Stochastic processes for indirectly interacting particles and stochastic quantum mechanics

This work has two objectives. The first is to begin a mathematical formalism appropriate to treating particles which only interact with each otherindirectly due to hypothesized memory effects in a stochastic medium. More specifically we treat a situation in which a sequence of particles consecutively passes through a region (e.g., a measuring apparatus) in such a way that one particle leaves the region before the next one enters. We want to study a situation in which a particle may interact with other particles that previously passed through the system via disturbances made in the region by these previous particles.Second, we apply the type of stochastic process appearing in this context to the stochastic interpretation of quantum mechanics to obtain a modified version of this interpretation. This version is free of many of the criticisms made against the stochastic interpretation of quantum mechanics.     

3D 13C–13C–13C correlation NMR for de novo distance determination of solid proteins and application to a human α-defensin

The de novo structure of an antimicrobial protein, human α-defensin 1 (HNP-1), is determined by combining a 3D ¹³C–¹³C–¹³C (CCC) magic-angle spinning (MAS) correlation experiment with standard resonance assignment experiments. Using a short spin diffusion mixing time to assign intra-residue cross peaks and a long mixing time to detect inter-residue correlation peaks, we show that the 3D CCC experiment not only reduces the ambiguity of resonance assignment, but more importantly yields two orders of magnitude more long-range distances without recourse to existing crystal structures. Most of these distance constraints could not be obtained in a de novo fashion from 2D correlation spectra due to significant resonance overlap. Combining the distance constraints from the 3D CCC experiment and the chemical-shift-derived torsion angles, we obtained a de novo high-resolution NMR structure of HNP-1, with a heavy-atom RMSD of 3.4 Å from the crystal structure of the analogous HNP-3. The average energy of the minimum-energy ensemble is less than of 40 kcal/mol. Thus, the 3D CCC experiment provides a reliable means of restraining the three-dimensional structure of insoluble proteins with unknown conformations.     

Hamiltonian and Brownian systems with long-range interactions: III. The BBGKY hierarchy for spatially inhomogeneous systems

We study the growth of correlations in systems with weak long-range interactions. Starting from the BBGKY hierarchy, we determine the evolution of the two-body correlation function by using an expansion of the solutions of the hierarchy in powers of 1/N in a proper thermodynamic limit N→+∞, where N is the number of particles. These correlations are responsible for the “collisional” evolution of the system beyond the Vlasov regime due to finite N effects. We obtain a general kinetic equation that can be applied to spatially inhomogeneous systems and that takes into account memory effects. These peculiarities are specific to systems with unshielded long-range interactions. For spatially homogeneous systems with short memory time like plasmas, we recover the classical Landau (or Lenard-Balescu) equations. An interest of our approach is to develop a formalism that remains in physical space (instead of Fourier space) and that can deal with spatially inhomogeneous systems. This enlightens the basic physics and provides novel kinetic equations with a clear physical interpretation. However, unless we restrict ourselves to spatially homogeneous systems, closed kinetic equations can be obtained only if we ignore some collective effects between particles. General exact coupled equations taking into account collective effects are also given. We use this kinetic theory to discuss the processes of violent collisionless relaxation and slow collisional relaxation in systems with weak long-range interactions. In particular, we investigate the dependence of the relaxation time with the system size N and try to provide a coherent discussion of all the numerical results obtained for these systems.     

On the Two Species Asymmetric Exclusion Process with Semi-Permeable Boundaries

We investigate the structure of the nonequilibrium stationary state (NESS) of a system of first and second class particles, as well as vacancies (holes), on L sites of a one-dimensional lattice in contact with first class particle reservoirs at the boundary sites; these particles can enter at site 1, when it is vacant, with rate α, and exit from site L with rate β. Second class particles can neither enter nor leave the system, so the boundaries are semi-permeable. The internal dynamics are described by the usual totally asymmetric exclusion process (TASEP) with second class particles. An exact solution of the NESS was found by Arita. Here we describe two consequences of the fact that the flux of second class particles is zero. First, there exist (pinned and unpinned) fat shocks which determine the general structure of the phase diagram and of the local measures; the latter describe the microscopic structure of the system at different macroscopic points (in the limit L→∞) in terms of superpositions of extremal measures of the infinite system. Second, the distribution of second class particles is given by an equilibrium ensemble in fixed volume, or equivalently but more simply by a pressure ensemble, in which the pair potential between neighboring particles grows logarithmically with distance. We also point out an unexpected feature in the microscopic structure of the NESS for finite L: if there are n second class particles in the system then the distribution of first class particles (respectively holes) on the first (respectively last) n sites is exchangeable.     

Deposition and evaporation ofk-mers: Dynamics of a many-state system

When the dynamics of a system partitions the phase space of configurations into very many disjoint sectors, we are faced with an assignment problem: Given a configuration, how can we tell which sector it belongs to? We study this problem in connection with the dynamics of deposition and evaporation ofk particles at a time, from a lattice substrate. Fork ≥ 3, the system shows complex behaviour: (a) The number of disjoint sectors in phase space grows exponentially with the size. (b) The asymptotic time dependence of the autocorrelation function shows slow decays, with power laws which depend on the sector. Both (a) and (b) are explained in terms of a nonlocal construct known as the irreducible string (IS), formed from a particle configuration by applying a deletion algorithm. The IS provides a label for sectors; the multiplicity of possible IS’s accounts for (a), and let us determine sector numbers and sizes. The elements of the IS are conserved; thus their motion is responsible for the slow modes of the system, and accounts for (b) as well.     

