Spin dynamics of low-dimensional excitons due to acoustic phonons

We investigate the spin dynamics of excitons interacting with acoustic phonons in quantum wells, quantum wires and quantum disks by employing a multiband model based on the $4\times4$ Luttinger Hamiltonian. We also use the Bir-Pikus Hamiltonian to model the coupling of excitons to both longitudinal acoustic phonons and transverse acoustic phonons, thereby providing us with a realistic framework in which to determine details of the spin dynamics of excitons. We use a fractional dimensional formulation to model the excitonic wavefunctions and we demonstrate explicitly the decrease of spin relaxation time with dimensionality. Our numerical results are consistent with experimental results of spin relaxation times for various configurations of the GaAs/Al$_{0.3}$Ga$_{0.7}$As material system. We find that longitudinal and transverse acoustic phonons are equally significant in processes of exciton spin relaxations involving acoustic phonons.Comment: 24 pages, 3 figure

Bogomol'nyi Equations of Maxwell-Chern-Simons vortices from a generalized Abelian Higgs Model

We consider a generalization of the abelian Higgs model with a Chern-Simons term by modifying two terms of the usual Lagrangian. We multiply a dielectric function with the Maxwell kinetic energy term and incorporate nonminimal interaction by considering generalized covariant derivative. We show that for a particular choice of the dielectric function this model admits both topological as well as nontopological charged vortices satisfying Bogomol'nyi bound for which the magnetic flux, charge and angular momentum are not quantized. However the energy for the topolgical vortices is quantized and in each sector these topological vortex solutions are infinitely degenerate. In the nonrelativistic limit, this model admits static self-dual soliton solutions with nonzero finite energy configuration. For the whole class of dielectric function for which the nontopological vortices exists in the relativistic theory, the charge density satisfies the same Liouville equation in the nonrelativistic limit.Comment: 30 pages(4 figures not included), RevTeX, IP/BBSR/93-6

On the Hydrogen Atom via Wigner-Heisenberg Algebra

We extend the usual Kustaanheimo-Stiefel $4D\to 3D$ mapping to study and discuss a constrained super-Wigner oscillator in four dimensions. We show that the physical hydrogen atom is the system that emerges in the bosonic sector of the mapped super 3D system.Comment: 14 pages, no figure. This work was initiated in collaboration with Jambunatha Jayaraman (In memory), whose advises and encouragement were fundamental. http://www.cbpf.b

A Precise Error Bound for Quantum Phase Estimation

Quantum phase estimation is one of the key algorithms in the field of quantum computing, but up until now, only approximate expressions have been derived for the probability of error. We revisit these derivations, and find that by ensuring symmetry in the error definitions, an exact formula can be found. This new approach may also have value in solving other related problems in quantum computing, where an expected error is calculated. Expressions for two special cases of the formula are also developed, in the limit as the number of qubits in the quantum computer approaches infinity and in the limit as the extra added qubits to improve reliability goes to infinity. It is found that this formula is useful in validating computer simulations of the phase estimation procedure and in avoiding the overestimation of the number of qubits required in order to achieve a given reliability. This formula thus brings improved precision in the design of quantum computers.Comment: 6 page

Kink fluctuation asymptotics and zero modes

In this paper we propose a refinement of the heat kernel/zeta function treatment of kink quantum fluctuations in scalar field theory, further analyzing the existence and implications of a zero energy fluctuation mode. Improved understanding of the interplay between zero modes and the kink heat kernel expansion delivers asymptotic estimations of one-loop kink mass shifts with remarkably higher precision than previously obtained by means of the standard Gilkey-DeWitt heat kernel expansion.Comment: 21 pages, 8 figures, to be published in The European Physical Journal

Equivalence between free quantum particles and those in harmonic potentials and its application to instantaneous changes

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly citedIn quantum physics the free particle and the harmonically trapped particle are arguably the most important systems a physicist needs to know about. It is little known that, mathematically, they are one and the same. This knowledge helps us to understand either from the viewpoint of the other. Here we show that all general time-dependent solutions of the free-particle Schrodinger equation can be mapped to solutions of the Schrodinger equation for harmonic potentials, both the trapping oscillator and the inverted `oscillator'. This map is fully invertible and therefore induces an isomorphism between both types of system, they are equivalent. A composition of the map and its inverse allows us to map from one harmonic oscillator to another with a different spring constant and different center position. The map is independent of the state of the system, consisting only of a coordinate transformation and multiplication by a form factor, and can be chosen such that the state is identical in both systems at one point in time. This transition point in time can be chosen freely, the wave function of the particle evolving in time in one system before the transition point can therefore be linked up smoothly with the wave function for the other system and its future evolution after the transition point. Such a cut-and-paste procedure allows us to describe the instantaneous changes of the environment a particle finds itself in. Transitions from free to trapped systems, between harmonic traps of different spring constants or center positions, or, from harmonic binding to repulsive harmonic potentials are straightforwardly modelled. This includes some time dependent harmonic potentials. The mappings introduced here are computationally more efficient than either state-projection or harmonic oscillator propagator techniques conventionally employed when describing instantaneous (non-adiabatic) changes of a quantum particle's environmentPeer reviewe

