Spin polarization in a T-shape conductor induced by strong Rashba spin-orbit coupling

We investigate numerically the spin polarization of the current in the presence of Rashba spin-orbit interaction in a T-shaped conductor proposed by A.A. Kiselev and K.W. Kim (Appl. Phys. Lett. {\bf 78} 775 (2001)). The recursive Green function method is used to calculate the three terminal spin dependent transmission probabilities. We focus on single-channel transport and show that the spin polarization becomes nearly 100 % with a conductance close to $e^{2}/h$ for sufficiently strong spin-orbit coupling. This is interpreted by the fact that electrons with opposite spin states are deflected into an opposite terminal by the spin dependent Lorentz force. The influence of the disorder on the predicted effect is also discussed. Cases for multi-channel transport are studied in connection with experiments

Witten's Invariants of Rational Homology Spheres at Prime Values of KK and Trivial Connection Contribution

We establish a relation between the coefficients of asymptotic expansion of trivial connection contribution to Witten's invariant of rational homology spheres and the invariants that T.~Ohtsuki extracted from Witten's invariant at prime values of $K$. We also rederive the properties of prime $K$ invariants discovered by H.~Murakami and T.~Ohtsuki. We do this by using the bounds on Taylor series expansion of the Jones polynomial of algebraically split links, studied in our previous paper. These bounds are enough to prove that Ohtsuki's invariants are of finite type. The relation between Ohtsuki's invariants and trivial connection contribution is verified explicitly for lens spaces and Seifert manifolds.Comment: 32 pages, no figures, LaTe

Higher Order Terms in the Melvin-Morton Expansion of the Colored Jones Polynomial

We formulate a conjecture about the structure of `upper lines' in the expansion of the colored Jones polynomial of a knot in powers of (q-1). The Melvin-Morton conjecture states that the bottom line in this expansion is equal to the inverse Alexander polynomial of the knot. We conjecture that the upper lines are rational functions whose denominators are powers of the Alexander polynomial. We prove this conjecture for torus knots and give experimental evidence that it is also true for other types of knots.Comment: 21 pages, 1 figure, LaTe

Quantum-Hall to insulator transition

The crossover from the quantum Hall regime to the Hall-insulator is investigated by varying the strength of the diagonal disorder in a 2d tight-binding model. The Hall and longitudinal conductivities and the behavior of the critical states are calculated numerically. We find that with increasing disorder the current carrying states close to the band center disappear first. Simultaneously, the quantized Hall conductivity drops monotonically to zero also from higher quantized values.Comment: 5 pages LaTeX2e, 5 ps-figures included. Proceedings SemiMag13, Nijmegen 1998; to appear in Physica

The Anderson transition: time reversal symmetry and universality

We report a finite size scaling study of the Anderson transition. Different scaling functions and different values for the critical exponent have been found, consistent with the existence of the orthogonal and unitary universality classes which occur in the field theory description of the transition. The critical conductance distribution at the Anderson transition has also been investigated and different distributions for the orthogonal and unitary classes obtained.Comment: To appear in Physical Review Letters. Latex 4 pages with 4 figure

Originator Dynamics

We study the origin of evolution. Evolution is based on replication, mutation, and selection. But how does evolution begin? When do chemical kinetics turn into evolutionary dynamics? We propose “prelife” and “prevolution” as the logical precursors of life and evolution. Prelife generates sequences of variable length. Prelife is a generative chemistry that proliferates information and produces diversity without replication. The resulting “prevolutionary dynamics” have mutation and selection. We propose an equation that allows us to investigate the origin of evolution. In one limit, this “originator equation” gives the classical selection equation. In the other limit, we obtain “prelife.” There is competition between life and prelife and there can be selection for or against replication. Simple prelife equations with uniform rate constants have the property that longer sequences are exponentially less frequent than shorter ones. But replication can reverse such an ordering. As the replication rate increases, some longer sequences can become more frequent than shorter ones. Thus, replication can lead to “reversals” in the equilibrium portraits. We study these reversals, which mark the transition from prelife to life in our model. If the replication potential exceeds a critical value, then life replicates into existence.MathematicsOrganismic and Evolutionary Biolog

The components of directional and disruptive selection in heterogeneous group-structured populations.

We derive how directional and disruptive selection operate on scalar traits in a heterogeneous group-structured population for a general class of models. In particular, we assume that each group in the population can be in one of a finite number of states, where states can affect group size and/or other environmental variables, at a given time. Using up to second-order perturbation expansions of the invasion fitness of a mutant allele, we derive expressions for the directional and disruptive selection coefficients, which are sufficient to classify the singular strategies of adaptive dynamics. These expressions include first- and second-order perturbations of individual fitness (expected number of settled offspring produced by an individual, possibly including self through survival); the first-order perturbation of the stationary distribution of mutants (derived here explicitly for the first time); the first-order perturbation of pairwise relatedness; and reproductive values, pairwise and three-way relatedness, and stationary distribution of mutants, each evaluated under neutrality. We introduce the concept of individual k-fitness (defined as the expected number of settled offspring of an individual for which k-1 randomly chosen neighbors are lineage members) and show its usefulness for calculating relatedness and its perturbation. We then demonstrate that the directional and disruptive selection coefficients can be expressed in terms individual k-fitnesses with k=1,2,3 only. This representation has two important benefits. First, it allows for a significant reduction in the dimensions of the system of equations describing the mutant dynamics that needs to be solved to evaluate explicitly the two selection coefficients. Second, it leads to a biologically meaningful interpretation of their components. As an application of our methodology, we analyze directional and disruptive selection in a lottery model with either hard or soft selection and show that many previous results about selection in group-structured populations can be reproduced as special cases of our model

Anderson transition in three-dimensional disordered systems with symplectic symmetry

The Anderson transition in a 3D system with symplectic symmetry is investigated numerically. From a one-parameter scaling analysis the critical exponent $\nu$ of the localization length is extracted and estimated to be $\nu = 1.3 \pm 0.2$. The level statistics at the critical point are also analyzed and shown to be scale independent. The form of the energy level spacing distribution $P(s)$ at the critical point is found to be different from that for the orthogonal ensemble suggesting that the breaking of spin rotation symmetry is relevant at the critical point.Comment: 4 pages, revtex, to appear in Physical Review Letters. 3 figures available on request either by fax or normal mail from [email protected] or [email protected]

The Anderson Transition in Two-Dimensional Systems with Spin-Orbit Coupling

We report a numerical investigation of the Anderson transition in two-dimensional systems with spin-orbit coupling. An accurate estimate of the critical exponent $\nu$ for the divergence of the localization length in this universality class has to our knowledge not been reported in the literature. Here we analyse the SU(2) model. We find that for this model corrections to scaling due to irrelevant scaling variables may be neglected permitting an accurate estimate of the exponent $\nu=2.73 \pm 0.02$

Coloured extension of GL_q(2) and its dual algebra

We address the problem of duality between the coloured extension of the quantised algebra of functions on a group and that of its quantised universal enveloping algebra i.e. its dual. In particular, we derive explicitly the algebra dual to the coloured extension of GL_q(2) using the coloured RLL relations and exhibit its Hopf structure. This leads to a coloured generalisation of the R-matrix procedure to construct a bicovariant differential calculus on the coloured version of GL_q(2). In addition, we also propose a coloured generalisation of the geometric approach to quantum group duality given by Sudbery and Dobrev.Comment: 10 pages LaTeX. Talk given at the "XXIII International Colloquium on Group Theoretical Methods in Physics", July 31 - August 05, 2000, Dubna (Russia); to appear in the proceeding