Birth, death, and flight: a theory of Malthusian flocks

I study "Malthusian flocks": moving aggregates of self-propelled entities (e.g., organisms, cytoskeletal actin, microtubules in mitotic spindles) that reproduce and die. Long-ranged order (i.e., the existence of a nonzero average velocity (v(r,t))≠0) is possible in these systems, even in spatial dimension d=2. Their spatiotemporal scaling structure can be determined exactly in d=2; furthermore, they lack both the longitudinal sound waves and the giant number fluctuations found in immortal flocks. Number fluctuations are very persistent, and propagate along the direction of flock motion, but at a different speed.     

Ergodic properties of an infinite system of particles moving independently in a periodic field

We investigate the ergodic properties of a general class of infinite systems of independent particles which undergo nontrivial collisions with an external field, e.g. fixed convex barriers (the Lorentz gas). We relate the ergodic properties of these systems to the ergodic properties for a single particle moving in a finite box (with periodic boundary conditions) with the same dynamics. We prove that when the one particle system is mixing or aK-system for a sequence of boxes approaching infinity so is the infinite particle system with an equilibrium measure obtained as a Poisson construction over the one particle phase space.Research sponsored in part by the Air Force Office of Scientific Research Grant No. 73-2430 A and The National Science Foundation Grant No. GP-16147 A, No. 1.     

A novel “magnetic” field and its dual non-commutative phase space

In this Letter we have studied a new form of non-commutative (NC) phase space with an operatorial form of noncommutativity. A point particle in this space feels the effect of an interaction with an “internal  ” magnetic field, that is singular at a specific position θ⁻¹${\theta }^{\mathrm{-1}}$. By “internal” we mean that the effective magnetic fields depends essentially on the particle properties and modifies the symplectic structure. Here θ is the NC parameter and induces the coupling between the particle and the “internal” magnetic field. The magnetic moment of the particle is computed. Interaction with an external physical magnetic field reveals interesting features induced by the inherent fuzziness of the NC phase space: introduction of non-trivial structures into the charge and mass of the particle and possibility of the particle dynamics collapsing to a Hall type of motion. The dynamics is studied both from Lagrangian and symplectic (Hamiltonian) points of view. The canonical (Darboux) variables are also identified. We briefly comment, that the model presented here, can play interesting role in the context of (recently observed) real space Berry curvature in material systems.     

First order phase transitions in lattice and continuous systems: Extension of Pirogov-Sinai theory

We generalize the notion of ground states in the Pirogov-Sinai theory of first order phase transitions at low temperatures, applicable to lattice systems with a finite number of periodic ground states to that of restricted ensembles with equal free energies. A restricted ensemble is a Gibbs ensemble, i.e. equilibrium probability measure, on a restricted set of configurations in the phase space of the system. When a restricted ensemble contains only one configuration it coincides with a ground state. In the more general case the entropy is also important.An example of a system we can treat by our methods is theq-state Potts model where we prove that forq sufficiently large there exists a temperature at which the system coexists inq+1 phases;q-ordered phases are small modifications of theq perfectly ordered ground states and one disordered phase which is a modification of the restricted ensemble consisting of all perfectly disordered (neighboring sites must have different spins) configurations. The free energy thus consists entirely of energy in the firstq-restricted ensembles and of entropy in the last one.Our main motivation for this work is to develop a rigorous theory for phase transitions in continuum fluids in which there is no symmetry between the phases, e.g. the liquid-vapour phase transition. The present work goes a certain way in that direction.Supported in part by NSF Grant N^r DMR81-14726-02     

A case of subdominant/suppressed “high energy” contribution to the baryon asymmetry of the Universe in flavoured leptogenesis

The CP-violation necessary for the generation of the baryon asymmetry of the Universe YB$Y_B$ in the “flavoured” leptogenesis scenario can arise from the “low energy” PMNS neutrino mixing matrix U   and/or from the “high energy” part of neutrino Yukawa couplings, which can mediate CP-violating phenomena only at some high energy scale. The possible interplay between these two types of CP-violation is analysed. The type I see-saw model with three heavy right-handed Majorana neutrinos having hierarchical spectrum is considered. We show that in the case of inverted hierarchical light neutrino mass spectrum, there exist regions in the corresponding leptogenesis parameter space where the relevant “high energy” phases have large CP-violating values, but the purely “high energy” contribution in YB$Y_B$ plays a subdominant role in the production of baryon asymmetry compatible with the observations. In some of these regions the purely “high energy” contribution in YB$Y_B$ is so strongly suppressed that one can have successful leptogenesis only if the requisite CP-violation is provided by the Majorana phase(s) in the neutrino mixing matrix.     

