311 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
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
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
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
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
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
Dyonic Non-Abelian Vortices
We study three-dimensional Yang-Mills-Higgs theories with and without a
Chern-Simons interaction. We find that these theories admit a rich spectrum of
vortex solitons carrying both a topological charge and a global flavour charge.
We further derive a low-energy description of the vortex dynamics from a gauged
linear sigma model on the vortex worldline.Comment: 16 pages, 3 figures; references added in section
Predictors of complications in gynaecological oncological surgery: a prospective multicentre study (UKGOSOC-UK gynaecological oncology surgical outcomes and complications)
Background: There are limited data on surgical outcomes in gynaecological oncology. We report on predictors of complications in a multicentre prospective study. / Methods: Data on surgical procedures and resulting complications were contemporaneously recorded on consented patients in 10 participating UK gynaecological cancer centres. Patients were sent follow-up letters to capture any further complications. Post-operative (Post-op) complications were graded (IâV) in increasing severity using the Clavien-Dindo system. Grade I complications were excluded from the analysis. Univariable and multivariable regression was used to identify predictors of complications using all surgery for intra-operative (Intra-op) and only those with both hospital and patient-reported data for Post-op complications. / Results: Prospective data were available on 2948 major operations undertaken between April 2010 and February 2012. Median age was 62 years, with 35% obese and 20.4% ASA grade â©Ÿ3. Consultant gynaecological oncologists performed 74.3% of operations. Intra-op complications were reported in 139 of 2948 and Grade IIâV Post-op complications in 379 of 1462 surgeries. The predictors of risk were different for Intra-op and Post-op complications. For Intra-op complications, previous abdominal surgery, metabolic/endocrine disorders (excluding diabetes), surgical complexity and final diagnosis were significant in univariable and multivariable regression (P<0.05), with diabetes only in multivariable regression (P=0.006). For Post-op complications, age, comorbidity status, diabetes, surgical approach, duration of surgery, and final diagnosis were significant in both univariable and multivariable regression (P<0.05). / Conclusions: This multicentre prospective audit benchmarks the considerable morbidity associated with gynaecological oncology surgery. There are significant patient and surgical factors that influence this risk
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