1,921 research outputs found
From Classical to Quantum Mechanics: "How to translate physical ideas into mathematical language"
In this paper, we investigate the connection between Classical and Quantum
Mechanics by dividing Quantum Theory in two parts: - General Quantum Axiomatics
(a system is described by a state in a Hilbert space, observables are
self-adjoint operators and so on) - Quantum Mechanics properly that specifies
the Hilbert space, the Heisenberg rule, the free Hamiltonian... We show that
General Quantum Axiomatics (up to a supplementary "axiom of classicity") can be
used as a non-standard mathematical ground to formulate all the ideas and
equations of ordinary Classical Statistical Mechanics. So the question of a
"true quantization" with "h" must be seen as an independent problem not
directly related with quantum formalism. Moreover, this non-standard
formulation of Classical Mechanics exhibits a new kind of operation with no
classical counterpart: this operation is related to the "quantization process",
and we show why quantization physically depends on group theory (Galileo
group). This analytical procedure of quantization replaces the "correspondence
principle" (or canonical quantization) and allows to map Classical Mechanics
into Quantum Mechanics, giving all operators of Quantum Mechanics and
Schrodinger equation. Moreover spins for particles are naturally generated,
including an approximation of their interaction with magnetic fields. We find
also that this approach gives a natural semi-classical formalism: some exact
quantum results are obtained only using classical-like formula. So this
procedure has the nice property of enlightening in a more comprehensible way
both logical and analytical connection between classical and quantum pictures.Comment: 47 page
Sensitivity of muscle and intervertebral disc force computations to variations in muscle attachment sites
Item does not contain fulltextThe current paper aims at assessing the sensitivity of muscle and intervertebral disc force computations against potential errors in modeling muscle attachment sites. We perturbed each attachment location in a complete and coherent musculoskeletal model of the human spine and quantified the changes in muscle and disc forces during standing upright, flexion, lateral bending, and axial rotation of the trunk. Although the majority of the muscles caused minor changes (less than 5%) in the disc forces, certain muscle groups, for example, quadratus lumborum, altered the shear and compressive forces as high as 353% and 17%, respectively. Furthermore, percent changes were higher in the shear forces than in the compressive forces. Our analyses identified certain muscles in the rib cage (intercostales interni and intercostales externi) and lumbar spine (quadratus lumborum and longissimus thoracis) as being more influential for computing muscle and disc forces. Furthermore, the disc forces at the L4/L5 joint were the most sensitive against muscle attachment sites, followed by T6/T7 and T12/L1 joints. Presented findings suggest that modeling muscle attachment sites based on solely anatomical illustrations might lead to erroneous evaluation of internal forces and promote using anatomical datasets where these locations were accurately measured. When developing a personalized model of the spine, certain care should also be paid especially for the muscles indicated in this work
Consistency of the Shannon entropy in quantum experiments
The consistency of the Shannon entropy, when applied to outcomes of quantum
experiments, is analysed. It is shown that the Shannon entropy is fully
consistent and its properties are never violated in quantum settings, but
attention must be paid to logical and experimental contexts. This last remark
is shown to apply regardless of the quantum or classical nature of the
experiments.Comment: 12 pages, LaTeX2e/REVTeX4. V5: slightly different than the published
versio
Chaos and quantum-nondemolition measurements
The problem of chaotic behavior in quantum mechanics is investigated against the background of the theory of quantum-nondemolition (QND) measurements. The analysis is based on two relevant features: The outcomes of a sequence of QND measurements are unambiguously predictable, and these measurements actually can be performed on one single system without perturbing its time evolution. Consequently, QND measurements represent an appropriate framework to analyze the conditions for the occurrence of ââdeterministic randomnessââ in quantum systems. The general arguments are illustrated by a discussion of a quantum system with a time evolution that possesses nonvanishing algorithmic complexity
INTRINSIC MECHANISM FOR ENTROPY CHANGE IN CLASSICAL AND QUANTUM EVOLUTION
