On the Free Carrier-Negative U Center Interacting Model for the High-Tc Oxide Superconductor

Using the free carrier-negative U center interacting model, we have investigated the superconducting transitionr,temperature T_c, the specific heat jump at T_c, the coherence length, the penetration depth, the thermodynamic critical field and the isotope effect for the high-T_c oxide superconductor. The theoretical values of these physical quantities are consistent with the experimental values. Further, the residual electronic specific heat in the superconducting state is explained as the result of the inherent instability in this superconductive mechanism.     

Nonlinear Theory of Quantum Brownian Motion

A nonlinear theory of quantum Brownian motion in classical environment is developed based on a thermodynamically enhanced nonlinear Schrödinger equation. The latter is transformed via the Madelung transformation into a nonlinear quantum Smoluchowski-like equation, which is proven to reproduce key results from the quantum and classical physics. The application of the theory to a free quantum Brownian particle results in a nonlinear dependence of the position dispersion on time, being quantum generalization of the Einstein law of Brownian motion. It is shown that the time of decoherence from quantum to classical diffusion is proportional to the square of the thermal de Broglie wavelength divided by the classical Einstein diffusion constant.     

Development of Oxidation Sources in Preparation of High-Tc Oxide Superconductor Thin Films Using the Molecular Beam Epitaxy Method

Film preparation of oxide superconductors, mainly of the 1-2-3 (RBa₂Cu₃O_x) and Bi-containing (Bi-Sr-Ca-Cu-O) systems, by evaporation of either metals or metal compounds by low pressure is summarized, with a particular focus on the development of oxidation sources essential to the technique. Oxidizing reagents that enable the oxidation of metal evaporates to take place in high (0·1 to 10_?3 Pa) or even ultra-high (<10_?5 Pa) vacuum are summarized using the experiments of those who tried to apply the molecular beam epitaxy method to atomically controlled fabrication of thin films of the material, especially for device processing. The evaporation in various kinds of oxidizing atmosphere, including the simple method of in situ annealing of the metal layers in oxygen to the more advanced in situ preparation of the films with strong oxidizing reagents such as atomic oxygen, ozone, nitric oxide, etc. along with the thermochemistry of the oxidation of metals by low pressure with these reagents is reviewed.     

Generalised Geometric Brownian Motion: Theory and Applications to Option Pricing

Classical option pricing schemes assume that the value of a financial asset follows a geometric Brownian motion (GBM). However, a growing body of studies suggest that a simple GBM trajectory is not an adequate representation for asset dynamics, due to irregularities found when comparing its properties with empirical distributions. As a solution, we investigate a generalisation of GBM where the introduction of a memory kernel critically determines the behaviour of the stochastic process. We find the general expressions for the moments, log-moments, and the expectation of the periodic log returns, and then obtain the corresponding probability density functions using the subordination approach. Particularly, we consider subdiffusive GBM (sGBM), tempered sGBM, a mix of GBM and sGBM, and a mix of sGBMs. We utilise the resulting generalised GBM (gGBM) in order to examine the empirical performance of a selected group of kernels in the pricing of European call options. Our results indicate that the performance of a kernel ultimately depends on the maturity of the option and its moneyness.     

Quantization of Brownian Motion

Following our work on the quantization of nonconservative systems using fractional calculus, the canonical quantization of a system with Brownian motion is carried out according to the Dirac method. A suitable Lagrangian corresponding to the Langevin equation is set up. Further, a Hamiltonian is constructed and is transformed to Schrödinger's equation which is solved.     

Loop-Erasure of Planar Brownian Motion

We use a coupling technique to prove that there exists a loop-erasure of the time-reversal of a planar Brownian motion stopped on exiting a simply connected domain, and that the loop-erased curve is a radial SLE₂ curve. This result extends to Brownian motions and Brownian excursions under certain conditioning in a finitely connected plane domain, and the loop-erased curve is a continuous LERW curve.     

