Fluctuations, Higher Order Anharmonicities, and Landau Expansion for Barium Titanate

Correct phenomenological description of ferroelectric phase transitions in barium titanate requires accounting for eighth-order terms in the free energy expansion, in addition to the conventional sixth-order contributions. Another unusual feature of BaTiO_3 crystal is that the coefficients B_1 and B_2 of the terms P_x^4 and P_x^2*P_y^2 in the Landau expansion depend on the temperature. It is shown that the temperature dependence of B_1 and B_2 may be caused by thermal fluctuations of the polarization, provided the fourth-order anharmonicity is anomalously small, i. e. the nonlinearity of P^4 type and higher-order ones play comparable roles. Non-singular (non-critical) fluctuation contributions to B_1 and B_2 are calculated in the first approximation in sixth-order and eighth-order anharmonic constants. Both contributions increase with the temperature, which is in agreement with available experimental data. Moreover, the theory makes it possible to estimate, without any additional assumptions, the ratio of fluctuation (temperature dependent) contributions to coefficients B_1 and B_2. Theoretical value of B_1/B_2 appears to be close to that given by experiments.Comment: 5 pages, 1 figur

First passage time of N excluded volume particles on a line

Motivated by recent single molecule studies of proteins sliding on a DNA molecule, we explore the targeting dynamics of N particles ("proteins") sliding diffusively along a line ("DNA") in search of their target site (specific target sequence). At lower particle densities, one observes an expected reduction of the mean first passage time proportional to 1/N**2, with corrections at higher concentrations. We explicitly take adsorption and desorption effects, to and from the DNA, into account. For this general case, we also consider finite size effects, when the continuum approximation based on the number density of particles, breaks down. Moreover, we address the first passage time problem of a tagged particle diffusing among other particles.Comment: 9 pages, REVTeX, 6 eps figure

Quantum Resonances of Kicked Rotor and SU(q) group

The quantum kicked rotor (QKR) map is embedded into a continuous unitary transformation generated by a time-independent quasi-Hamiltonian. In some vicinity of a quantum resonance of order $q$, we relate the problem to the {\it regular} motion along a circle in a $(q^2-1)$-component inhomogeneous "magnetic" field of a quantum particle with $q$ intrinsic degrees of freedom described by the $SU(q)$ group. This motion is in parallel with the classical phase oscillations near a non-linear resonance.Comment: RevTeX, 4 pages, 3 figure

Intersubband plasmons in quasi-one-dimensional electron systems on a liquid helium surface

The collective excitation spectra are studied for a multisubband quasi-one-dimensional electron gas on the surface of liquid helium. Different intersubband plasmon modes are identified by calculating the spectral weight function of the electron gas within a 12 subband model. Strong intersubband coupling and depolarization shifts are found. When the plasmon energy is close to the energy differences between two subbands, Landau damping in this finite temperature system leads to plasmon gaps at small wavevectors.Comment: To be published as a Rapid Communication in Phys. Rev.

Towards deterministic equations for Levy walks: the fractional material derivative

Levy walks are random processes with an underlying spatiotemporal coupling. This coupling penalizes long jumps, and therefore Levy walks give a proper stochastic description for a particle's motion with broad jump length distribution. We derive a generalized dynamical formulation for Levy walks in which the fractional equivalent of the material derivative occurs. Our approach will be useful for the dynamical formulation of Levy walks in an external force field or in phase space for which the description in terms of the continuous time random walk or its corresponding generalized master equation are less well suited

Understanding Anomalous Transport in Intermittent Maps: From Continuous Time Random Walks to Fractals

We show that the generalized diffusion coefficient of a subdiffusive intermittent map is a fractal function of control parameters. A modified continuous time random walk theory yields its coarse functional form and correctly describes a dynamical phase transition from normal to anomalous diffusion marked by strong suppression of diffusion. Similarly, the probability density of moving particles is governed by a time-fractional diffusion equation on coarse scales while exhibiting a specific fine structure. Approximations beyond stochastic theory are derived from a generalized Taylor-Green-Kubo formula.Comment: 4 pages, 3 eps figure