128 research outputs found
Quantum models related to fouled Hamiltonians of the harmonic oscillator
We study a pair of canonoid (fouled) Hamiltonians of the harmonic oscillator
which provide, at the classical level, the same equation of motion as the
conventional Hamiltonian. These Hamiltonians, say and , result
to be explicitly time-dependent and can be expressed as a formal rotation of
two cubic polynomial functions, and , of the canonical variables
(q,p).
We investigate the role of these fouled Hamiltonians at the quantum level.
Adopting a canonical quantization procedure, we construct some quantum models
and analyze the related eigenvalue equations. One of these models is described
by a Hamiltonian admitting infinite self-adjoint extensions, each of them has a
discrete spectrum on the real line. A self-adjoint extension is fixed by
choosing the spectral parameter of the associated eigenvalue
equation equal to zero. The spectral problem is discussed in the context of
three different representations. For , the eigenvalue equation is
exactly solved in all these representations, in which square-integrable
solutions are explicity found. A set of constants of motion corresponding to
these quantum models is also obtained. Furthermore, the algebraic structure
underlying the quantum models is explored. This turns out to be a nonlinear
(quadratic) algebra, which could be applied for the determination of
approximate solutions to the eigenvalue equations.Comment: 24 pages, no figures, accepted for publication on JM
Properties of equations of the continuous Toda type
We study a modified version of an equation of the continuous Toda type in 1+1
dimensions. This equation contains a friction-like term which can be switched
off by annihilating a free parameter \ep. We apply the prolongation method,
the symmetry and the approximate symmetry approach. This strategy allows us to
get insight into both the equations for \ep =0 and \ep \ne 0, whose
properties arising in the above frameworks are mutually compared. For \ep =0,
the related prolongation equations are solved by means of certain series
expansions which lead to an infinite- dimensional Lie algebra. Furthermore,
using a realization of the Lie algebra of the Euclidean group , a
connection is shown between the continuous Toda equation and a linear wave
equation which resembles a special case of a three-dimensional wave equation
that occurs in a generalized Gibbons-Hawking ansatz \cite{lebrun}. Nontrivial
solutions to the wave equation expressed in terms of Bessel functions are
determined.
For \ep\,\ne\,0, we obtain a finite-dimensional Lie algebra with four
elements. A matrix representation of this algebra yields solutions of the
modified continuous Toda equation associated with a reduced form of a
perturbative Liouville equation. This result coincides with that achieved in
the context of the approximate symmetry approach. Example of exact solutions
are also provided. In particular, the inverse of the exponential-integral
function turns out to be defined by the reduced differential equation coming
from a linear combination of the time and space translations. Finally, a Lie
algebra characterizing the approximate symmetries is discussed.Comment: LaTex file, 27 page
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
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
Entanglement of electrons in interacting molecules
Quantum entanglement is a concept commonly used with reference to the
existence of certain correlations in quantum systems that have no classical
interpretation. It is a useful resource to enhance the mutual information of
memory channels or to accelerate some quantum processes as, for example, the
factorization in Shor's Algorithm. Moreover, entanglement is a physical
observable directly measured by the von Neumann entropy of the system. We have
used this concept in order to give a physical meaning to the electron
correlation energy in systems of interacting electrons. The electronic
correlation is not directly observable, since it is defined as the difference
between the exact ground state energy of the many--electrons Schroedinger
equation and the Hartree--Fock energy. We have calculated the correlation
energy and compared with the entanglement, as functions of the nucleus--nucleus
separation using, for the hydrogen molecule, the Configuration Interaction
method. Then, in the same spirit, we have analyzed a dimer of ethylene, which
represents the simplest organic conjugate system, changing the relative
orientation and distance of the molecules, in order to obtain the configuration
corresponding to maximum entanglement.Comment: 15 pages, 7 figures, standard late
Unified Treatment of Heterodyne Detection: the Shapiro-Wagner and Caves Frameworks
A comparative study is performed on two heterodyne systems of photon
detectors expressed in terms of a signal annihilation operator and an image
band creation operator called Shapiro-Wagner and Caves' frame, respectively.
This approach is based on the introduction of a convenient operator
which allows a unified formulation of both cases. For the Shapiro-Wagner
scheme, where , quantum phase and amplitude
are exactly defined in the context of relative number state (RNS)
representation, while a procedure is devised to handle suitably and in a
consistent way Caves' framework, characterized by , within the approximate simultaneous measurements of
noncommuting variables. In such a case RNS phase and amplitude make sense only
approximately.Comment: 25 pages. Just very minor editorial cosmetic change
A class of nonlinear wave equations containing the continuous Toda case
We consider a nonlinear field equation which can be derived from a binomial
lattice as a continuous limit. This equation, containing a perturbative
friction-like term and a free parameter , reproduces the Toda case (in
absence of the friction-like term) and other equations of physical interest, by
choosing particular values of . We apply the symmetry and the
approximate symmetry approach, and the prolongation technique. Our main purpose
is to check the limits of validity of different analytical methods in the study
of nonlinear field equations. We show that the equation under investigation
with the friction-like term is characterized by a finite-dimensional Lie
algebra admitting a realization in terms of boson annhilation and creation
operators. In absence of the friction-like term, the equation is linearized and
connected with equations of the Bessel type. Examples of exact solutions are
displayed, and the algebraic structure of the equation is discussed.Comment: Latex file + [equations.sty], 22 p
Mesh-tissue integration of synthetic and biologic meshes in wall surgery: brief state of art
Many studies show that surgical hernia repair with the use of prosthetic meshes can result in pain, hernia recurrence, contraction and mesh rupture. Numerous experimental studies have been conducted to understand the effect of mesh stiffness, pore size and mesh patterns on mesh biocompatibility.
The purpose of this mini review is to present an overview of the contracture, adhesion, tissue regrowth and histological response characteristics of permanent and absorbable mesh. Indeed, the mechanics of mesh-human tissue interaction is poorly understood in the literature. It has been shown that early integration of biological meshes is critical for sustained hernia repair.
One of the emerging experimental approaches is to combine cell-based regenerative medicine with mesh materials. Studies in preclinical models show that the use of synthetic and biological meshes with autologous cell implantation improves the biocompatibility of biomaterials, promoting key tissue regeneration processes such as adhesion and vascularisation
Adjustment to colostomy: stoma acceptance, stoma care self-efficacy and interpersonal relationships
âThe definitive version is available at www.blackwell-synergy.com.â Copyright Blackwell Publishing. DOI: 10.1111/j.1365-2648.2007.04446.xThis paper is a report of a study to examine adjustment and its relationship with stoma acceptance and social interaction, and the link between stoma care self-efficacy and adjustment in the presence of acceptance and social interactions.Peer reviewe
Chern - Simons Gauge Field Theory of Two - Dimensional Ferromagnets
A Chern-Simons gauged Nonlinear Schr\"odinger Equation is derived from the
continuous Heisenberg model in 2+1 dimensions. The corresponding planar magnets
can be analyzed whithin the anyon theory. Thus, we show that static magnetic
vortices correspond to the self-dual Chern - Simons solitons and are described
by the Liouville equation. The related magnetic topological charge is
associated with the electric charge of anyons. Furthermore, vortex - antivortex
configurations are described by the sinh-Gordon equation and its conformally
invariant extension. Physical consequences of these results are discussed.Comment: 15 pages, Plain TeX, Lecce, June 199
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