It is shown that the existence of a time operator in the Liouville space
representation of both classical and quantum evolution provides a mechanism for
effective entropy change of physical states. In particular, an initially
effectively pure state can evolve under the usual unitary evolution to an
effectively mixed state.Comment: 20 pages. For more information or comments contact E. Eisenberg at
[email protected] (internet)
Mechanical similarity as a generalization of scale symmetry
In this paper we study the symmetry known as mechanical similarity (LMS) and
present for any monomial potential. We analyze it in the framework of the
Koopman-von Neumann formulation of classical mechanics and prove that in this
framework the LMS can be given a canonical implementation. We also show that
the LMS is a generalization of the scale symmetry which is present only for the
inverse square potential. Finally we study the main obstructions which one
encounters in implementing the LMS at the quantum mechanical level.Comment: 9 pages, Latex, a new section adde
Evolution of Liouville density of a chaotic system
An area-preserving map of the unit sphere, consisting of alternating twists
and turns, is mostly chaotic. A Liouville density on that sphere is specified
by means of its expansion into spherical harmonics. That expansion initially
necessitates only a finite number of basis functions. As the dynamical mapping
proceeds, it is found that the number of non-negligible coefficients increases
exponentially with the number of steps. This is to be contrasted with the
behavior of a Schr\"odinger wave function which requires, for the analogous
quantum system, a basis of fixed size.Comment: LaTeX 4 pages (27 kB) followed by four short PostScript files (2 kB +
2 kB + 1 kB + 4 kB
Chaotic Evolution in Quantum Mechanics
A quantum system is described, whose wave function has a complexity which
increases exponentially with time. Namely, for any fixed orthonormal basis, the
number of components required for an accurate representation of the wave
function increases exponentially.Comment: 8 pages (LaTeX 16 kB, followed by PostScript 2 kB for figure
Quantum Mechanics as an Approximation to Classical Mechanics in Hilbert Space
Classical mechanics is formulated in complex Hilbert space with the
introduction of a commutative product of operators, an antisymmetric bracket,
and a quasidensity operator. These are analogues of the star product, the Moyal
bracket, and the Wigner function in the phase space formulation of quantum
mechanics. Classical mechanics can now be viewed as a deformation of quantum
mechanics. The forms of semiquantum approximations to classical mechanics are
indicated.Comment: 10 pages, Latex2e file, references added, minor clarifications mad
The mast cell stabiliser ketotifen decreases visceral hypersensitivity and improves intestinal symptoms in patients with irritable bowel syndrome
Background Mast cell activation is thought to be involved in visceral hypersensitivity, one of the main characteristics of the irritable bowel syndrome (IBS). A study was therefore undertaken to investigate the effect of the mast cell stabiliser ketotifen on rectal sensitivity and symptoms in patients with IBS. Methods 60 patients with IBS underwent a barostat study to assess rectal sensitivity before and after 8 weeks of treatment. After the initial barostat, patients were randomised to receive ketotifen or placebo. IBS symptoms and health-related quality of life were scored. In addition, mast cells were quantified and spontaneous release of tryptase and histamine was determined in rectal biopsies and compared with biopsies from 22 age- and gender-matched healthy volunteers. Results Ketotifen but not placebo increased the threshold for discomfort in patients with IBS with visceral hypersensitivity. This effect was not observed in normosensitive patients with IBS. Ketotifen significantly decreased abdominal pain and other IBS symptoms and improved quality of life. The number of mast cells in rectal biopsies and spontaneous release of tryptase were lower in patients with IBS than in healthy volunteers. Spontaneous release of histamine was mostly undetectable but was slightly increased in patients with IBS compared with healthy volunteers. Histamine and tryptase release were not altered by ketotifen. Conclusions This study shows that ketotifen increases the threshold for discomfort in patients with IBS with visceral hypersensitivity, reduces IBS symptoms and improves health-related quality of life. Whether this effect is secondary to the mast cell stabilising properties of ketotifen or H-1 receptor antagonism remains to be further investigate
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