Stochastic resonance in neuron models

We study Axiom A flows and introduce a new definition of Gibbs states which is modeled after a current one for diffeomorphisms and by which Gibbs states are locally characterized by their transformation when pulled back by conjugating homeomorphisms. We show that Gibbs states are equilibrium states and vice versa. We also show that for subshifts this equivalence can be strengthened.     

Investigation of Galilean invariance of multi-phase lattice Boltzmann methods

We examine the Galilean invariance of standard lattice Boltzmann methods for two-phase fluids. We show that the known Galilean invariant term that is cubic in the velocities, and is usually neglected, is a major source of Galilean invariance violations. We show that incorporating a correction term can improve the Galilean invariance of the method by up to two orders of magnitude for large velocities. We found that this is true in particular for methods in which the interactions are incorporated through a forcing term. Methods in which interactions are incorporated through a non-ideal pressure tensor only benefit for large velocities.     

Classical Versus Quantum Probability in Sequential Measurements

We demonstrate in this paper that the probabilities for sequential measurements have features very different from those of single-time measurements. First, they cannot be modelled by a classical stochastic process. Second, they are contextual, namely they depend strongly on the specific measurement scheme through which they are determined. We construct Positive-Operator-Valued measures (POVM) that provide such probabilities. For observables with continuous spectrum, the constructed POVMs depend strongly on the resolution of the measurement device, a conclusion that persists even if we consider a quantum mechanical measurement device or the presence of an environment. We then examine the same issues in alternative interpretations of quantum theory. We first show that multi-time probabilities cannot be naturally defined in terms of a frequency operator. We next prove that local hidden variable theories cannot reproduce the predictions of quantum theory for sequential measurements, even when the degrees of freedom of the measuring apparatus are taken into account. Bohmian mechanics, however, does not fall in this category. We finally examine an alternative proposal that sequential measurements can be modeled by a process that does not satisfy the Kolmogorov axioms of probability. This removes contextuality without introducing non-locality, but implies that the empirical probabilities cannot be always defined (the event frequencies do not converge). We argue that the predictions of this hypothesis are not ruled out by existing experimental results (examining in particular the “which way” experiments); they are, however, distinguishable in principle.     

Spontaneous breakdown in two dimensional space-time

We prove that in two-dimensional space-time, symmetry transformations which are generated by Poincaré covariant currents can not be spontaneously broken. This is also the case with the dilation current. We argue that other currents which involve explicit space-time dependence might lead to spontaneously broken symmetries accompanied by massless Goldstone bosons. We construct a trivial example where this phenomenon occurs.     

Many-body spin interactions and the ground state of a dense Rydberg lattice gas

We study a one-dimensional atomic lattice gas in which Rydberg atoms are excited by a laser and whose external dynamics is frozen. We identify a parameter regime in which the Hamiltonian is well approximated by a spin Hamiltonian with quasilocal many-body interactions which possesses an exact analytic ground state solution. This state is a superposition of all states of the system that are compatible with an interaction induced constraint weighted by a fugacity. We perform a detailed analysis of this state which exhibits a crossover between a paramagnetic phase with short-ranged correlations and a crystal. This study also leads us to a class of spin models with many-body interactions that permit an analytic ground state solution.     

Interactions between global and grazing bifurcations in an impacting system

It is well known that the locus of boundary crises in smooth systems contains gaps that give rise to periodic windows. We show that this phenomenon can also be observed in an impacting system, and that the mechanism by which these gaps are created is different. Namely, here gaps are created and disappear at points along the branches of boundary crises where they are intersected by branches of grazing bifurcations. We locate a novel type of double-crisis vertex which we call a grazing-crisis vertex. Additionally, we illustrate several types of basin-boundary metamorphosis that are intricately related with grazing bifurcations.     