Testing of Multifractional Brownian Motion

Fractional Brownian motion (FBM) is a generalization of the classical Brownian motion. Most of its statistical properties are characterized by the self-similarity (Hurst) index 0<H<1. In nature one often observes changes in the dynamics of a system over time. For example, this is true in single-particle tracking experiments where a transient behavior is revealed. The stationarity of increments of FBM restricts substantially its applicability to model such phenomena. Several generalizations of FBM have been proposed in the literature. One of these is called multifractional Brownian motion (MFBM) where the Hurst index becomes a function of time. In this paper, we introduce a rigorous statistical test on MFBM based on its covariance function. We consider three examples of the functions of the Hurst parameter: linear, logistic, and periodic. We study the power of the test for alternatives being MFBMs with different linear, logistic, and periodic Hurst exponent functions by utilizing Monte Carlo simulations. We also analyze mean-squared displacement (MSD) for the three cases of MFBM by comparing the ensemble average MSD and ensemble average time average MSD, which is related to the notion of ergodicity breaking. We believe that the presented results will be helpful in the analysis of various anomalous diffusion phenomena.     

New Type of Brownian Motion

We consider an oscillator with a random mass for which the particles of the surrounding medium adhere to the oscillator for some random time after the collision (Brownian motion with adhesion for a harmonically bound particle). This is another form of a stochastic oscillator, different from oscillator usually studied that is subject to a random force or having random frequency or random damping. Calculation of the first two stationary moments shows that for white multiplicative noise of week strength the second moment coincides with that of usual Brownian motion, but for symmetric dichotomous noise, the second moment may appear the same type of the “energetic” instability, which exists for white noise random frequency or damping coefficient.     

Noncolliding Brownian Motion and Determinantal Processes

A system of one-dimensional Brownian motions (BMs) conditioned never to collide with each other is realized as (i) Dyson’s BM model, which is a process of eigenvalues of hermitian matrix-valued diffusion process in the Gaussian unitary ensemble (GUE), and as (ii) the h-transform of absorbing BM in a Weyl chamber, where the harmonic function h is the product of differences of variables (the Vandermonde determinant). The Karlin–McGregor formula gives determinantal expression to the transition probability density of absorbing BM. We show from the Karlin–McGregor formula, if the initial state is in the eigenvalue distribution of GUE, the noncolliding BM is a determinantal process, in the sense that any multitime correlation function is given by a determinant specified by a matrix-kernel. By taking appropriate scaling limits, spatially homogeneous and inhomogeneous infinite determinantal processes are derived. We note that the determinantal processes related with noncolliding particle systems have a feature in common such that the matrix-kernels are expressed using spectral projections of appropriate effective Hamiltonians. On the common structure of matrix-kernels, continuity of processes in time is proved and general property of the determinantal processes is discussed.     

Motion of Coupled Magnetic Vortices in Parallel Nanostripes

Physics of the Solid State - The periodic motion of the interacting vortex domain walls in a pair of nanostripes has been theoretically investigated. As a model, two parallel nanostripes with...     

Rotational Brownian Motion: Trajectory,Reversibility and Stochastic Entropy

Stochastic motion of macrospins is similar to driven diffusion of Brownian particles on the surface of a sphere. One crucial difference is in how the micro-states transform under time reversal. This dictates the form of stochastic entropy production (sEP). An excess sEP in the reservoir, in addition to a Clausius term, may appear depending on the interpretation of stochastic trajectory, thereby, precluding such analysis without a detailed knowledge of the governing dynamics. To show this, we derive expressions of sEP using Fokker–Planck equation, and the ratio of probability distributions of time-forward and time-reversed trajectories. We calculate probability distributions of sEP using numerical simulations, and obtain good agreement with the detailed fluctuation theorem. Within adiabatic approximation, analytic form for the distribution function is also derived.     

