A quantum evaporation effect

A small momentum transfer to a particle interacting with a steep potential barrier gives rise to a quantum evaporation effect which increases the transmission appreciably. This effect results from the unexpectedly large population of quantum states with energies above the height of the barrier. Its characteristic properties are studied and an example of physical system in which it may be observed is given.Comment: 7 pages + 3 figure

Charge Transfer in Partition Theory

The recently proposed Partition Theory (PT) [J.Phys.Chem.A 111, 2229 (2007)] is illustrated on a simple one-dimensional model of a heteronuclear diatomic molecule. It is shown that a sharp definition for the charge of molecular fragments emerges from PT, and that the ensuing population analysis can be used to study how charge redistributes during dissociation and the implications of that redistribution for the dipole moment. Interpreting small differences between the isolated parts' ionization potentials as due to environmental inhomogeneities, we gain insight into how electron localization takes place in H2+ as the molecule dissociates. Furthermore, by studying the preservation of the shapes of the parts as different parameters of the model are varied, we address the issue of transferability of the parts. We find good transferability within the chemically meaningful parameter regime, raising hopes that PT will prove useful in chemical applications.Comment: 12 pages, 16 figure

Effects of noise upon human information processing

Studies of noise effects upon human information processing are described which investigated whether or not effects of noise upon performance are dependent upon specific characteristics of noise stimulation and their interaction with task conditions. The difficulty of predicting noise effects was emphasized. Arousal theory was considered to have explanatory value in interpreting the findings of all the studies. Performance under noise was found to involve a psychophysiological cost, measured by vasoconstriction response, with the degree of response cost being related to scores on a noise annoyance sensitivity scale. Noise sensitive subjects showed a greater autonomic response under noise stimulation

Vortices Clustering: The Origin of the Second Peak in the Magnetisation Loops of High Temperature Superconductors

We study vortex clustering in type II Superconductors. We demonstrate that the ``second peak'' observed in magnetisation loops may be a dynamical effect associated with a density driven instability of the vortex system. At the microscopic level the instability shows up as the clustering of individual vortices at (rare) preferential regions of the pinning potential. In the limit of quasi-static ramping the instability is related to a phase transition in the equilibrium vortex system.Comment: 11 pages + 3 figure

Evolutionary game dynamics of controlled and automatic decision-making

We integrate dual-process theories of human cognition with evolutionary game theory to study the evolution of automatic and controlled decision-making processes. We introduce a model where agents who make decisions using either automatic or controlled processing compete with each other for survival. Agents using automatic processing act quickly and so are more likely to acquire resources, but agents using controlled processing are better planners and so make more effective use of the resources they have. Using the replicator equation, we characterize the conditions under which automatic or controlled agents dominate, when coexistence is possible, and when bistability occurs. We then extend the replicator equation to consider feedback between the state of the population and the environment. Under conditions where having a greater proportion of controlled agents either enriches the environment or enhances the competitive advantage of automatic agents, we find that limit cycles can occur, leading to persistent oscillations in the population dynamics. Critically, however, these limit cycles only emerge when feedback occurs on a sufficiently long time scale. Our results shed light on the connection between evolution and human cognition, and demonstrate necessary conditions for the rise and fall of rationality.Comment: 9 pages, 7 figure

Lattice formulation of N=4{\cal N}=4 super Yang-Mills theory

We construct a lattice action for ${\cal N}=4$ super Yang-Mills theory in four dimensions which is local, gauge invariant, free of spectrum doubling and possesses a single exact supersymmetry. Our construction starts from the observation that the fermions of the continuum theory can be mapped into the component fields of a single real anticommuting Kahler-Dirac field. The original supersymmetry algebra then implies the existence of a nilpotent scalar supercharge $Q$ and a corresponding set of bosonic superpartners. Using this field content we write down a $Q$-exact action and show that, with an appropriate change of variables, it reduces to a well-known twist of ${\cal N}=4$ super Yang-Mills theory due to Marcus. Using the discretization prescription developed in an earlier paper on the ${\cal N}=2$ theory in two dimensions we are able to translate this geometrical action to the lattice.Comment: 15 pages. 1 reference correcte

Storage of classical information in quantum spins

Digital magnetic recording is based on the storage of a bit of information in the orientation of a magnetic system with two stable ground states. Here we address two fundamental problems that arise when this is done on a quantized spin: quantum spin tunneling and back-action of the readout process. We show that fundamental differences exist between integer and semi-integer spins when it comes to both, read and record classical information in a quantized spin. Our findings imply fundamental limits to the miniaturization of magnetic bits and are relevant to recent experiments where spin polarized scanning tunneling microscope reads and records a classical bit in the spin orientation of a single magnetic atom

Categorification of persistent homology

We redevelop persistent homology (topological persistence) from a categorical point of view. The main objects of study are diagrams, indexed by the poset of real numbers, in some target category. The set of such diagrams has an interleaving distance, which we show generalizes the previously-studied bottleneck distance. To illustrate the utility of this approach, we greatly generalize previous stability results for persistence, extended persistence, and kernel, image and cokernel persistence. We give a natural construction of a category of interleavings of these diagrams, and show that if the target category is abelian, so is this category of interleavings.Comment: 27 pages, v3: minor changes, to appear in Discrete & Computational Geometr

Twisted-light-induced optical transitions in semiconductors: Free-carrier quantum kinetics

We theoretically investigate the interband transitions and quantum kinetics induced by light carrying orbital angular momentum, or twisted light, in bulk semiconductors. We pose the problem in terms of the Heisenberg equations of motion of the electron populations, and inter- and intra-band coherences. Our theory extends the free-carrier Semiconductor Bloch Equations to the case of photo-excitation by twisted light. The theory is formulated using cylindrical coordinates, which are better suited to describe the interaction with twisted light than the usual cartesian coordinates used to study regular optical excitation. We solve the equations of motion in the low excitation regime, and obtain analytical expressions for the coherences and populations; with these, we calculate the orbital angular momentum transferred from the light to the electrons and the paramagnetic and diamagnetic electric current densities.Comment: 11 pages, 3 figure

Relations among Supersymmetric Lattice Gauge Theories via Orbifolding

We show how to derive Catterall's supersymmetric lattice gauge theories directly from the general principle of orbifolding followed by a variant of the usual deconstruction. These theories are forced to be complexified due to a clash between charge assignments under U(1)-symmetries and lattice assignments in terms of scalar, vector and tensor components for the fermions. Other prescriptions for how to discretize the theory follow automatically by orbifolding and deconstruction. We find that Catterall's complexified model for the two-dimensional N=(2,2) theory has two independent preserved supersymmetries. We comment on consistent truncations to lattice theories without this complexification and with the correct continuum limit. The construction of lattice theories this way is general, and can be used to derive new supersymmetric lattice theories through the orbifolding procedure. As an example, we apply the prescription to topologically twisted four-dimensional N=2 supersymmetric Yang-Mills theory. We show that a consistent truncation is closely related to the lattice formulation previously given by Sugino.Comment: 20 pages, LaTeX2e, no figur