Optimal transport in a ratchet coupled to a modulated environment: The role of Levy walks

We consider a Brownian particle in a ratchet potential coupled to a modulated environment and subjected to an external oscillating force. The modulated environment is modelled by a finite number N of uncoupled harmonic oscillators. Superdiffusive motion and Levy walks (anomalous random walks) are observed for any N and for low values of the external amplitude F. The coexistence of left and right running states enhances the power α from the time dependence of the mean square displacement (MSD). It is shown that α is twice the average of the power of the separated left and right MSDs. Normal random walks are obtained by increasing F. We show that the maximal mobility of particles along the periodic structure occurs just before superdiffusive motion disappears and Levy walks are transformed into normal random walks.     

Transport properties of coupled Brownian particles confined to a microchannel in an asymmetric periodic potential

On the basis of the transport features and experimental phenomena observed in studies of molecular motors, we investigated an overdamped Brownian motion of two coupled particles with an asymmetric periodic potential in a two-dimensional microchannel theoretically and numerically, to reveal the dynamical mechanism of cooperative transport of particles with two heads, where the interactions between two particles are taken into consideration. Moreover, while moving in a confined structure, Brownian particles also could exhibit peculiar kinetic behavior. The dependence of directed current on various parameters is systematically studied. Our results indicate that the direction of motion can be reversed by modulating the coupling strength, free length, and microchannel width. In addition, we have achieved the conditions of forward motion in this study. That is, when the interparticle average horizontal interval Δx > 0.25L, where L is the spatial period of the external potential, the forward motion of coupled Brownian particles effected by the synchronized noise and confined to a microchannel can be generated in the strong-coupling case.     

Pre-asymptotic corrections to fractional diffusion equations

The motion of contaminant particles through complex environments such as fractured rocks or porous sediments is often characterized by anomalous diffusion: the spread of the transported quantity is found to grow sublinearly in time due to the presence of obstacles which hinder particle migration. The asymptotic behavior of these systems is usually well described by fractional diffusion, which provides an elegant and unified framework for modeling anomalous transport. We show that pre-asymptotic corrections to fractional diffusion might become relevant, depending on the microscopic dynamics of the particles. To incorporate these effects, we derive a modified transport equation and validate its effectiveness by a Monte Carlo simulation.     

Effect of anomalously slow motions of particles with spins of 1/2 on the shape of the magnetic resonance line of pairs of particles

A non-Markovian version of the Liouville stochastic equation was used to analyze spin relaxation in a pair of particles with spins 1/2 and the dipole-dipole interaction between the spins. The particles were involved in anomalously slow stochastic relative rotation described by the angular correlation function K(t) ～ 1/t ^α with α < 1. The Liouville stochastic equation could be used to describe memory effects in the kinetic dependence of rotational relaxation resulting in a very slow descent of K(t). Our analysis showed that the anomalous relative motion of radicals manifested itself in special features of the shape of the magnetic resonance line of the particle pair.     

Exact quantum mechanical description of the motion of spin-1/2 particles and of spin motion in a uniform magnetic field

The Dirac-Pauli equation is used to obtain the exact equation of spin motion for spin-1/2 particles with an anomalous magnetic moment in a constant and uniform magnetic field. Exact formulas are established for the angular velocity of the revolution of such particles along circular orbits and the rotation of the particle spin with respect to momentum. Finally, a quantum mechanical equation for the motion of the particles in a strong magnetic field is derived. Zh. éksp. Teor. Fiz. 114, 448–457 (August 1998)     

Kähler spinning particles

We construct the U(N) spinning particle theories, which describe particles moving on Kähler spaces. These particles have the same relation to the N = 2 string as usual spinning particles have to the NSR string. We find the restrictions on the target space of the theories coming from supersymmetry and from global anomalies. Finally, we show that the partition functions of the theories agree with what is expected from their spectra, unlike that of the N = 2 string in which there is an anomalous dependence on the proper time.     

Biased diffusion in a piecewise linear random potential

We study the biased diffusion of particles moving in one direction under the action of a constant force in the presence of a piecewise linear random potential. Using the overdamped equation of motion, we represent the first and second moments of the particle position as inverse Laplace transforms. By applying to these transforms the ordinary and the modified Tauberian theorem, we determine the short- and long-time behavior of the mean-square displacement of particles. Our results show that while at short times the biased diffusion is always ballistic, at long times it can be either normal or anomalous. We formulate the conditions for normal and anomalous behavior and derive the laws of biased diffusion in both these cases.     

