Thermally activated escape rates of uniaxial spin systems with transverse field

Classical escape rates of uniaxial spin systems are characterized by a prefactor differing from and much smaller than that of the particle problem, since the maximum of the spin energy is attained everywhere on the line of constant latitude: theta=const, 0 =< phi =< 2*pi. If a transverse field is applied, a saddle point of the energy is formed, and high, moderate, and low damping regimes (similar to those for particles) appear. Here we present the first analytical and numerical study of crossovers between the uniaxial and other regimes for spin systems. It is shown that there is one HD-Uniaxial crossover, whereas at low damping the uniaxial and LD regimes are separated by two crossovers.Comment: 4 PR pages, 3 figures, final published versio

Field dependence of the temperature at the peak of the ZFC magnetization

The effect of an applied magnetic field on the temperature at the maximum of the ZFC magnetization, $M_{ZFC}$, is studied using the recently obtained analytic results of Coffey et al. (Phys. Rev. Lett. {\bf 80}(1998) 5655) for the prefactor of the N\'{e}el relaxation time which allow one to precisely calculate the prefactor in the N\'{e}el-Brown model and thus the blocking temperature as a function of the coefficients of the Taylor series expansion of the magnetocrystalline anisotropy. The present calculations indicate that even a precise determination of the prefactor in the N\'{e}el-Brown theory, which always predicts a monotonic decrease of the relaxation time with increasing field, is insufficient to explain the effect of an applied magnetic field on the temperature at the maximum of the ZFC magnetization. On the other hand, we find that the non linear field-dependence of the magnetization along with the magnetocrystalline anisotropy appears to be of crucial importance to the existence of this maximum.Comment: 14 LaTex209 pages, 6 EPS figures. To appear in J. Phys.: Condensed Matte

Monte Carlo simulation with time step quantification in terms of Langevin dynamics

For the description of thermally activated dynamics in systems of classical magnetic moments numerical methods are desirable. We consider a simple model for isolated magnetic particles in a uniform field with an oblique angle to the easy axis of the particles. For this model, a comparison of the Monte Carlo method with Langevin dynamics yields new insight in the interpretation of the Monte Carlo process, leading to the implementation of a new algorithm where the Monte Carlo step is time-quantified. The numeric results for the characteristic time of the magnetisation reversal are in excellent agreement with asymptotic solutions which itself are in agreement with the exact numerical results obtained from the Fokker-Planck equation for the Neel-Brown model.Comment: 5 pages, Revtex, 4 Figures include

Greenberger-Horne-Zeilinger state protocols for fully connected qubit networks

We generalize the recently proposed Greenberger-Horne-Zeilinger (GHZ) tripartite protocol [A. Galiautdinov, J. M. Martinis, Phys. Rev. A 78, 010305(R) (2008)] to fully connected networks of weakly coupled qubits interacting by way of anisotropic Heisenberg exchange g(XX+YY)+g1*ZZ. Our model adopted here differs from the more familiar Ising-Heisenberg chain in that here every qubit interacts with every other qubit in the circuit. The assumption of identical couplings on all qubit pairs allows an elegant proof of the protocol for arbitrary N. In order to further make contact with experiment, we study fidelity degradation due to coupling imperfections by numerically simulating the N=3 and N=4 cases. Our simulations indicate that the best fidelity at unequal couplings is achieved when (a) the system is initially prepared in the uniform superposition state (similarly to how it is done in the ideal case), and (b) the entangling time and the final rotations on each of the qubits are appropriately adjusted.Comment: 11 pages, 1 figur

Role of interactions in ferrofluid thermal ratchets

Orientational fluctuations of colloidal particles with magnetic moments may be rectified with the help of external magnetic fields with suitably chosen time dependence. As a result a noise-driven rotation of particles occurs giving rise to a macroscopic torque per volume of the carrier liquid. We investigate the influence of mutual interactions between the particles on this ratchet effect by studying a model system with mean-field interactions. The stochastic dynamics may be described by a nonlinear Fokker-Planck equation for the collective orientation of the particles which we solve approximately by using the effective field method. We determine an interval for the ratio between coupling strength and noise intensity for which a self-sustained rectification of fluctuations becomes possible. The ratchet effect then operates under conditions for which it were impossible in the absence of interactions.Comment: 18 pages, 10 figure

On hypergeometric series reductions from integral representations, the Kampe de Feriet function, and elsewhere

Single variable hypergeometric functions pFq arise in connection with the power series solution of the Schrodinger equation or in the summation of perturbation expansions in quantum mechanics. For these applications, it is of interest to obtain analytic expressions, and we present the reduction of a number of cases of pFp and p+1F_p, mainly for p=2 and p=3. These and related series have additional applications in quantum and statistical physics and chemistry.Comment: 17 pages, no figure

Trends in stratospheric minor constituents

Photochemical models predict that increasing source gas concentrations are also expected to lead to changes in the concentrations of both catalytically active radical species (such as NO2, ClO, and OH) and inactive reservoir species (such as HNO3, HCl, and H2O). For simplicity, we will refer to all these as trace species. Those species that are expected to have increasing concentration levels are investigated. Additionally, the trace species concentration levels are monitored for unexpected changes on the basis of the measure increase in source gases. Carrying out these investigations is difficult due to the limited data base of measurements of stratospheric trace species. In situ measurements are made only infrequently, and there are few satelliteborne measurements, most over a time space insufficient for trend determination. Instead, ground-based measurements of column content must be used for many species, and interpretation is complicated by contributions from the troposphere or mesosphere or both. In this chapter, we examine existing measurements as published or tabulated

Transient rectification of Brownian diffusion with asymmetric initial distribution

In an ensemble of non-interacting Brownian particles, a finite systematic average velocity may temporarily develop, even if it is zero initially. The effect originates from a small nonlinear correction to the dissipative force, causing the equation for the first moment of velocity to couple to moments of higher order. The effect may be relevant when a complex system dissociates in a viscous medium with conservation of momentum