Fuzzy set Theory and Quantum Chemistry

Es discuteixen breument algunes consideracions sobre l'aplicació de la Teoria dels Conjunts difusos a la Química quàntica. Es demostra aqui que molts conceptes químics associats a la teoria són adequats per ésser connectats amb l'estructura dels Conjunts difusos. També s'explica com algunes descripcions teoriques dels observables quàntics es potencien tractant-les amb les eines associades als esmentats Conjunts difusos. La funció densitat es pren com a exemple de l'ús de distribucions de possibilitat al mateix temps que les distribucions de probabilitat quàntiques

Molecular quantum similarity in QSAR: applications in computer-aided molecular design

La present tesi està centrada en l'ús de la Teoria de Semblança Quàntica per a calcular descriptors moleculars. Aquests descriptors s'utilitzen com a paràmetres estructurals per a derivar correlacions entre l'estructura i la funció o activitat experimental per a un conjunt de compostos. Els estudis de Relacions Quantitatives Estructura-Activitat són d'especial interès per al disseny racional de molècules assistit per ordinador i, en particular, per al disseny de fàrmacs. Aquesta memòria consta de quatre parts diferenciades. En els dos primers blocs es revisen els fonaments de la teoria de semblança quàntica, així com l'aproximació topològica basada en la teoria de grafs. Ambdues teories es fan servir per a calcular els descriptors moleculars. En el segon bloc, s'ha de remarcar la programació i implementació de programari per a calcular els anomenats índexs topològics de semblança quàntica. La tercera secció detalla les bases de les Relacions Quantitatives Estructura-Activitat i, finalment, el darrer apartat recull els resultats d'aplicació obtinguts per a diferents sistemes biològics.

The Stern-Gerlach Phenomenon According to Classical Electrodynamics

We present a description of the Stem-Gerlach type experiments using only the concepts of classical electrodynamics and the Newton`s equations of motion. The quantization of the projections of the spin (or the projections of the magnetic dipole) is not introduced in our calculations. The main characteristic of our approach is a quantitative analysis of the motion of the magnetic atoms at the entrance of the magnetic field region. This study reveals a mechanism which modifies continuously the orientation of the magnetic dipole of the atom in a very short time interval, at the entrance of the magnetic field region. The mechanism is based on the conservation of the total energy associated with a magnetic dipole which moves in a non uniform magnetic field generated by an electromagnet. A detailed quantitative comparison with the (1922) Stem-Gerlach experiment and the didactical (1967) experiment by J.R. Zacharias is presented. We conclude, contrary to the original Stern-Gerlach statement, that the classical explanations are not ruled out by the experimental data.

Canonical quantum potential scattering theory

A new formulation of potential scattering in quantum mechanics is developed using a close structural analogy between partial waves and the classical dynamics of many non-interacting fields. Using a canonical formalism we find nonlinear first-order differential equations for the low-energy scattering parameters such as scattering length and effective range. They significantly simplify typical calculations, as we illustrate for atom-atom and neutron-nucleus scattering systems. A generalization to charged particle scattering is also possible.

Genesis of quantum nonlocality

We revisit the problem of an otherwise classical particle immersed in the zero-point radiation field, with the purpose of tracing the origin of the nonlocality characteristic of Schrodinger`s equation. The Fokker-Planck-type equation in the particles phase-space leads to an infinite hierarchy of equations in configuration space. In the radiationless limit the first two equations decouple from the rest. The first is the continuity equation: the second one, for the particle flux, contains a nonlocal term due to the momentum fluctuations impressed by the field. These equations are shown to lead to Schrodinger`s equation. Nonlocality (obtained here for the one-particle system) appears thus as a property of the description, not of Nature. (C) 2011 Elsevier B.V. All rights reserved.

Path integral representations in noncommutative quantum mechanics and noncommutative version of Berezin-Marinov action

It is known that the actions of field theories on a noncommutative space-time can be written as some modified (we call them theta-modified) classical actions already on the commutative space-time (introducing a star product). Then the quantization of such modified actions reproduces both space-time noncommutativity and the usual quantum mechanical features of the corresponding field theory. In the present article, we discuss the problem of constructing theta-modified actions for relativistic QM. We construct such actions for relativistic spinless and spinning particles. The key idea is to extract theta-modified actions of the relativistic particles from path-integral representations of the corresponding noncommutative field theory propagators. We consider the Klein-Gordon and Dirac equations for the causal propagators in such theories. Then we construct for the propagators path-integral representations. Effective actions in such representations we treat as theta-modified actions of the relativistic particles. To confirm the interpretation, we canonically quantize these actions. Thus, we obtain the Klein-Gordon and Dirac equations in the noncommutative field theories. The theta-modified action of the relativistic spinning particle is just a generalization of the Berezin-Marinov pseudoclassical action for the noncommutative case.