The Motion of Repulsive Brownian Particles in Quenched Disorder

Brownian motion of the particles with repulsive interaction is investigated. When the potential condition is satisfied, the eigenvalue problem of interaction Fokker-Planck equation under certain conditions can be transformed to that of a many-particle Schrödinger equation. Using the Green's function method, we obtain the effective single-variable Fokker-Planck equation in the low density limit. We find that the diffusion of coupled Brownian particles in quenched disorder media is also anomalous in 2D. The Mittag-Leffler relaxation of pancake vortices is investigated by fractional Fokker-Planck equation.     

Anomalous diffusion probes microstructure dynamics of entangled F-actin networks

We study the thermal motion of colloidal tracer particles in entangled actin filament (F-actin) networks, where the particle radius is comparable to the mesh size of the F-actin network. In this regime, the ensemble-averaged mean-squared displacement of the particles is proportional to tau(gamma), where 0相似文献   

Noncompact N=2 supergravity

A massive spin-one multiplet with central charge is coupled to N=2 supergravity. Compared to conventional gauge fields the anomalous magnetic moment of the spin-one particles is of the opposite sign. The construction of this theory is based on an N=2 supersymmetric gauge theory associated with the noncompact group SO(2,1). As a byproduct we present a convenient expression for the N=2 Einstein-Yang-Mills lagrangian.     

A classical theory of superparamagnetic relaxation

A Fokker-Planck equation for the relaxation of a classical ferromagnetic particle coupled to a classical heat bath is derived from the Nakajima-Zwanzig equation. The equation of motion for the mean magnetization of an ensemble of particles is found to be closed only under special circumstances. In the strong motional narrowing limit the equation of motion reduces to the Bloch equations in the limit MH ? k_BT, i.e. for small particles, and to the Landau-Lifshitz equation in the opposite limit. For the motional narrowing region in toto the particular case of uniaxial anisotropy is analysed, giving an equation of motion which for large particles reduces to a modified Landau-Lifshitz equation with g-shift and a reduced damping constant. This equation cannot be meaningfully identified with the Gilbert equation.Approximate expressions for superparamagnetic relaxation rates by Kramers' method are obtained for the case of (i) triaxial (i.e. orthorhombic) and (ii) cubic (K +ve and ?ve) anisotropy, assuming large energy barriers. The results supplement Brown's expression for uniaxial anisotropy and show a more complicated dependence on the Landau-Lifshitz parameter λ than the linear dependence found by Brown. For small λ the rates tend to constant values compatible with the transition.     

A semi-statistical model of high-energy collisions

The emission of particles directly created in high-energy collisions is considered to be only partly governed by statistical laws as in Fermi's model. The motion of the created particles is to some degree related to the former motion of the incoming colliding particles. In first approximation this intermediate state is built up of two extremes: two Lorentz systems are introduced from which the particles are emitted isotropically and according to statistical laws. In the centre-of-momentum system (CMS) of the collision these two systems move in the directions of the incoming particles after collision. This approximation corresponds to the two-fireball model which we regard as a representative of a mathematical method of dealing with correlations. In further approximation phase space distributions are replaced by the thermodynamic Fermi or Bose distributions for relativistic particles. Both experimental data such as the nearly constant mean transverse momentum¯p _t and phase space calculations with constant interaction volume show that the temperaturekT reaches an upper limit asymptotically at high energies; the asymptotic region begins at about 30 GeV. The comparison with experimental particle spectra from accelerators in the 10–30GeV region shows good agreement if one uses a smooth dependence ofkT on the collision energyE ₀ and, for each independent set of measurements, an individual choice of \(\bar \gamma _f \) , the mean Lorentz factor of the “fireballs” in the CMS, and of ¯n, the mean number of created particles. The p_t-distribution of pions and the dependence of¯p _t on the particle mass can also be successfully described. At very high energies the model gives production ratios of the various kinds of particles which lie within the range of the experimental determinations. The dependence of \(\bar \gamma _f \) onE ₀ is concluded to be of the form \(\bar \gamma _f \propto E_0^{1/2} /\bar n(E_0 ) \approx 0.5E_0^{1/4} \) , i.e. CMS anisotropy is related to multiplicity.     

One-loop generated anomalous gauge couplings

We compute, at one loop, the CP-violating anomalous trilinear gauge-boson form factors which couple theW (or theZ) to the photon and theZ. In order to see which form factors are generated by which types of underlying interactions, we work with as general an underlying model as is possible. After identifying which form factors can arise at one loop in a completely general renormalizable model of spin-half and spin-zero particles, we provide explicit formulae for the induced form factors in a very broad class of such models. Our results include some previous calculations as special cases, and we identify errors in some of these.     

