Études de l’effet tunnel des spins quantiques macroscopiques

Dans cette thèse, nous présentons quelques analyses théoriques récentes ainsi que des observations expérimentales de l’effet tunnel quantique macroscopique et des tran- sitions de phase classique-quantique dans le taux d’échappement des systèmes de spins élevés. Nous considérons les systèmes de spin biaxial et ferromagnétiques. Grâce à l’approche de l’intégral de chemin utilisant les états cohérents de spin exprimés dans le système de coordonnées, nous calculons l’interférence des phases quantiques et leur distribution énergétique. Nous présentons une exposition claire de l’effet tunnel dans les systèmes antiferromagnétiques en présence d’un couplage d’échange dimère et d’une anisotropie le long de l’axe de magnétisation aisé. Nous obtenons l’énergie et la fonc- tion d’onde de l’état fondamentale ainsi que le premier état excité pour les systèmes de spins entiers et demi-entiers impairs. Nos résultats sont confirmés par un calcul utilisant la théorie des perturbations à grand ordre et avec la méthode de l’intégral de chemin qui est indépendant du système de coordonnées. Nous présentons aussi une explica- tion claire de la méthode du potentiel effectif, qui nous laisse faire une application d’un système de spin quantique vers un problème de mécanique quantique d’une particule. Nous utilisons cette méthode pour analyser nos modèles, mais avec la contrainte d’un champ magnétique externe ajouté. La méthode nous permet de considérer les transitions classiques-quantique dans le taux d’échappement dans ces systèmes. Nous obtenons le diagramme de phases ainsi que les températures critiques du passage entre les deux régimes. Nous étendons notre analyse à une chaine de spins d’Heisenberg antiferro- magnétique avec une anisotropie le long d’un axe pour N sites, prenant des conditions frontière périodiques. Pour N paire, nous montrons que l’état fondamental est non- dégénéré et donné par la superposition des deux états de Néel. Pour N impair, l’état de Néel contient un soliton, et, car la position du soliton est indéterminée, l’état fondamen- tal est N fois dégénéré. Dans la limite perturbative pour l’interaction d’Heisenberg, les fluctuations quantiques lèvent la dégénérescence et les N états se réorganisent dans une bande. Nous montrons qu’à l’ordre 2s, où s est la valeur de chaque spin dans la théorie des perturbations dégénérées, la bande est formée. L’état fondamental est dégénéré pour s entier, mais deux fois dégénéré pour s un demi-entier impair, comme prévu par le théorème de Kramer

Quantum decay of metastable states in small magnetic particles

We present an imaginary-time path-integral study of the problem of quantum decay of a metastable state of a uniaxial magnetic particle placed in the magnetic field at an arbitrary angle. Our findings agree with earlier results of Zaslavskii obtained by mapping the spin Hamiltonian onto a particle Hamiltonian. In the limit of low barrier, weak dependence of the decay rate on the angle is found, except for the field which is almost normal to the anisotropy axis, where the rate is sharply peaked, and for the field approaching the parallel orientation, where the rate rapidly goes to zero. This distinct angular dependence, together with the dependence of the rate on the field strength, provides an independent test for macroscopic spin tunneling.

Star products made (somewhat) easier

We develop an approach to the deformation quantization on the real plane with an arbitrary Poisson structure which is based on Weyl symmetrically ordered operator products. By using a polydifferential representation for the deformed coordinates, xj we are able to formulate a simple and effective iterative procedure which allowed us to calculate the fourth-order star product (and may be extended to the fifth order at the expense of tedious but otherwise straightforward calculations). Modulo some cohomology issues which we do not consider here, the method gives an explicit and physics-friendly description of the star products.

Fock space for fermion-like lattices and the linear Glauber model

The concept of Fock space representation is developed to deal with stochastic spin lattices written in terms of fermion operators. A density operator is introduced in order to follow in parallel the developments of the case of bosons in the literature. Some general conceptual quantities for spin lattices are then derived, including the notion of generating function and path integral via Grassmann variables. The formalism is used to derive the Liouvillian of the d-dimensional Linear Glauber dynamics in the Fock-space representation. Then the time evolution equations for the magnetization and the two-point correlation function are derived in terms of the number operator. (C) 2008 Elsevier B.V. All rights reserved.

