Risto Tammelo

Three and four current reversals versus temperature in correlation ratchets with a simple sawtooth potential.

Transport of Brownian particles in a simple sawtooth potential subjected to both unbiased thermal and nonequilibrium symmetric three-level Markovian noise is considered. The effects of three and four current reversals as a function of temperature are established in such correlation ratchets. The parameter space coordinates of the fixed points associated with these current reversals and the necessary and sufficient conditions for the existence of the current reversals are found.

Diffusion and current of Brownian particles in tilted piecewise linear potentials: Amplification and coherence

Overdamped motion of Brownian particles in tilted piecewise linear periodic potentials is considered. Explicit algebraic expressions for the diffusion coefficient, current, and coherence level of Brownian transport are derived. Their dependencies on temperature, tilting force, and the shape of the potential are analyzed. The necessary and sufficient conditions for the nonmonotonic behavior of the diffusion coefficient as a function of temperature are determined. The diffusion coefficient and coherence level are found to be extremely sensitive to the asymmetry of the potential. It is established that at the values of the external force, for which the enhancement of diffusion is most rapid, the level of coherence has a wide plateau at low temperatures with the value of the Péclet factor 2. An interpretation of the amplification of diffusion in comparison with free thermal diffusion in terms of probability distribution is proposed.

A new approach to electromagnetic wave tails on a curved spacetime

We present an alternative method for constructing the exact and approximate solutions of electromagnetic wave equations whose source terms are arbitrary order multipoles on a curved spacetime. The developed method is based on the higher-order Greens functions for wave equations which are defined as distributions that satisfy wave equations with the corresponding order covariant derivatives of the Dirac delta function as the source terms. The constructed solution is applied to the study of various geometric effects on the generation and propagation of electromagnetic wave tails to first order in the Riemann tensor. Generally the received radiation tail occurs after a time delay which represents geometrical backscattering by the central gravitational source. It is shown that the truly nonlocal wave-propagation correction (the tail term) takes a universal form which is independent of multipole order. In a particular case, if the radiation pulse is generated by the source during a finite time interval, the tail term after the primary pulse is entirely determined by the energy-momentum vector of the gravitational field source: the form of the tail term is independent of the multipole structure of the gravitational source. We apply the results to a compact binary system and conclude that under certain conditions the tail energy can be a noticeable fraction of the primary pulse energy. We argue that the wave tails should be carefully considered in energy calculations of such systems.

Higher-order fundamental solutions of second-order wave equations on a curved spacetime

Higher-order fundamental solutions are defined as the distributions that satisfy the wave equations with inhomogeneous terms which are point distributions of the corresponding order. Starting from the Hadamard fundamental solution, the construction of the local higher-order fundamental solutions of the covariant scalar wave equation on a causal domain is considered. A simple recurrent algorithm for calculating such solutions is found.

Quadrupole Test Particle as a Detector of Gravitational Waves

In this paper it is shown that in general relativity the theory of motion of quadrupole test particles (QTPs) can be used to describe the energy and angular momentum absorption by detectors of gravitational waves. By specifying the form of the quadrupole moment tensor Taubs [7] equations of motion of QTPs are simplified. In these equations the terms describing the change of the mass and of the angular momentum of a QTP due to external gravitational waves are found to occur. The limiting case of the flat space-time is also briefly discussed.

On phase transition and the critical size in spatially restricted systems

We study the finite-size effects on the critical temperature in spatially restricted systems with bulk second-order phase transition using the Fokker–Planck equation approach. It is established that the dependence of the transition temperature on system size is characterized by the competition of two length scales. The first scale is similar to the correlation length, determining the critical behavior in sufficiently large samples. The second scale appears as a consequence of the stochastic nature of the order parameter and controls the transitional features in small samples, particularly in the vicinity of the critical size. It is also found that the rate of the critical slowdown of relaxation of the order parameter fluctuations increases as the volume of the system decreases.

Correlation between diffusion and coherence in Brownian motion on a tilted periodic potential

The paper studies the overdamped motion of Brownian particles in a tilted sawtooth potential. The dependencies of the diffusion coefficient and coherence level of Brownian transport on temperature, tilting force, and the shape of the potential are analyzed. It is demonstrated that at low temperatures the coherence level of Brownian transport stabilizes in the extensive domain of the tilting force where the value of the Peclet factor is Pe=2. This domain coincides with the one where the enhancement of the diffusion coefficient versus the tilting force is the most rapid. The necessary and sufficient conditions for the non-monotonic behaviour of the diffusion coefficient as a function of temperature are found. The effect of the acceleration of diffusion by bias and temperature is demonstrated to be very sensitive to the value of the asymmetry parameter of the potential.

Exact Solutions of Covariant Wave Equations with a Multipole Source Term on Curved Spacetimes

A formalism is presented for calculating exactsolutions of covariant inhomogeneous scalar and tensorwave equations whose source terms are arbitrary ordermultipoles on a curved background spacetime. The developed formalism is based on the theory ofthe higher-order fundamental solutions for wave equationwhich are the distributions that satisfy theinhomogeneous wave equation with the corresponding order covariant derivatives of the Dirac deltafunction on the right-hand side. Like the classicalGreens function for a scalar wave equation, thehigher-order fundamental solutions contain a direct termwhich has support on the light cone as well as a tailterm which has support inside the light cone. Knowinghow to compute the fundamental solutions of arbitraryorder, one can find exact multipole solutions of wave equations on curved spacetimes. Wepresent complete recurrent algorithms for calculatingthe arbitrary-order fundamental solutions and the exactmultipole solutions in a form convenient for practical computations. As an example we apply thealgorithm to a massless scalar wave field on aparticular Robertson-Walker spacetime.

A new method for solving covariant wave equations by means of higher-order fundamental solutions: proof of an algorithm

Proceeding from the classical fundamental solution (Greens function), a new method for solving covariant inhomogeneous wave equations on a causal domain of curved spacetimes is considered. A simple recurrent algorithm for calculating the solutions of the wave equation by means of higher-order fundamental solutions is presented and the corresponding theorems are proved. The method can be applied both for obtaining exact multipole solutions of the wave equation on curved spacetimes, if the exact form of the classical fundamental solution and multipole expansion of the source term are known, as well as for obtaining approximate ones. The efficiency of the proposed method is demonstrated by way of giving a short and elegant proof of a result known earlier, namely, the universality of the form of the tail correction term in the Schwarzschild spacetime.

Complete algorithms for calculating the higher-order fundamental solutions of wave equations

Complete recurrent algorithms for calculating the higher-order fundamental solutions of covariant linear wave equations for scalar and tensor wave fields on an arbitrary curved spacetime are derived. The higher-order fundamental solutions are the distributions that satisfy the wave equations with the corresponding order covariant derivatives of the Dirac delta function as the source terms. Like the classical Greens function for a scalar wave equation, the higher-order fundamental solutions contain the terms which have support on, and only on, the lightcone as well as tail terms which have support inside the lightcone. With the help of the higher-order fundamental solutions found it is possible to compute the exact multipole solutions of wave equations in a form convenient for practical computations. As applications we consider the exact field of a dipole source of variable strength travelling in an arbitrary curved spacetime and the tail term of scalar multipole waves in the Friedman dust-dominated universe for the case of minimal coupling.