Coherent states for the hydrogen atom

We construct wave packets for the hydrogen atom labelled by the classical action-angle variables with the following properties. i) The time evolution is exactly given by classical evolution of the angle variables. (The angle variable corresponding to the position on the orbit is now non-compact and we do not get exactly the same state after one period. However the gross features do not change. In particular the wave packet remains peaked around the labels.) ii) Resolution of identity using this overcomplete set involves exactly the classical phase space measure. iii) Semi-classical limit is related to Bohr-Sommerfield quantization. iv) They are almost minimum uncertainty wave packets in position and momentum.Comment: 9 pages, 2 figures, minor change in language and journal reference adde

Coarse grained description of the protein folding

We consider two- and three-dimensional lattice models of proteins which were characterized previously. We coarse grain their folding dynamics by reducing it to transitions between effective states. We consider two methods of selection of the effective states. The first method is based on the steepest descent mapping of states to underlying local energy minima and the other involves an additional projection to maximally compact conformations. Both methods generate connectivity patterns that allow to distinguish between the good and bad folders. Connectivity graphs corresponding to the folding funnel have few loops and are thus tree-like. The Arrhenius law for the median folding time of a 16-monomer sequence is established and the corresponding barrier is related to easily identifiable kinetic trap states.Comment: REVTeX, 9 pages, 15 EPS figures, to appear in Phys. Rev.

Geometric and Statistical Properties of the Mean-Field HP Model, the LS Model and Real Protein Sequences

Lattice models, for their coarse-grained nature, are best suited for the study of the ``designability problem'', the phenomenon in which most of the about 16,000 proteins of known structure have their native conformations concentrated in a relatively small number of about 500 topological classes of conformations. Here it is shown that on a lattice the most highly designable simulated protein structures are those that have the largest number of surface-core switchbacks. A combination of physical, mathematical and biological reasons that causes the phenomenon is given. By comparing the most foldable model peptides with protein sequences in the Protein Data Bank, it is shown that whereas different models may yield similar designabilities, predicted foldable peptides will simulate natural proteins only when the model incorporates the correct physics and biology, in this case if the main folding force arises from the differing hydrophobicity of the residues, but does not originate, say, from the steric hindrance effect caused by the differing sizes of the residues.Comment: 12 pages, 10 figure

The effect of parallel static and microwave electric fields on excited hydrogen atoms

Motivated by recent experiments we analyse the classical dynamics of a hydrogen atom in parallel static and microwave electric fields. Using an appropriate representation and averaging approximations we show that resonant ionisation is controlled by a separatrix, and provide necessary conditions for a dynamical resonance to affect the ionisation probability. The position of the dynamical resonance is computed using a high-order perturbation series, and estimate its radius of convergence. We show that the position of the dynamical resonance does not coincide precisely with the ionisation maxima, and that the field switch-on time can dramatically affect the ionisation signal which, for long switch times, reflects the shape of an incipient homoclinic. Similarly, the resonance ionisation time can reflect the time-scale of the separatrix motion, which is therefore longer than conventional static field Stark ionisation. We explain why these effects should be observed in the quantum dynamics. PACs: 32.80.Rm, 33.40.+f, 34.10.+x, 05.45.Ac, 05.45.MtComment: 47 pages, 20 figure

Excitation of Small Quantum Systems by High-Frequency Fields

The excitation by a high frequency field of multi--level quantum systems with a slowly varying density of states is investigated. A general approach to study such systems is presented. The Floquet eigenstates are characterized on several energy scales. On a small scale, sharp universal quasi--resonances are found, whose shape is independent of the field parameters and the details of the system. On a larger scale an effective tight--binding equation is constructed for the amplitudes of these quasi--resonances. This equation is non--universal; two classes of examples are discussed in detail.Comment: 4 pages, revtex, no figure