The double Caldeira-Leggett model: Derivation and solutions of the master equations, reservoir-induced interactions and decoherence

In this paper we analyze the double Caldeira-Leggett model: the path integral approach to two interacting dissipative harmonic oscillators. Assuming a general form of the interaction between the oscillators, we consider two different situations: (i) when each oscillator is coupled to its own reservoir, and (ii) when both oscillators are coupled to a common reservoir. After deriving and solving the master equation for each case, we analyze the decoherence process of particular entanglements in the positional space of both oscillators. To analyze the decoherence mechanism we have derived a general decay function, for the off-diagonal peaks of the density matrix, which applies both to common and separate reservoirs. We have also identified the expected interaction between the two dissipative oscillators induced by their common reservoir. Such a reservoir-induced interaction, which gives rise to interesting collective damping effects, such as the emergence of relaxation- and decoherence-free subspaces, is shown to be blurred by the high-temperature regime considered in this study. However, we find that different interactions between the dissipative oscillators, described by rotating or counter-rotating terms, result in different decay rates for the interference terms of the density matrix. (C) 2010 Elsevier B.V. All rights reserved.

Equivalence of many-photon Green's functions in the Duffin-Kemmer-Petiau and Klein-Gordon-Fock statistical quantum field theories

Using the functional integral formalism for the statistical generating functional in the statistical (finite temperature) quantum field theory, we prove the equivalence of many-photon Greens functions in the Duffin-Kennner-Petiau and Klein-Gordon-Fock statistical quantum field theories. As an illustration, we calculate the one-loop polarization operators in both theories and demonstrate their coincidence.

Renormalized new solutions for the massless Thirring model

We present a nonperturbative study of the (1 + 1)-dimensional massless Thirring model by using path integral methods. The regularization ambiguities - coming from the computation of the fermionic determinant - allow to find new solution types for the model. At quantum level the Ward identity for the 1PI 2-point function for the fermionic current separates such solutions in two phases or sectors, the first one has a local gauge symmetry that is implemented at quantum level and the other one without this symmetry. The symmetric phase is a new solution which is unrelated to the previous studies of the model and, in the nonsymmetric phase there are solutions that for some values of the ambiguity parameter are related to well-known solutions of the model. We construct the Schwinger-Dyson equations and the Ward identities. We make a detailed analysis of their UV divergence structure and, after, we perform a nonperturbative regularization and renormalization of the model.

Bose-Einstein condensation and free DKP field

The thermodynamical partition function of the Duffin-Kemmer-Petiau theory is evaluated using the imaginary-time formalism of quantum field theory at finite temperature and path integral methods. The DKP partition function displays two features: (i) full equivalence with the partition function for charged scalar particles and charged massive spin 1 particles; and (ii) the zero mode sector which is essential to reproduce the well-known relativistic Bose-Einstein condensation for both theories. (C) 2003 Published by Elsevier B.V.

STRONG COUPLING LIMITS and QUANTUM ISOMORPHISMS of THE GAUGED THIRRING MODEL

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Decoupling of unphysical states in the minimal pure spinor formalism II

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Black hole partition function using the hybrid formalism of superstrings

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Matsubara-Fradkin thermodynamical quantization of Podolsky electrodynamics

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Equivalence of many-gluon Green's functions in the Duffin-Kemmer-Petieu and Klein-Gordon-Fock statistical quantum field theories

We prove the equivalence of many-gluon Green's functions in the Duffin-Kemmer-Petieu and Klein-Gordon-Fock statistical quantum field theories. The proof is based on the functional integral formulation for the statistical generating functional in a finite-temperature quantum field theory. As an illustration, we calculate one-loop polarization operators in both theories and show that their expressions indeed coincide.

ON THE INDEPENDENT-PARTICLE APPROXIMATION OF GAUGE-THEORIES - A SIMPLE EXAMPLE

In this work the independent particle model formulation is studied as a mean-field approximation of gauge theories using the path integral approach in the framework of quantum electrodynamics in 1 + 1 dimensions. It is shown how a mean-field approximation scheme can be applied to fit an effective potential to an independent particle model, building a straightforward relation between the model and the associated gauge field theory. An example is made considering the problem of massive Dirac fermions on a line, the so called massive Schwinger model. An interesting result is found, indicating a behaviour of screening of the charges in the relativistic limit of strong coupling. A forthcoming application of the method developed to confining potentials in independent quark models for QCD is in view and is briefly discussed.

On the quantum mechanical propagator for driven coupled harmonic oscillators

The exact propagator beyond and at caustics for a pair of coupled and driven oscillators with different frequencies and masses is calculated using the path-integral approach. The exact wavefunctions and energies are also presented. Finally the propagator is re-calculated through an alternative method, using the δfunction. © 1992 IOP Publishing Ltd.