Stationary nonequilibrium states in boundary-driven Hamiltonian systems: Shear flow

We investigate stationary nonequilibrium states of systems of particles moving according to Hamiltonian dynamics with specified potentials. The systems are driven away from equilibrium by Maxwell-demon reflection rules at the walls. These deterministic rules conserve energy but not phase space volume, and the resulting global dynamics may or may not be time reversible (or even invertible). Using rules designed to simulate moving walls, we can obtain a stationary shear flow. Assuming that for macroscopic systems this flow satisfies the Navier-Stokes equations, we compare the hydrodynamic entropy production with the average rate of phase-space volume compression. We find that they are equalwhen the velocity distribution of particles incident on the walls is a local Maxwellian. An argument for a general equality of this kind, based on the assumption of local thermodynamic equilibrium, is given. Molecular dynamic simulations of hard disks in a channel produce a steady shear flow with the predicted behavior.     

Pt-induced structures on Si(1 1 0) studied by STM

The structures induced by platinum (Pt) adsorption on Si(1 1 0) surface have been studied by scanning tunneling microscopy (STM) for coverage up to 2 monolayers (ML). Three surface phases have been found to form: “5×4”, “13×2” and “6×5” for Pt coverages 0.3, 0.5 and 1 ML respectively. All structures are formed by one-dimensional rows aligned along the direction. At the coverage >1 ML islands of, probably, Pt silicide start to form in form of 1D nanowires.     

Use of spectral method for solving nonlinear problems in oscillation theory

To solve nonlinear partial differential equations which describe nearly periodic processes with dispersion and delay in the nonlinear part of the system one proceeds by slowly varying in time and in the coordinate current space-time spectral densities (spectra) of amplitudes and of phases of quasiharmonic components of the function appearing in the equation. One replaces all the derivatives of the latter on the left-hand side of the equation by their expressions in terms of the spectrum and on the right-hand side in the nonlinear perturbation one separates the terms which provide a contribution to every form of dynamic equilibrium of the system motion in accordance with the resonance conditions; this results in a set of differential equations of the first order for the amplitude and phase spectra of the quasiharmonic component which reflects their space-time dynamics.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, Vol. 16, No. 9, pp. 22–29, September, 1973.The authors are grateful to G. A. Medvedev and A. B. Sapozhnikov for the interest shown in their work.     

The Sagnac Vortex Optical Effect

It is shown that the Sagnac phenomenon observed experimentally is in conflict with special (and also general) relativity. The calculation of the magnitude of the Sagnac effect within the framework of a relativistic theory results in a paradox. Thus, for the moving relativistic observer, the simultaneous events of meeting of ± rays with the radiant are nonsimultaneous for the events of meeting of the radiant with ± rays. Here, the index + denotes a ray propagating in the direction of motion of the observer, while the index – denotes a ray propagating against the motion. The paradox is resolved within the framework of the theory of a luminiferous ether at rest.     

Glass models on Bethe lattices

We consider lattice glass models in which each site can be occupied by at most one particle, and any particle may have at most occupied nearest neighbors. Using the cavity method for locally tree-like lattices, we derive the phase diagram, with a particular focus on the vitreous phase and the highest packing limit. We also study the energy landscape via the configurational entropy, and discuss different equilibrium glassy phases. Finally, we show that a kinetic freezing, depending on the particular dynamical rules chosen for the model, can prevent the equilibrium glass transitions.Received: 23 July 2003, Published online: 19 February 2004PACS: 64.70.Pf Glass transitions - 64.60.Cn Order-disorder and statistical mechanics of model systems - 75.10.Nr Spin-glass and other random models     

Quantum dynamics of atomic coherence in a spin-1 condensate: Mean-field versus many-body simulation

We analyse and numerically simulate the full many-body quantum dynamics of a spin-1 condensate in the single spatial mode approximation. Initially, the condensate is in a “ferromagnetic” state with all spins aligned along the y axis and the magnetic field pointing along the z axis. In the course of evolution the spinor condensate undergoes a characteristic change of symmetry, which in a real experiment could be a signature of spin-mixing many-body interactions. The results of our simulations are conveniently visualised within the picture of irreducible tensor operators.     

Phase Structure of Systems with Infinite Numbers of Absorbing States

Critical properties of systems exhibiting phase transitions into phases with infinite numbers of absorbing states are studied. We analyze a non-Markovian Langevin equation recently proposed to describe the critical behavior of such systems, and also introduce and study a non-Markovian discrete model, which is argued to present the same critical features. On the basis of mean-field analysis, Monte Carlo simulations, and theoretical arguments, we conclude that the phenomenology of the non-Markovian models closely parallels that of systems with many absorbing states in one and two dimensions. The bulk or static critical properties of these systems fall in the directed percolation (DP) universality class. By contrast, the critical properties associated with the spread of an initially localized seed exhibit a more complex behavior: Depending on parameter values they can, both in one and two dimensions, fall either in the dynamical percolation or DP universality class, or else exhibit apparently nonuniversal exponents. In contrast to previous results, however, the nonuniversal exponents in 2D are found to satisfy a scaling law which implies that a particular linear combination of them is universal and assumes DP values. These results demonstrate the efficacy of the non-Markovian approach for understanding systems with many absorbing states, which are difficult to analyze in their original microscopic formulation.     