Spontaneous Magnetization in the Plane

The Arak process is a solvable stochastic process which generates coloured patterns in the plane. Patterns are made up of a variable number of random non-intersecting polygons. We show that the distribution of Arak process states is the Gibbs distribution of its states in thermodynamic equilibrium in the grand canonical ensemble. The sequence of Gibbs distributions forms a new model parameterised by temperature. We prove that there is a phase transition in this model, for some non-zero temperature. We illustrate this conclusion with simulation results. We measure the critical exponents of this off-lattice model and find they are consistent with those of the Ising model in two dimensions.     

Coupled oscillator models with no scale separation

We consider a class of spatially discrete wave equations that describe the motion of a system of linearly coupled oscillators perturbed by a nonlinear potential. We show that the dynamical behavior of this system cannot be understood by considering the slowest modes only: there is an “inverse cascade” in which the effects of changes in small scales are felt by the largest scales and the mean-field closure does not work. Despite this, a one and a half degree of freedom model is derived that includes the influence of the small-scale dynamics and predicts global conformational changes accurately. Thus, we provide a reduced model for a system in which there is no separation of scales. We analyze a specific coupled-oscillator system that models global conformation change in biomolecules, introduced in [I. Mezi?, On the dynamics of molecular conformation, Proc. Natl. Acad. Sci. 103 (20) (2006) 7542-7547]. In this model, the conformational states are stable to random perturbations, yet global conformation change can be quickly and robustly induced by the action of a targeted control. We study the efficiency of small-scale perturbations on conformational change and show that “zipper” traveling wave perturbations provide an efficient means for inducing such change. A visualization method for the transport barriers in the reduced model yields insight into the mechanism by which the conformation change occurs.     

Superheating and solid-liquid phase coexistence in nanoparticles with nonmelting surfaces

We present a phenomenological model of melting in nanoparticles with facets that are only partially wet by their liquid phase. We show that in this model, as the solid nanoparticle seeks to avoid coexistence with the liquid, the microcanonical melting temperature can exceed the bulk melting point and that the onset of coexistence is a first-order transition. We show that these results are consistent with molecular dynamics simulations of aluminum nanoparticles which remain solid above the bulk melting temperature.     

A nonlinear Fokker–Planck equation approach for interacting systems: Anomalous diffusion and Tsallis statistics

We investigate the solutions for a set of coupled nonlinear Fokker–Planck equations coupled by the diffusion coefficient in presence of external forces. The coupling by the diffusion coefficient implies that the diffusion of each species is influenced by the other and vice versa due to this term, which represents an interaction among them. The solutions for the stationary case are given in terms of the Tsallis distributions, when arbitrary external forces are considered. We also use the Tsallis distributions to obtain a time dependent solution for a linear external force. The results obtained from this analysis show a rich class of behavior related to anomalous diffusion, which can be characterized by compact or long-tailed distributions.     

Network coherence and imperfect superfluidity in the quantum Hall bilayer

Recently, superfluid-like properties have been observed in bilayer quantum Hall systems, in which the effective bosonic particles are understood to be electron-hole pairs. While experimental results are highly suggestive of superfluidity, the linear response of this system remains dissipative down to the lowest available temperatures. We demonstrate that these results may be understood in terms of a unique disorder-dominated state, in which the system organizes into a coherence network, with large incoherent regions separated by quasi-one-dimensional coherent strips with vortices and antivortices at their edges. We demonstrate that this novel state supports nearly dissipationless response at non-vanishing temperatures which can explain a number of puzzling experimental results.     

Lau fringes and subjective refraction

Lau fringes formed in the far field of a pair of gratings illuminated by spatially incoherent light are known to disappear when one grating is rotated slightly (+/-3 degrees ) with respect to the other. We observed that a cylindrical lens that was appropriately rotated could restore the high-contrast Lau fringes by bringing together the rays that are coherent with respect to each other. We have developed a new refractometer based on this phenomenon, the details of which are presented. Measurement of the cylinder power and axis of the human eye is possible with good accuracy and repeatability with this instrument.     

