33,551 research outputs found
Equivalence between different classical treatments of the O(N) nonlinear sigma model and their functional Schrodinger equations
In this work we derive the Hamiltonian formalism of the O(N) non-linear sigma
model in its original version as a second-class constrained field theory and
then as a first-class constrained field theory. We treat the model as a
second-class constrained field theory by two different methods: the
unconstrained and the Dirac second-class formalisms. We show that the
Hamiltonians for all these versions of the model are equivalent. Then, for a
particular factor-ordering choice, we write the functional Schrodinger equation
for each derived Hamiltonian. We show that they are all identical which
justifies our factor-ordering choice and opens the way for a future
quantization of the model via the functional Schrodinger representation.Comment: Revtex version, 17 pages, substantial change
Wyman's solution, self-similarity and critical behaviour
We show that the Wyman's solution may be obtained from the four-dimensional
Einstein's equations for a spherically symmetric, minimally coupled, massless
scalar field by using the continuous self-similarity of those equations. The
Wyman's solution depends on two parameters, the mass and the scalar charge
. If one fixes to a positive value, say , and let
take values along the real line we show that this solution exhibits critical
behaviour. For the space-times have eternal naked singularities,
for one has a Schwarzschild black hole of mass and finally
for one has eternal bouncing solutions.Comment: Revtex version, 15pages, 6 figure
Chaos and a Resonance Mechanism for Structure Formation in Inflationary Models
We exhibit a resonance mechanism of amplification of density perturbations in
inflationary mo-dels, using a minimal set of ingredients (an effective
cosmological constant, a scalar field minimally coupled to the gravitational
field and matter), common to most models in the literature of inflation. This
mechanism is based on the structure of homoclinic cylinders, emanating from an
unstable periodic orbit in the neighborhood of a saddle-center critical point,
present in the phase space of the model. The cylindrical structure induces
oscillatory motions of the scales of the universe whenever the orbit visits the
neighborhood of the saddle-center, before the universe enters a period of
exponential expansion. The oscillations of the scale functions produce, by a
resonance mechanism, the amplification of a selected wave number spectrum of
density perturbations, and can explain the hierarchy of scales observed in the
actual universe. The transversal crossings of the homoclinic cylinders induce
chaos in the dynamics of the model, a fact intimately connected to the
resonance mechanism occuring immediately before the exit to inflation.Comment: 4 pages. This essay received an Honorable Mention from the Gravity
Research Foundation, 1998-Ed. To appear in Mod. Phys. Lett.
Entanglement and Bell's inequality violation above room temperature in metal carboxylates
In the present work we show that a special family of materials, the metal
carboxylates, may have entangled states up to very high temperatures. From
magnetic susceptibility measurements, we have estimated the critical
temperature below which entanglement exists in the cooper carboxylate
\{Cu(OCH)\}\{Cu(OCH)(2-methylpyridine)\}, and we have
found this to be above room temperature ( K). Furthermore, the
results show that the system remains maximally entangled until close to K and the Bell's inequality is violated up to nearly room temperature
( K)
Experimental realization of the Yang-Baxter Equation via NMR interferometry
The Yang-Baxter equation is an important tool in theoretical physics, with
many applications in different domains that span from condensed matter to
string theory. Recently, the interest on the equation has increased due to its
connection to quantum information processing. It has been shown that the
Yang-Baxter equation is closely related to quantum entanglement and quantum
computation. Therefore, owing to the broad relevance of this equation, besides
theoretical studies, it also became significant to pursue its experimental
implementation. Here, we show an experimental realization of the Yang-Baxter
equation and verify its validity through a Nuclear Magnetic Resonance (NMR)
interferometric setup. Our experiment was performed on a liquid state
Iodotrifluoroethylene sample which contains molecules with three qubits. We use
Controlled-transfer gates that allow us to build a pseudo-pure state from which
we are able to apply a quantum information protocol that implements the
Yang-Baxter equation.Comment: 10 pages and 6 figure
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