Semiclassical and quantum motions on the non-commutative plane

We study the canonical and the coherent state quantizations of a particle moving in a magnetic field on the non-commutative plane. Using a theta-modified action, we perform the canonical quantization and analyze the gauge dependence of the theory. We compare coherent states quantizations obtained through Malkin-Man`ko states and circular squeezed states. The relation between these states and the ""classical"" trajectories is investigated, and we present numerical explorations of some semiclassical quantities. (C) 2009 Elsevier B.V. All rights reserved.

The Hilbert space of the Chern-Simons theory on a cylinder: a loop quantum gravity approach

As a laboratory for loop quantum gravity, we consider the canonical quantization of the three-dimensional Chern-Simons theory on a noncompact space with the topology of a cylinder. Working within the loop quantization formalism, we define at the quantum level the constraints appearing in the canonical approach and completely solve them, thus constructing a gauge and diffeomorphism invariant physical Hilbert space for the theory. This space turns out to be infinite dimensional, but separable.

Quantum toy model for black-hole backreaction

We propose a simple quantum field theoretical toy model for black-hole evaporation and study the backreaction of Hawking radiation onto the classical background. It turns out that the horizon is also pushed back in this situation (i.e., the interior region shrinks) though this backreaction is not caused by energy conservation but by momentum balance. The effective heat capacity and induced entropy variation can have both signs-depending on the parameters of the model.

Schwinger and Pegg-Barnett approaches and a relationship between angular and Cartesian quantum descriptions: II. Phase spaces

Following the discussion-in state-space language-presented in a preceding paper, we work on the passage from the phase-space description of a degree of freedom described by a finite number of states (without classical counterpart) to one described by an infinite (and continuously labelled) number of states. With this it is possible to relate an original Schwinger idea to the Pegg-Barnett approach to the phase problem. In phase-space language, this discussion shows that one can obtain the Weyl-Wigner formalism, for both Cartesian and angular coordinates, as limiting elements of the discrete phase-space formalism.

Time evolution of the Wigner function in discrete quantum phase space for a soluble quasi-spin model

The discrete phase space approach to quantum mechanics of degrees of freedom without classical counterparts is applied to the many-fermions/quasi-spin Lipkin model. The Wi:ner function is written for some chosen states associated to discrete angle and angular momentum variables, and the rime evolution is numerically calculated using the discrete von Neumnnn-Liouville equation. Direct evidences in the lime evolution of the Wigner function are extracted that identify a tunnelling effect. A connection with a SU(2)-based semiclassical continuous approach to the Lipkin model is also presented.

Gravitational deflection of massive particles in classical and semiclassical general relativity

We calculate the gravitational deflection of massive particles moving with relativistic velocity in the solar system to second post-Newtonian order. For a particle passing close to the Sun with impact parameter b, the deflection in classical general relativity is Phi(C)[GRAPHICS]where v(0) is the particle speed at infinity and M is the Sun's mass. We compute afterwards the gravitational deflection of a spinless neutral particle of mass m in the same static gravitational field as above, treated now as an external field. For a scalar boson with energy E, the deflection in semiclassical general relativity (SGR) is Phisc[GRAPHICS]This result shows that the propagation of the =2E spinless massive boson produces inexorably dispersive effects. It also shows that the semiclassical prediction is always greater than the geometrical one, no matter what the boson mass is. In addition, it is found that SGR predicts a deflection angle of similar to2.6 arcsec for a nonrelativistic spinless massive boson passing at the Sun's limb.

Finite-volume form factors in semi-classical approximation

A semi-classical approach is used to obtain Lorentz covariant expressions for the form factors between the kink states of a quantum field theory with degenerate vacua. Implemented on a cylinder geometry it provides an estimate of the spectral representation of correlation functions in a finite volume. Illustrative examples of the applicability of the method are provided by the sine-Gordon and the broken phi(4) theories in 1 + 1 dimensions. (C) 2003 Elsevier B.V. All rights reserved.