Two interacting particles in a random potential: mapping onto one parameter localization theories without interaction

We consider two models for a pair of interacting particles in a random potential: (i) two particles with a Hubbard interaction in arbitrary dimensions and (ii) a strongly bound pair in one dimension. Establishing suitable correspondences we demonstrate that both cases can be described in terms familiar from theories of non-interacting particles. In particular, these two cases are shown to be controlled by a single scaling variable, namely the pair conductance g ₂. For an attractive or repulsive Hubbard interaction and starting from a certain effective Hamiltonian we derive a supersymmetric nonlinear σ model. Its action turns out to be closely related to the one found by Efetov for noninteracting electrons in disordered metals. This enables us to describe the diffusive motion of the particle pair on scales exceeding the oneparticle localization length L ₁ and to discuss the corresponding level statistics. For tightly bound pairs in one dimension, on the other hand, we follow early work by Dorokhov and exploit the analogy with the transfer matrix approach to quasi-1d conductors. Extending our study to M particles we obtain a M-particle localization length scaling like the Mth power of the one-particle localization length.     

Critical mass of bacterial populations and critical temperature of self-gravitating Brownian particles in two dimensions

We show that the critical mass M_c=8π of bacterial populations in two dimensions in the chemotactic problem is the counterpart of the critical temperature T_c=GMm/4k_B of self-gravitating Brownian particles in two-dimensional gravity. We obtain these critical values by using the Virial theorem or by considering stationary solutions of the Keller-Segel model and Smoluchowski-Poisson system. We also consider the case of one-dimensional systems and develop the connection with the Burgers equation. Finally, we discuss the evolution of the system as a function of M or T in bounded and unbounded domains in dimensions d=1, 2 and 3 and show the specificities of each dimension. This paper aims to point out the numerous analogies between bacterial populations, self-gravitating Brownian particles and, occasionally, two-dimensional vortices.     

The supersymmetric Standard Models with decaying and stable dark matters

We propose two supersymmetric Standard Models (SMs) with decaying and stable dark matter (DM) particles. To explain the SM fermion masses and mixings and have a heavy decay DM particle S, we consider the Froggatt–Nielsen mechanism by introducing an anomalous U(1) _X gauge symmetry. Around the string scale, the U(1) _X gauge symmetry is broken down to a Z ₂ symmetry under which S is odd while all the SM particles are even. S obtains a vacuum expectation value around the TeV scale, and then it can three-body decay dominantly to the second/third family of the SM leptons in Model I and to the first family of the SM leptons in Model II. Choosing a benchmark point in the constrained minimal supersymmetric SM with exact R parity, we show that the lightest neutralino DM is consistent with the CDMS II experiment. Considering S three-body decay and choosing suitable parameters, we show that the PAMELA and Fermi-LAT experiments and the PAMELA and ATIC experiments can be explained in Model I and Model II, respectively.     

A physical interpretation of the discrete ambiguities in the optical potential for composite particles

It is shown that the appearance of discrete ambiguities in the optical potential of composite particles is caused by the existence of partly Pauli-forbidden states. The given interpretation is tested in the case ofα-⁵⁸Ni scattering atE _α=50.2 MeV where seven different optical potentials give satisfactory agreement with experiment.     

Nonequilibrium Steady States of Some Simple 1-D Mechanical Chains

We study nonequilibrium steady states of some 1-D mechanical models with N moving particles on a line segment connected to unequal heat baths. For a system in which particles move freely, exchanging energy as they collide with one another, we prove that the mean energy along the chain is constant and equal to \(\frac{1}{2} \sqrt{T_{L}T_{R}}\) where T _L and T _R are the temperatures of the two baths. We then consider systems in which particles are trapped, i.e., each confined to its designated interval in the phase space, but these intervals overlap to permit interaction of neighbors. For these systems, we show numerically that the system has well defined local temperatures and obeys Fourier’s Law (with energy-dependent conductivity) provided we vary the masses randomly to enable the repartitioning of energy. Dynamical systems issues that arise in this study are discussed though their resolution is beyond reach.     

Acceleration of Convergence to Equilibrium in Markov Chains by Breaking Detailed Balance

We analyse and interpret the effects of breaking detailed balance on the convergence to equilibrium of conservative interacting particle systems and their hydrodynamic scaling limits. For finite systems of interacting particles, we review existing results showing that irreversible processes converge faster to their steady state than reversible ones. We show how this behaviour appears in the hydrodynamic limit of such processes, as described by macroscopic fluctuation theory, and we provide a quantitative expression for the acceleration of convergence in this setting. We give a geometrical interpretation of this acceleration, in terms of currents that are antisymmetric under time-reversal and orthogonal to the free energy gradient, which act to drive the system away from states where (reversible) gradient-descent dynamics result in slow convergence to equilibrium.     