A note on the Lie symmetries of complex partial differential equations and their split real systems

Folklore suggests that the split Lie-like operators of a complex partial differential equation are symmetries of the split system of real partial differential equations. However, this is not the case generally. We illustrate this by using the complex heat equation, wave equation with dissipation, the nonlinear Burgers equation and nonlinear KdV equations. We split the Lie symmetries of a complex partial differential equation in the real domain and obtain real Lie-like operators. Further, the complex partial differential equation is split into two coupled or uncoupled real partial differential equations which constitute a system of two equations for two real functions of two real variables. The Lie symmetries of this system are constructed by the classical Lie approach. We compare these Lie symmetries with the split Lie-like operators of the given complex partial differential equation for the examples considered. We conclude that the split Lie-like operators of complex partial differential equations are not in general symmetries of the split system of real partial differential equations. We prove a proposition that gives the criteria when the Lie-like operators are symmetries of the split system.     

Tangency properties of a pentagonal tiling generated by a piecewise isometry

Piecewise isometries (PWIs) are known to have dynamical properties that generate interesting geometric planar packings. We analyze a particular PWI introduced by Goetz that generates a packing by periodically coded cells, each of which is a pentagon. Our main result is that the tangency graph associated with this packing is a forest (i.e., has no nontrivial cycles). We show, however, that this is not a general property of PWIs by giving an example that has an infinite number of cycles in the tangency graph of its periodically coded cells.     

Equality of the Bulk and Edge Hall Conductances in a Mobility Gap

We consider the edge and bulk conductances for 2D quantum Hall systems in which the Fermi energy falls in a band where bulk states are localized. We show that the resulting quantities are equal, when appropriately defined. An appropriate definition of the edge conductance may be obtained through a suitable time averaging procedure or by including a contribution from states in the localized band. In a further result on the Harper Hamiltonian, we show that this contribution is essential. In an appendix we establish quantized plateaus for the conductance of systems which need not be translation ergodic. An erratum to this article is available at .     

Approximate degeneracies of zone boundary phonons in alkali halide crystals

We point out the existence of a pervasive pattern of near degeneracies of phonon frequencies in isobaric alkali halide crystals (NaBr, KCl, RbBr, CsI) which strongly suggests that their dynamical matrices are almost invariant under transformations which exchange positive and negative ions. We extend this hypothesis to a relation between phonon properties of “mirror” alkali halides in which the ions of one crystal are replaced by the oppositely charged isobaric ions of the other, such as RbCl and KBr. Experimental evidence supporting this can also be adduced. Similar near degeneracies universally occurring in NaCl structure alkali halides and alkaline earth oxides are also noted and a possible dynamical basis for understanding these suggested.     

High-speed properties of a phase-modulation scheme based on electromagnetically induced transparency

Recently a cross-phase modulation scheme that yields giant Kerr nonlinearities by use of an electromagnetically induced transparency (EIT) was proposed [Schmidt and Imamoglu, Opt. Lett. 21, 1936 (1996)]. We analyze the high-speed properties of this scheme for short-pulse propagation. We discuss the relevant losses in this system and show that for short pulses one-photon losses are dominant. We demonstrate that over the entire bandwidth the attainable phase shift in an EIT scheme with a quasi-cw coupling field is orders of magnitude higher than in a conventional three-level scheme or in EIT schemes, in which matched pulses are used to create the transparency.     

Subluminal and superluminal propagation in a three-level atom in the radiative limit based on coherent population oscillations

We investigate a three-level atomic system in the radiative limit to control the light propagation from the subluminal regime to the superluminal one. Here the three levels are connected between them by radiative transitions. We show that depending on the decay rates, this scheme, which is based on coherent population oscillations, allows to switch from one regime to the other by changing the Rabi frequencies of the driving fields. We also show that this scheme is also capable of producing absorptionless self-phase modulation.     

The velocity-dependent source function in radiative transfer theory

We consider the effect of velocity fields upon the transfer of line radiation by two-level atoms. We show that a simultaneous solution of the radiation transfer equation and the time-dependent rate equations leads to an equation for the source function which contains the Lagrangian derivative. We discuss a physical interpretation of the derivative term and present a method for solving this type of problem.We exhibit calculations which show that, for quite reasonable velocity fields, large errors can be produced if the derivative terms in the rate equations are neglected.