A field theoretic approach to master equations and a variational method beyond the Poisson ansatz

We develop a variational scheme in a field theoretic approach to a stochastic process. While various stochastic processes can be expressed using master equations, in general it is difficult to solve the master equations exactly, and it is also hard to solve the master equations numerically because of the curse of dimensionality. The field theoretic approach has been used in order to study such complicated master equations, and the variational scheme achieves tremendous reduction in the dimensionality of master equations. For the variational method, only the Poisson ansatz has been used, in which one restricts the variational function to a Poisson distribution. Hence, one has dealt with only restricted fluctuation effects. We develop the variational method further, which enables us to treat an arbitrary variational function. It is shown that the variational scheme developed gives a quantitatively good approximation for master equations which describe a stochastic gene regulatory network.Comment: 13 pages, 2 figure

The stochastic pump current and the non-adiabatic geometrical phase

We calculate a pump current in a classical two-state stochastic chemical kinetics by means of the non-adiabatic geometrical phase interpretation. The two-state system is attached to two particle reservoirs, and under a periodic perturbation of the kinetic rates, it gives rise to a pump current between the two-state system and the absorbing states. In order to calculate the pump current, the Floquet theory for the non-adiabatic geometrical phase is extended from a Hermitian case to a non-Hermitian case. The dependence of the pump current on the frequency of the perturbative kinetic rates is explicitly derived, and a stochastic resonance-like behavior is obtained.Comment: 11 page

Current and fluctuation in a two-state stochastic system under non-adiabatic periodic perturbation

We calculate a current and its fluctuation in a two-state stochastic system under a periodic perturbation. The system could be interpreted as a channel on a cell surface or a single Michaelis-Menten catalyzing enzyme. It has been shown that the periodic perturbation induces so-called pump current, and the pump current and its fluctuation are calculated with the aid of the geometrical phase interpretation. We give a simple calculation recipe for the statistics of the current, especially in a non-adiabatic case. The calculation scheme is based on the non-adiabatic geometrical phase interpretation. Using the Floquet theory, the total current and its fluctuation are calculated, and it is revealed that the average of the current shows a stochastic-resonance-like behavior. In contrast, the fluctuation of the current does not show such behavior.Comment: 7 pages, 1 figur

In-situ photoemission study of Pr_{1-x}Ca_xMnO_3 epitaxial thin films with suppressed charge fluctuations

We have performed an {\it in-situ} photoemission study of Pr_{1-x}Ca_xMnO_3 (PCMO) thin films grown on LaAlO_3 (001) substrates and observed the effect of epitaxial strain on the electronic structure. We found that the chemical potential shifted monotonically with doping, unlike bulk PCMO, implying the disappearance of incommensurate charge fluctuations of bulk PCMO. In the valence-band spectra, we found a doping-induced energy shift toward the Fermi level (E_F) but there was no spectral weight transfer, which was observed in bulk PCMO. The gap at E_F was clearly seen in the experimental band dispersions determined by angle-resolved photoemission spectroscopy and could not be explained by the metallic band structure of the C-type antiferromagnetic state, probably due to localization of electrons along the ferromagnetic chain direction or due to another type of spin-orbital ordering.Comment: 5 pages, 4 figure

Infrared anomalous Hall effect in SrRuO3_3: Evidence for crossover to intrinsic behavior

The origin of the Hall effect in many itinerant ferromagnets is still not resolved, with an anomalous contribution from the sample magnetization that can exhibit extrinsic or intrinsic behavior. We report the first mid-infared (MIR) measurements of the complex Hall ($\theta_H$), Faraday ($\theta_F$), and Kerr ($\theta_K$) angles, as well as the Hall conductivity ($\sigma_{xy}$) in a SrRuO$_3$ film in the 115-1400 meV energy range. The magnetic field, temperature, and frequency dependence of the Hall effect is explored. The MIR magneto-optical response shows very strong frequency dependence, including sign changes. Below 200 meV, the MIR $\theta_H (T)$ changes sign between 120 and 150 K, as is observed in dc Hall measurements. Above 200 meV, the temperature dependence of $\theta_H$ is similar to that of the dc magnetization and the measurements are in good agreement with predictions from a band calculation for the intrinsic anomalous Hall effect (AHE). The temperature and frequency dependence of the measured Hall effect suggests that whereas the behavior above 200 meV is consistent with an intrinsic AHE, the extrinsic AHE plays an important role in the lower energy response.Comment: The resolution of figures is improve

Observations of snowpack properties to evaluate ground-based microwave remote sensing

Active microwave radar has been shown to have great potential for estimating snow water equivalent (SWE) globally from space. To help evaluate optimal active microwave sensor configurations to observe SWE, we evaluated ground-based Frequency Modulated Continuous Wave (FMCW) radar (12–18 GHz, cross-polarisation) using very high resolution in-situ observations of snowpack layering, dielectric permittivity and density over a 10 m snow trench on Toolik Lake, Alaska. Results showed that the thicknesses of layers within the 10 m trench were highly variable over short distances (< 1 m), even where total snow depth changed very little. Layer boundaries observed using NIR photography identified all bands of high radar backscatter. Although additional observations of density and dielectric permittivity helped to explain the causes of backscatter, not all snowpack properties which cause backscatter were coincident with strong vertical changes in density or permittivity. Further observations of high surface roughness in layer boundaries explained some areas of weak backscatter, nonetheless it was shown that a suite of coincident observations, rather than a single technique in isolation, were required to adequately explain the variability of backscatter and the influence of snowpack properties upon it