Some Recent Developments on Kink Collisions and Related Topics

We review recent works on modeling of dynamics of kinks in 1+1 dimensional $\phi^4$ theory and other related models, like sine-Gordon model or $\phi^6$ theory. We discuss how the spectral structure of small perturbations can affect the dynamics of non-perturbative states, such as kinks or oscillons. We describe different mechanisms, which may lead to the occurrence of the resonant structure in the kink-antikink collisions. We explain the origin of the radiation pressure mechanism, in particular, the appearance of the negative radiation pressure in the $\phi^4$ and $\phi^6$ models. We also show that the process of production of the kink-antikink pairs, induced by radiation is chaotic.Comment: 26 pages, 9 figures; invited chapter to "A dynamical perspective on the {\phi}4 model: Past, present and future", Eds. P.G. Kevrekidis and J. Cuevas-Maraver; Springer book class with svmult.cls include

A Step Beyond the Bounce: Bubble Dynamics in Quantum Phase Transitions

We study the dynamical evolution of a phase interface or bubble in the context of a \lambda \phi^4 + g \phi^6 scalar quantum field theory. We use a self-consistent mean-field approximation derived from a 2PI effective action to construct an initial value problem for the expectation value of the quantum field and two-point function. We solve the equations of motion numerically in (1+1)-dimensions and compare the results to the purely classical evolution. We find that the quantum fluctuations dress the classical profile, affecting both the early time expansion of the bubble and the behavior upon collision with a neighboring interface.Comment: 12 pages, multiple figure

Novel simple sequence repeats (SSRs) detected by ND-FISH in heterochromatin of Drosophila melanogaster

<p>Abstract</p> <p>Background</p> <p>In recent years, substantial progress has been made in understanding the organization of sequences in heterochromatin regions containing single-copy genes and transposable elements. However, the sequence and organization of tandem repeat DNA sequences, which are by far the majority fraction of <it>D. melanogaster </it>heterochromatin, are little understood.</p> <p>Results</p> <p>This paper reports that the heterochromatin, as well as containing long tandem arrays of pentanucleotide satellites (AAGAG, AAGAC, AATAT, AATAC and AACAC), is also enriched in other simple sequence repeats (SSRs) such as A, AC, AG, AAG, ACT, GATA and GACA. Non-denaturing FISH (ND-FISH) showed these SSRs to localize to the chromocentre of polytene chromosomes, and was used to map them on mitotic chromosomes. Different distributions were detected ranging from single heterochromatic clusters to complex combinations on different chromosomes. ND-FISH performed on extended DNA fibres, along with Southern blotting, showed the complex organization of these heterochromatin sequences in long tracts, and revealed subclusters of SSRs (several kilobase in length) flanked by other DNA sequences. The chromosomal characterization of C, AAC, AGG, AAT, CCG, ACG, AGC, ATC and ACC provided further detailed information on the SSR content of <it>D. melanogaster </it>at the whole genome level.</p> <p>Conclusion</p> <p>These data clearly show the variation in the abundance of different SSR motifs and reveal their non-random distribution within and between chromosomes. The greater representation of certain SSRs in <it>D. melanogaster </it>heterochromatin suggests that its complexity may be greater than previously thought.</p

Cis-by-Trans Regulatory Divergence Causes the Asymmetric Lethal Effects of an Ancestral Hybrid Incompatibility Gene

The Dobzhansky and Muller (D-M) model explains the evolution of hybrid incompatibility (HI) through the interaction between lineage-specific derived alleles at two or more loci. In agreement with the expectation that HI results from functional divergence, many protein-coding genes that contribute to incompatibilities between species show signatures of adaptive evolution, including Lhr, which encodes a heterochromatin protein whose amino acid sequence has diverged extensively between Drosophila melanogaster and D. simulans by natural selection. The lethality of D. melanogaster/D. simulans F1 hybrid sons is rescued by removing D. simulans Lhr, but not D. melanogaster Lhr, suggesting that the lethal effect results from adaptive evolution in the D. simulans lineage. It has been proposed that adaptive protein divergence in Lhr reflects antagonistic coevolution with species-specific heterochromatin sequences and that defects in LHR protein localization cause hybrid lethality. Here we present surprising results that are inconsistent with this coding-sequence-based model. Using Lhr transgenes expressed under native conditions, we find no evidence that LHR localization differs between D. melanogaster and D. simulans, nor do we find evidence that it mislocalizes in their interspecific hybrids. Rather, we demonstrate that Lhr orthologs are differentially expressed in the hybrid background, with the levels of D. simulans Lhr double that of D. melanogaster Lhr. We further show that this asymmetric expression is caused by cis-by-trans regulatory divergence of Lhr. Therefore, the non-equivalent hybrid lethal effects of Lhr orthologs can be explained by asymmetric expression of a molecular function that is shared by both orthologs and thus was presumably inherited from the ancestral allele of Lhr. We present a model whereby hybrid lethality occurs by the interaction between evolutionarily ancestral and derived alleles