Mesonic rare decays inN=1 supergravity

We consider mesonic rare decays mediated by flavour changing neutral currents in the context of spontaneously brokenN=1 supergravity and derive new bounds on masses of supersymmetric particles. In particular we study the supersymmetric contributions toK ⁺ → π⁺ + “nothing” in view of the planned BNL experiment and extend this analysis to theB andD mesonic systems.     

Proton Resonance Assignments in Oligosaccharides Containing Multiple Monosaccharide Residues of the Same Type

A technique is described for assisting the resonance assignment process in oligosaccharide proton NMR spectra, where multiple residues of the same type generate extreme resonance overlap in the spectrum. The approach involves the modification of a conventional HOHAHA experiment with constant-time acquisition in t₁, which effectively proton decouples the C-1 protons of residues whose resonances overlap, thus affording a significant increase in effective resolution in that dimension. For a sufficiently long spin-lock time, complete one-dimensional subspectra are obtained essentially free of cross talk from adjacent resonances. Further simplification of the assignment process is illustrated by incorporation of the constant-time modification into a three-dimensional HOHAHA-HOHAHA experiment.     

The R2PI Spectroscopy of Tyrosine: A Vibronic Analysis

Based on an infrared spectrum in an atlas, and on a Raman spectrum that we acquired ourselves, we have made a frequency assignment for the vibrational modes of tyrosine. This assignment was aided by the results of a GAUSSIAN frequency calculation that we performed at the Hartree-Fock level, using the 3-21G basis set. We have made a vibronic assignment of the bands in a jet-cooled LD-R2PI spectrum that we obtained for tyrosine, using the aforementioned ground-state analysis as a guide. By UV hole burning, we have verified which of the low-frequency R2PI peaks are origins, assigning the others as torsions. We have assigned the various origin bands, with their associated bands to higher energy, to configurations in which the amino acid backbone is either gauche or anti to the ring.     

Coherency matrix description for statistical linear regression of Stokes parameters in rough small-particle scattering

A statistical analysis of the Stokes parameters in light scattering by randomly rough small particles shows a linear regression law between the squares of the first two components I_s and Q_s of the Stokes vector. While the coefficients of this linear regression contain physical characteristics of the particles, they cannot be directly interpreted in terms of the degree of polarization of the scattered field. We propose an interpretation of this relationship between the Stokes parameters on the basis of the general coherence-density matrix formalism. The link between the statistical regression results and the polarization properties of the stochastic scattered components of the field is established through the coherency matrix elements.     

Geometrical aspects and quantum brachistochrone problem for a collection of N spin-s system with long-range Ising-type interaction

We consider a physical system of N interacting qudits consisting of N spin-s particles coupled via the long-range interaction of Ising-type. We investigate the corresponding dynamics, define the associated quantum state manifold and we give the related Fubini-Study metric. We derive the Gaussian curvature and using the Gauss-Bonnet theorem, we show that the dynamics happen on a two-parametric manifold of spherical topology. We examine the geometrical phase acquired by the system under arbitrary and cyclic evolutions. Further, we study the quantum brachistochrone problem concerning the determination of the smallest possible time to realize a time-optimal evolution. By restricting our study to a two-qubit system under the Ising interaction, a detailed analysis is performed for the Fubini-Study metric, the Gaussian curvature, the geometrical phase and the optimal time in relation with the entanglement of the two qubits.     

Families of equilibria and dynamics in a population kinetics model with cosymmetry

We consider a system of nonlinear parabolic equations with an additional property—the so-called cosymmetry—which implies the appearance of a nontrivial family of equilibria. By nontrivial we mean that the stability spectrum is not constant along the family of stationary states. The present system generalizes a special case of a distributed population model discussed in [Computing 16 (Suppl.) (2002) 67] from two to three species. The components of the system have the interpretation of interacting populations which inhabit a common domain. For this Letter we concentrate on the 1D case and apply a finite-difference scheme which respects the cosymmetry. We describe the scenario of instability for the state of rest and observe a rich palette of regimes depending on model parameters and on the initial state.     

Low-scale neutrino seesaw mechanism and scalar dark matter

Recently the AMS-02 experiment has released the data of positron fraction with a very small statistical error. Because of the small error, it is no longer easy to fit the data with single dark matter for a fixed diffusion model and dark matter profile. In this paper, we propose a new interpretation of the data: that it originates from decay of two-component dark matter. This interpretation gives a rough threshold of the lighter DM component. When DM decays into leptons, the positron fraction in the cosmic rays depends on the flavor of the final states, and this is fixed by imposing a non-Abelian discrete symmetry on our model. By assuming two gauge-singlet fermionic decaying DM particles, we show that a model with non-Abelian discrete flavor symmetry, e.g. $T_{13}$ , can give a much better fitting to the AMS-02 data compared with a single-component dark matter scenario. Few dimension-six operators of the universal leptonic decay of DM particles are allowed in our model, since its decay operators are constrained by the $T_{13}$ symmetry. We also show that the lepton masses and mixings are consistent with current experimental data, due to the flavor symmetry.