Survival of Near-Critical Branching Brownian Motion

Consider a system of particles performing branching Brownian motion with negative drift \(\mu= \sqrt{2 - \varepsilon}\) and killed upon hitting zero. Initially there is one particle at x>0. Kesten (Stoch. Process. Appl. 7:9–47, 1978) showed that the process survives with positive probability if and only if ε>0. Here we are interested in the asymptotics as ε→0 of the survival probability Q _μ (x). It is proved that if \(L=\pi/\sqrt{\varepsilon}\) then for all x∈?, lim? _ε→0 Q _μ (L+x)=θ(x)∈(0,1) exists and is a traveling wave solution of the Fisher-KPP equation. Furthermore, we obtain sharp asymptotics of the survival probability when x<L and L?x→∞. The proofs rely on probabilistic methods developed by the authors in (Berestycki et al. in arXiv:1001.2337, 2010). This completes earlier work by Harris, Harris and Kyprianou (Ann. Inst. Henri Poincaré Probab. Stat. 42:125–145, 2006) and confirms predictions made by Derrida and Simon (Europhys. Lett. 78:60006, 2007), which were obtained using nonrigorous PDE methods.     

Information and Entropy in Quantum Brownian Motion

We compare the thermodynamic entropy of a quantum Brownian oscillator derived from the partition function of the subsystem with the von Neumann entropy of its reduced density matrix. At low temperatures we find deviations between these two entropies which are due to the fact that the Brownian particle and its environment are entangled. We give an explanation for these findings and point out that these deviations become important in cases where statements about the information capacity of the subsystem are associated with thermodynamic properties, as it is the case for the Landauer principle.     

Stochastic Spacetime and Brownian Motion of Test Particles

The operational meaning of spacetime fluctuations is discussed. Classical spacetime geometry can be viewed as encoding the relations between the motions of test particles in the geometry. By analogy, quantum fluctuations of spacetime geometry can be interpreted in terms of the fluctuations of these motions. Thus, one can give meaning to spacetime fluctuations in terms of observables which describe the Brownian motion of test particles. We will first discuss some electromagnetic analogies, where quantum fluctuations of the electromagnetic field induce Brownian motion of test particles. We next discuss several explicit examples of Brownian motion caused by a fluctuating gravitational field. These examples include lightcone fluctuations, variations in the flight times of photons through the fluctuating geometry, and fluctuations in the expansion parameter given by a Langevin version of the Raychaudhuri equation. The fluctuations in this parameter lead to variations in the luminosity of sources. Other phenomena that can be linked to spacetime fluctuations are spectral line broadening and angular blurring of distant sources.     

A Comparative Study of the Determination of Ferrofluid Particle Size by Means of Rotational Brownian Motion and Translational Brownian Motion

Two methods, the Toroidal Technique and the Forced Rayleigh Scattering (FRS) method, were used in the determination of the size of magnetic particles and their aggregates in magnetic fluids. The toroidal technique was used in the determination of the complex, frequency dependent magnetic susceptibility, x(w)=x'(w) - ix"(w) of magnetic fluids consisting of two colloidal suspensions of cobalt ferrite in hexadecene and a colloidal suspension of magnetite in isopar m with corresponding saturation magnetisation of 45.5 mT, 20 mT and 90 mT, respectively. Plots of the susceptibility components against frequency f over the range 10 Hz to 1 MHz, are shown to have approximate Debye-type profiles with the presence of relaxation components being indicated by the frequency, f _max, of the maximum of the loss-peak in the x"(w) profiles. The FRS method (the interference of two intense laser beams in the thin film of magnetic fluid) was used to create the periodical structure of needle like clusters of magnetic particles. This creation is caused by a thermodiffusion effect known as the Soret effect. The obtained structures are indicative of as a self diffraction effect of the used primary laser beams. The relaxation phenomena arising from the switching off of the laser interference field is discussed in terms of a spectrum of relaxation times. This spectrum is proportional to the hydrodynamic particle size distribution. Corresponding calculations of particle hydrodynamic radius obtained by both mentioned methods indicate the presence of aggregates of magnetic particles.