281 research outputs found
Correlation Energy and Entanglement Gap in Continuous Models
Our goal is to clarify the relation between entanglement and correlation
energy in a bipartite system with infinite dimensional Hilbert space. To this
aim we consider the completely solvable Moshinsky's model of two linearly
coupled harmonic oscillators. Also for small values of the couplings the
entanglement of the ground state is nonlinearly related to the correlation
energy, involving logarithmic or algebraic corrections. Then, looking for
witness observables of the entanglement, we show how to give a physical
interpretation of the correlation energy. In particular, we have proven that
there exists a set of separable states, continuously connected with the
Hartree-Fock state, which may have a larger overlap with the exact ground
state, but also a larger energy expectation value. In this sense, the
correlation energy provides an entanglement gap, i.e. an energy scale, under
which measurements performed on the 1-particle harmonic sub-system can
discriminate the ground state from any other separated state of the system.
However, in order to verify the generality of the procedure, we have compared
the energy distribution cumulants for the 1-particle harmonic sub-system of the
Moshinsky's model with the case of a coupling with a damping Ohmic bath at 0
temperature.Comment: 26 pages, 6 figure
The symmetry structure of the heavenly equation
We show that excitations of physical interest of the heavenly equation are
generated by symmetry operators which yields two reduced equations with
different characteristics. One equation is of the Liouville type and gives rise
to gravitational instantons, including those found by Eguchi-Hanson and
Gibbons-Hawking. The second equation appears for the first time in the theory
of heavenly spaces and provides meron-like configurations endowed with a
fractional topological charge. A link is also established between the heavenly
equation and the socalled Schr{\"o}der equation, which plays a crucial role in
the bootstrap model and in the renormalization theory.Comment: LaTex, 13 page
Topological Field Theory and Nonlinear -Models on Symmetric Spaces
We show that the classical non-abelian pure Chern-Simons action is related to
nonrelativistic models in (2+1)-dimensions, via reductions of the gauge
connection in Hermitian symmetric spaces. In such models the matter fields are
coupled to gauge Chern-Simons fields, which are associated with the isotropy
subgroup of the considered symmetric space. Moreover, they can be related to
certain (integrable and non-integrable) evolution systems, as the Ishimori and
the Heisenberg model. The main classical and quantum properties of these
systems are discussed in connection with the topological field theory and the
condensed matter physics.Comment: LaTeX format, 31 page
Continuous approximation of binomial lattices
A systematic analysis of a continuous version of a binomial lattice,
containing a real parameter and covering the Toda field equation as
, is carried out in the framework of group theory. The
symmetry algebra of the equation is derived. Reductions by one-dimensional and
two-dimensional subalgebras of the symmetry algebra and their corresponding
subgroups, yield notable field equations in lower dimensions whose solutions
allow to find exact solutions to the original equation. Some reduced equations
turn out to be related to potentials of physical interest, such as the
Fermi-Pasta-Ulam and the Killingbeck potentials, and others. An instanton-like
approximate solution is also obtained which reproduces the Eguchi-Hanson
instanton configuration for . Furthermore, the equation under
consideration is extended to --dimensions. A spherically symmetric form
of this equation, studied by means of the symmetry approach, provides
conformally invariant classes of field equations comprising remarkable special
cases. One of these enables us to establish a connection with the
Euclidean Yang-Mills equations, another appears in the context of Differential
Geometry in relation to the socalled Yamabe problem. All the properties of the
reduced equations are shared by the spherically symmetric generalized field
equation.Comment: 30 pages, LaTeX, no figures. Submitted to Annals of Physic
Chern-Simons Field Theory and Completely Integrable Systems
We show that the classical non-abelian pure Chern-Simons action is related in
a natural way to completely integrable systems of the Davey-Stewartson
hyerarchy, via reductions of the gauge connection in Hermitian spaces and by
performing certain gauge choices. The B\"acklund Transformations are
interpreted in terms of Chern-Simons equations of motion or, on the other hand,
as a consistency condition on the gauge. A mapping with a nonlinear
-model is discussed.Comment: 11 pages, Late
Information transmission through lossy bosonic memory channels
We study the information transmission through a quantum channel, defined over
a continuous alphabet and losing its energy en route, in presence of correlated
noise among different channel uses. We then show that entangled inputs improve
the rate of transmission of such a channel.Comment: 6 pages revtex, 2 eps figure
Deformation surfaces, integrable systems and Chern - Simons theory
A few years ago, some of us devised a method to obtain integrable systems in
(2+1)-dimensions from the classical non-Abelian pure Chern-Simons action via
reduction of the gauge connection in Hermitian symmetric spaces. In this paper
we show that the methods developed in studying classical non-Abelian pure
Chern-Simons actions, can be naturally implemented by means of a geometrical
interpretation of such systems. The Chern-Simons equation of motion turns out
to be related to time evolving 2-dimensional surfaces in such a way that these
deformations are both locally compatible with the Gauss-Mainardi-Codazzi
equations and completely integrable. The properties of these relationships are
investigated together with the most relevant consequences. Explicit examples of
integrable surface deformations are displayed and discussed.Comment: 24 pages, 1 figure, submitted to J. Math. Phy
Neuropsychological and behavioral disorders as presentation symptoms in two brothers with early-infantile niemann-pick type C
Background: Niemann-Pick disease type C (NPC) is a lysosomal storage disease caused by mutations in NPC1 or NPC2 genes. Case presentation: We present two brothers with the same compound heterozygous variants in exon 13 of the NPC1 gene (18q11.2), the first one (c.1955C> G, p. Ser652Trp), inherited from the mother, the second (c.2107T>A p.Phe703Ile) inherited from the father, associated to the classical biochemical phenotype of NPC. The two brothers presented unspecific neurologic symptoms with difference in age of onset: one presented and previously described dyspraxia and motor clumsiness at age 7 years, the other showed a systemic presentation with hepatosplenomegaly noted at the age of two months and neurological symptoms onset at age 4 with speech disturbance. Clinical evolution and neuroimaging data led to the final diagnosis. Systemic signs did not correlate with the onset of neurological symptoms. Miglustat therapy was started in both patients. Conclusions: We highlight the extreme phenotypic heterogeneity of NP-C in the presence of the same genetic variant and the unspecificity of neurologic signs at onset as previously reported. We report some positive effects of miglustat on disease progression assessed also with neuropsychological follow-up, with an age-dependent response
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