Multi-Timescale Perceptual History Resolves Visual Ambiguity

When visual input is inconclusive, does previous experience aid the visual system in attaining an accurate perceptual interpretation? Prolonged viewing of a visually ambiguous stimulus causes perception to alternate between conflicting interpretations. When viewed intermittently, however, ambiguous stimuli tend to evoke the same percept on many consecutive presentations. This perceptual stabilization has been suggested to reflect persistence of the most recent percept throughout the blank that separates two presentations. Here we show that the memory trace that causes stabilization reflects not just the latest percept, but perception during a much longer period. That is, the choice between competing percepts at stimulus reappearance is determined by an elaborate history of prior perception. Specifically, we demonstrate a seconds-long influence of the latest percept, as well as a more persistent influence based on the relative proportion of dominance during a preceding period of at least one minute. In case short-term perceptual history and long-term perceptual history are opposed (because perception has recently switched after prolonged stabilization), the long-term influence recovers after the effect of the latest percept has worn off, indicating independence between time scales. We accommodate these results by adding two positive adaptation terms, one with a short time constant and one with a long time constant, to a standard model of perceptual switching

Role of Secondary Motifs in Fast Folding Polymers: A Dynamical Variational Principle

A fascinating and open question challenging biochemistry, physics and even geometry is the presence of highly regular motifs such as alpha-helices in the folded state of biopolymers and proteins. Stimulating explanations ranging from chemical propensity to simple geometrical reasoning have been invoked to rationalize the existence of such secondary structures. We formulate a dynamical variational principle for selection in conformation space based on the requirement that the backbone of the native state of biologically viable polymers be rapidly accessible from the denatured state. The variational principle is shown to result in the emergence of helical order in compact structures.Comment: 4 pages, RevTex, 4 eps figure

Basins of attraction on random topography

We investigate the consequences of fluid flowing on a continuous surface upon the geometric and statistical distribution of the flow. We find that the ability of a surface to collect water by its mere geometrical shape is proportional to the curvature of the contour line divided by the local slope. Consequently, rivers tend to lie in locations of high curvature and flat slopes. Gaussian surfaces are introduced as a model of random topography. For Gaussian surfaces the relation between convergence and slope is obtained analytically. The convergence of flow lines correlates positively with drainage area, so that lower slopes are associated with larger basins. As a consequence, we explain the observed relation between the local slope of a landscape and the area of the drainage basin geometrically. To some extent, the slope-area relation comes about not because of fluvial erosion of the landscape, but because of the way rivers choose their path. Our results are supported by numerically generated surfaces as well as by real landscapes

Geometry of River Networks II: Distributions of Component Size and Number

The structure of a river network may be seen as a discrete set of nested sub-networks built out of individual stream segments. These network components are assigned an integral stream order via a hierarchical and discrete ordering method. Exponential relationships, known as Horton's laws, between stream order and ensemble-averaged quantities pertaining to network components are observed. We extend these observations to incorporate fluctuations and all higher moments by developing functional relationships between distributions. The relationships determined are drawn from a combination of theoretical analysis, analysis of real river networks including the Mississippi, Amazon and Nile, and numerical simulations on a model of directed, random networks. Underlying distributions of stream segment lengths are identified as exponential. Combinations of these distributions form single-humped distributions with exponential tails, the sums of which are in turn shown to give power law distributions of stream lengths. Distributions of basin area and stream segment frequency are also addressed. The calculations identify a single length-scale as a measure of size fluctuations in network components. This article is the second in a series of three addressing the geometry of river networks.Comment: 16 pages, 13 figures, 4 tables, Revtex4, submitted to PR

Statics, metastable states and barriers in protein folding: A replica variational approach

Protein folding is analyzed using a replica variational formalism to investigate some free energy landscape characteristics relevant for dynamics. A random contact interaction model that satisfies the minimum frustration principle is used to describe the coil-globule transition (characterized by T_CG), glass transitions (by T_A and T_K) and folding transition (by T_F). Trapping on the free energy landscape is characterized by two characteristic temperatures, one dynamic, T_A the other static, T_K (T_A> T_K), which are similar to those found in mean field theories of the Potts glass. 1)Above T_A, the free energy landscape is monotonous and polymer is melted both dynamically and statically. 2)Between T_A and T_K, the melted phase is still dominant thermodynamically, but frozen metastable states, exponentially large in number, appear. 3)A few lowest minima become thermodynamically dominant below T_K, where the polymer is totally frozen. In the temperature range between T_A and T_K, barriers between metastable states are shown to grow with decreasing temperature suggesting super-Arrhenius behavior in a sufficiently large system. Due to evolutionary constraints on fast folding, the folding temperature T_F is expected to be higher than T_K, but may or may not be higher than T_A. Diverse scenarios of the folding kinetics are discussed based on phase diagrams that take into account the dynamical transition, as well as the static ones.Comment: 41 pages, LaTeX, 9 EPS figure