A physical limitation of the Wigner “distribution” function in molecular transport

We present an example revealing that the sign of the “momentum” P   of the Wigner “distribution” function f(q,P)$f(q,P)$ is not necessarily associated with the direction of motion in the real world. This aspect, which is not related to the well-known limitation of the Wigner function that traces back to the Heisenberg?s uncertainty principle, is particularly relevant in transport studies, wherein it is helpful to distinguish between electrons flowing from electrodes into devices and vice versa.     

On the positivity of correlations in nonequilibrium spin systems

We consider Ising spin systems, equivalently lattice gases evolving under discrete- or continuous-time Markov processes, i.e., stochastic cellular automata or interacting particle systems. We show that for certain spin-flip probabilities or rates and suitable initial states the expectation values of products of spin variables taken at equal or different times are nonnegative; they satisfy the same inequalities as the equal-time correlations of ferromagnetic systems in equilibrium (first Griffiths inequality). Extensions of FKG inequalities to time-displaced correlations are also discussed.     

Anisotropic in-plane misfit strains dependence of phase diagrams and dielectric behavior in epitaxial Pb(Zr1−xTix)O3 thin films

A phenomenological Landau–Devonshire thermodynamic theory is used to describe the effects of anisotropic in-plane misfit strains on equilibrium polarization states and dielectric properties of single domain epitaxial Pb(Zr_1−xTi_x)O₃ thin films grown on dissimilar orthorhombic substrates. Compared with the “isotropic in-plane misfit strains-temperature” phase diagrams, the characteristic features of “misfit strain-misfit strain” and “misfit strain-temperature” phase diagrams under the circumstance of strain anisotropy are the presence of four different phases (a^′$a^{\prime }$, a^″$a^{″}$, a^′c$a^{\prime }c$, and a^″c$a^{″}c$) and the direct 90° polarization switching between c   phase and a^′$a^{\prime }$ phase (or a^″$a^{″}$ phase), between a^′$a^{\prime }$ phase and a^″$a^{″}$ phase. The misfit strain dependence of polarization components, the small-signal dielectric responses and the tunabilities at room temperature are also calculated. We find that the phase diagrams and dielectric properties largely depend on anisotropic in-plane misfit strains as well. Moreover, the strain anisotropy will lead to the polarization and dielectric anisotropy.     

Modeling of Phase Separation in Alloys with Coherent Elastic Misfit

Elastic interactions arising from a difference of lattice spacing between two coherent phases can have a strong influence on the phase separation (coarsening) behavior of alloys. If the elastic moduli are different in the two phases, the elastic interactions may accelerate, slow down or even stop the phase separation process. If the material is elastically anisotropic, the precipitates can be shaped like plates or needles instead of spheres and can arrange themselves into highly correlated patterns. Tensions or compressions applied externally to the specimen may have a strong effect on the shapes and arrangement of the precipitates. In this paper, we review the main theoretical approaches that have been used to model these effects and we relate them to experimental observations. The theoretical approaches considered are (i) macroscopic models treating the two phases as elastic media separated by a sharp interface, (ii) mesoscopic models in which the concentration varies continuously across the interface, and (iii) microscopic models which use the positions of individual atoms.     

Thermodynamics and phase stabilities of the ternary system Li-In-Sb

Electrochemical investigations of the phase equilibria of the ternary system Li-In-Sb show the existence of two new ternary phases, Li₃InSb₂ and nominally Li₆InSb₃ which has a wide range of stoichiometry along the quasi-binary cut InSb-Li₃Sb. Both compounds are stable in equilibrium with elemental indium and antimony. The lithium activities are limited to ranges from 6.6×10^–8 to 3.6×10^–7 and 9.3×10^–8 to 1.1 ×10^–5, respectively, at 400 °C. The standard Gibbs energies of formation of Li₃InSb₂ and Li₆InSb₃ are –296.2 and –568.8 kJ/mol, respectively, at 400 °C and ideal stoichiometry. The activity ranges of Li, In and Sb are given for the stability of all phases of the ternary system.On leave from Institut für Physikalische und Theoretische Chemie, Technische Universität Graz, Austria     

Quantum phase properties associated to solvable quantum systems using the nonlinear coherent states approach

In this paper we study the quantum phase properties of “nonlinear coherent states” and “solvable quantum systems with discrete spectra” using the Pegg-Barnett formalism in a unified approach. The presented procedure will then be applied to few special solvable quantum systems with known discrete spectrum as well as to some new classes of nonlinear oscillators with particular nonlinearity functions. Finally the associated phase distributions and their nonclasscial properties such as the squeezing in number and phase operators have been investigated, numerically.