Quantum entanglement and fixed point Hopf bifurcation

We present the qualitative differences in the phase transitions of the mono-mode Dicke model in its integrable and chaotic versions. These qualitative differences are shown to be connected to the degree of entanglement of the ground state correlations as measured by the linear entropy. We show that a first order phase transition occurs in the integrable case whereas a second order in the chaotic one. This difference is also reflected in the classical limit: for the integrable case the stable fixed point in phase space undergoes a Hopf type whereas the second one a pitchfork type bifurcation. The calculation of the atomic Wigner functions of the ground state follows the same trends. Moreover, strong correlations are evidenced by its negative parts. (c) 2006 Elsevier B.V. All rights reserved.

Optical studies of the correlation between interface disorder and the photoluminescence line shape in GaAs/InGaP quantum wells

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

An introduction to numerical methods in low-dimensional quantum systems

This is an introductory course to the Lanczos Method and Density Matrix Renormalization Group Algorithms (DMRG), two among the leading numerical techniques applied in studies of low-dimensional quantum models. The idea of studying the models on clusters of a finite size in order to extract their physical properties is briefly discussed. The important role played by the model symmetries is also examined. Special emphasis is given to the DMRG.

Optical and structural properties of GaAs/GaInP quantum wells grown by Chemical Beam Epitaxy

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

Effects of varying curvature and width on the electronic states of GaAs quantum rings

Stationary states of an electron in thin GaAs elliptical quantum rings are calculated within the effective-mass approximation. The width of the ring varies smoothly along the centerline, which is an ellipse. The solutions of the Schrödinger equation with Dirichlet boundary conditions are approximated by a product of longitudinal and transversal wave functions. The ground-state probability density shows peaks: (i) where the curvature is larger in a constant-with ring, and (ii) in thicker parts of a circular ring. For rings of typical dimensions, it is shown that the effects of a varying width may be stronger than those of the varying curvature. Also, a width profile which compensates the main localization effects of the varying curvature is obtained.

Lattice discretization in quantum scattering

The utility of lattice discretization technique is demonstrated for solving nonrelativistic quantum scattering problems and specially for the treatment of ultraviolet divergences in these problems with some potentials singular at the origin in two- and three-space dimensions. This shows that the lattice discretization technique could be a useful tool for the numerical solution of scattering problems in general. The approach is illustrated in the case of the Dirac delta function potential.

GENERATING FUNCTION FOR CLEBSCH-GORDAN-COEFFICIENTS, OF THE SUQ(2) QUANTUM ALGEBRA

Some methods have been developed to calculate the su(q)(2) Clebsch-Gordan coefficients (CGC). Here we develop a method based on the calculation of Clebsch-Gordan generating functions through the use of 'quantum algebraic' coherent states. Calculating the su(q)(2) CGC by means of this generating function is an easy and straightforward task.

Photoluminescence temperature dependence of doped parabolic quantum wells

Parabolic quantum wells (PQWs) have been studied by temperature dependent photoluminescence (PL). Two kind of samples have been studied. Concerning the undoped sample, the dominant luminescences were the bulk GaAs and the fundamental transition of the PQW. The evolution on temperature of the energy position of both PL emissions follows the well known Varshing formula. For the doped samples strong radiative recombination of the electron gas with photogenerated holes was observed. At low temperature strong Fermi level enhancement occurs in the luminescence as a result of the multi-electron-hole scattering, which is smear out increasing the temperature.

2-DIMENSIONAL QUANTUM GAS

Identical impenetrable particles in a 2-dimensional configuration space obey braid statistics, intermediate between bosons and fermions. This statistics, based on braid groups, is introduced as a generalization of the usual statistics founded on the symmetric groups. The main properties of an ideal gas of such particles are presented. They do interpolate the properties of bosons and fermions but include classical particles as a special case. Restriction to 2 dimensions precludes lambda points but originates a peculiar symmetry, responsible in particular for the identity of boson and fermion specific heats.

Renormalization in non-relativistic quantum mechanics

The importance and usefulness of renormalization are emphasized in non-relativistic quantum mechanics. The momentum space treatment of both two-body bound state and scattering problems involving some potentials singular at the origin exhibits ultraviolet divergence. The use of renormalization techniques in these problems leads to finite converged results for both the exact and perturbative solutions. The renormalization procedure is carried out for the quantum two-body problem in different partial waves for a minimal potential possessing only the threshold behaviour and no form factors. The renormalized perturbative and exact solutions for this problem are found to be consistent with each other. The useful role of the renormalization group equations for this problem is also pointed out.

Generalized point interactions in one-dimensional quantum mechanics

There is a four-parameter family of point interactions in one-dimensional quantum mechanics. They represent all possible self-adjoint extensions of the kinetic energy operator. If time-reversal invariance is imposed, the number of parameters is reduced to three. One of these point interactions is the familiar delta function potential but the other generalized ones do not seem to be widely known. We present a pedestrian approach to this subject and comment on a recent controversy in the literature concerning the so-called delta' interaction. We emphasize that there is little resemblance between the delta' interaction and what its name suggests.

A Bethe ansatz solution for the closed U-q[sl(2)] Temperley-Lieb quantum spin chains

We solve the spectrum of the closed Temperley-Lieb quantum spin chains using the coordinate Bethe ansatz. These models are invariant under the quantum group U-q[sl(2)].

Quantum equivalence between the self-dual and the Maxwell-Chern-Simons models nonlinearly coupled to U(1) scalar fields

The use of master actions to prove duality at quantum level becomes cumbersome if one of the dual fields interacts nonlinearly with other fields. This is the case of the theory considered here consisting of U(1) scalar fields coupled to a self-dual field through a linear and a quadratic term in the self-dual field. Integrating perturbatively over the scalar fields and deriving effective actions for the self-dual and the gauge field we are able to consistently neglect awkward extra terms generated via master action and establish quantum duality up to cubic terms in the coupling constant. The duality holds for the partition function and some correlation functions. The absence of ghosts imposes restrictions on the coupling with the scalar fields.

Supersymmetric quantum mechanics and partially solvable potential

Supersymmetric quantum mechanics can be used to obtain the spectrum and eigenstates of one-dimensional Hamiltonians. It is particularly useful when applied to partially solvable potentials because a superalgebra allows us to compute the spectrum state by state. Some solutions for the truncated Coulomb potential, an asymptotically linear potential, and a nonpolynomial potential are shown to exemplify the method.