Crossover from normal to anomalous diffusion in systems of field-aligned dipolar particles

Using molecular dynamics simulations we investigate the translational dynamics of particles with dipolar interactions in homogenous external fields. For a broad range of concentrations, we find that the anisotropic, yet normal diffusive behavior characterizing weakly coupled systems becomes anomalous both parallel and perpendicular to the field at sufficiently high dipolar coupling and field strength. After the ballistic regime, chain formation first yields cagelike motion in all directions, followed by transient, mixed diffusive-superdiffusive behavior resulting from cooperative motion of the chains. The enhanced dynamics disappears only at higher densities close to crystallization.     

Tachyons in X-ray films deep under the lead and soil

The study of double extensive air showers (EAS) with N _e ≥ 5 · 10⁶ particles separated in time by intervals of the order of 100 ns showed (JETP Lett. 85, 101 (2007)) that to explain the origin of “delayed” showers as a result of formation in the first interaction of heavy particles, the mass of such particles must reach 5 · 10⁵ GeV. Such an explanation seems improbable. That is why it was assumed that advanced showers can be generated by tachyons. In this connection we decided to return to the analysis of our unpublished data on the anomalous events in X-ray films deep under the lead and soil. These events, we believe, can also be explained by the tachyon hypothesis.     

On Distributions of Functionals of Anomalous Diffusion Paths

Functionals of Brownian motion have diverse applications in physics, mathematics, and other fields. The probability density function (PDF) of Brownian functionals satisfies the Feynman-Kac formula, which is a Schrödinger equation in imaginary time. In recent years there is a growing interest in particular functionals of non-Brownian motion, or anomalous diffusion, but no equation existed for their PDF. Here, we derive a fractional generalization of the Feynman-Kac equation for functionals of anomalous paths based on sub-diffusive continuous-time random walk. We also derive a backward equation and a generalization to Lévy flights. Solutions are presented for a wide number of applications including the occupation time in half space and in an interval, the first passage time, the maximal displacement, and the hitting probability. We briefly discuss other fractional Schrödinger equations that recently appeared in the literature.     

Magnetic susceptibility of KMnF3 below 80°K

The temperature dependence of the a.c. susceptibility of the canted antiferromagnet KMnF₃, at frequencies of 10 MHz and less, has an anomalous maximum near 50°K. An unusual field dependence is also found. This behaviour is absent in particles smaller than ～ 20μm, and thus appears to be associated with domain wall motion.     

Spontaneously broken scale invariance and gravitation

It is proposed to combine the scalar-tensor theory of gravitation with the hypothesis of ‘spontaneously broken scale invariance’, which has been developed in quantum field theory and seems to give a better understanding of the origin of the masses of elementary particles. The general theoretical background of this approach is reviewed. In our model theory we predict that the Newtonian gravitational potential acquires an anomalous part with a force-range typically of the order of 10⁵ cm.The experimental consequences are also discussed.     

Probing scalar particle and unparticle couplings in e^{+}e^{-}\to t\bar{t} with transversely polarized beams

In searching for indications of new-physics scalar particle and unparticle couplings in $e^{+}e^{-}\to t\bar{t}$ , we consider the role of transversely polarized initial beams at e ⁺ e ^? colliders. By using a general relativistic spin density matrix formalism for describing the particles spin states, we find analytical expressions for the differential cross section of the process with t or $\bar{t}$ polarization measured, including the anomalous coupling contributions. Thanks to the transversely polarized initial beams these contributions are first order anomalous coupling corrections to the Standard Model (SM) contributions. We present and analyze the main features of the SM and anomalous coupling contributions. We show how differences between SM and anomalous coupling contributions provide means to search for anomalous coupling manifestations at future e ⁺ e ^? linear colliders.     

Quantum ergodicity in small molecules: The continuum fluorescence of nitrogen dioxide

The failure of selection rules on K_a, v, and vibronic symmetry in the visible band systems of NO₂ are interpreted as resulting from the coupling of the excited electronic state with vibrational levels of the ground electronic state which are above the threshold for ergodic motion and therefore retain no quantization of those observables. This failure is shown to lead directly to the anomalous continuum fluorescence of NO₂, and is intimately related to the anomalous lengthening of the radiative lifetime of the excited state (the Douglas effect). It is predicted that most molecules which exhibit anomalous lifetime lengthening will also exhibit anomalous selection rules and, consequently, anomalous continuum emission.