Probab. Appl. 23, 411 (1978)] and Curlander [Ph.D. Thesis,
MIT, 1979]. A modification to the minimal principle of Cocha and Poor
[Proceedings of the 6th International Conference on Quantum Communication,
Measurement, and Computing (Rinton, Princeton, NJ, 2003)] is used to derive a
suboptimal measurement which has an error rate within a factor of 2 of the
optimal by construction. This measurement is quadratically weighted and has
appeared as the first iterate of a sequence of measurements proposed by Jezek
et al. [Phys. Rev. A 65, 060301 (2002)]. Unlike the so-called pretty good
measurement, it coincides with Holevo's asymptotically optimal measurement in
the case of nonequiprobable pure states. A quadratically weighted version of
the measurement bound by Barnum and Knill [J. Math. Phys. 43, 2097 (2002)] is
proven. Bounds on the distinguishability of syndromes in the sense of
Schumacher and Westmoreland [Phys. Rev. A 56, 131 (1997)] appear as a
corollary. An appendix relates our bounds to the trace-Jensen inequality.Comment: It was not realized at the time of publication that the lower bound
of Theorem 10 has a simple generalization using matrix monotonicity (See [J.
Math. Phys. 50, 062102]). Furthermore, this generalization is a trivial
variation of a previously-obtained bound of Ogawa and Nagaoka [IEEE Trans.
Inf. Theory 45, 2486-2489 (1999)], which had been overlooked by the autho
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