Direct numerical method for counting statistics in stochastic processes

We propose a direct numerical method to calculate the statistics of the number of transitions in stochastic processes, without having to resort to Monte Carlo calculations. The method is based on a generating function method, and arbitrary moments of the probability distribution of the number of transitions are in principle calculated by solving numerically a system of coupled differential equations. As an example, a two state model with a time-dependent transition matrix is considered and the first, second and third moments of the current are calculated. This calculation scheme is applicable for any stochastic process with a finite state space, and it would be helpful to study current statistics in nonequilibrium systems.Comment: 8 pages, 2 figure

Noncyclic and nonadiabatic geometric phase for counting statistics

We propose a general framework of the geometric-phase interpretation for counting statistics. Counting statistics is a scheme to count the number of specific transitions in a stochastic process. The cumulant generating function for the counting statistics can be interpreted as a `phase', and it is generally divided into two parts: the dynamical phase and a remaining one. It has already been shown that for cyclic evolution the remaining phase corresponds to a geometric phase, such as the Berry phase or Aharonov-Anandan phase. We here show that the remaining phase also has an interpretation as a geometric phase even in noncyclic and nonadiabatic evolution.Comment: 12 pages, 1 figur

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

Static and Dynamic Chain Structures in the Mean-Field Theory

We give a brief overview of recent work examining the presence of $\alpha$-clusters in light nuclei within the Skyrme-force Hartree-Fock model. Of special significance are investigations into $\alpha$-chain structures in carbon isotopes and $^{16}$O. Their stability and possible role in fusion reactions are examined in static and time-dependent Hartree-Fock calculations. We find a new type of shape transition in collisions and a centrifugal stabilization of the $4\alpha$ chain state in a limited range of angular momenta. No stabilization is found for the $3\alpha$ chain.Comment: Fusionn 11 Conference, St. Malo, France, 201

Statistical-mechanical iterative algorithms on complex networks

The Ising models have been applied for various problems on information sciences, social sciences, and so on. In many cases, solving these problems corresponds to minimizing the Bethe free energy. To minimize the Bethe free energy, a statistical-mechanical iterative algorithm is often used. We study the statistical-mechanical iterative algorithm on complex networks. To investigate effects of heterogeneous structures on the iterative algorithm, we introduce an iterative algorithm based on information of heterogeneity of complex networks, in which higher-degree nodes are likely to be updated more frequently than lower-degree ones. Numerical experiments clarified that the usage of the information of heterogeneity affects the algorithm in BA networks, but does not influence that in ER networks. It is revealed that information of the whole system propagates rapidly through such high-degree nodes in the case of Barab{\'a}si-Albert's scale-free networks.Comment: 7 pages, 6 figure

An improved continuous compositional-spread technique based on pulsed-laser deposition and applicable to large substrate areas

A new method for continuous compositional-spread (CCS) thin-film fabrication based on pulsed-laser deposition (PLD) is introduced. This approach is based on a translation of the substrate heater and the synchronized firing of the excimer laser, with the deposition occurring through a slit-shaped aperture. Alloying is achieved during film growth (possible at elevated temperature) by the repeated sequential deposition of sub-monolayer amounts. Our approach overcomes serious shortcomings in previous in-situ implementations of CCS based on sputtering or PLD, in particular the variations of thickness across the compositional spread and the differing deposition energetics as function of position. While moving-shutter techniques are appropriate for PLD-approaches yielding complete spreads on small substrates (i.e. small as compared to distances over which the deposition parameters in PLD vary, typically about 1 cm), our method can be used to fabricate samples that are large enough for individual compositions to be analyzed by conventional techniques, including temperature-dependent measurements of resistivity and dielectric and magnetic and properties (i.e. SQUID magnetometry). Initial results are shown for spreads of (Sr,Ca)RuO$_3$.Comment: 6 pages, 8 figures, accepted for publication in Rev. Sci. Instru

Two Langevin equations in the Doi-Peliti formalism

A system-size expansion method is incorporated into the Doi-Peliti formalism for stochastic chemical kinetics. The basic idea of the incorporation is to introduce a new decomposition of unity associated with a so-called Cole-Hopf transformation. This approach elucidates a relationship between two different Langevin equations; one is associated with a coherent-state path-integral expression and the other describes density fluctuations. A simple reaction scheme $X \rightleftarrows X+X$ is investigated as an illustrative example.Comment: 14page

Particle current in symmetric exclusion process with time-dependent hopping rates

In a recent study, (Jain et al 2007 Phys. Rev. Lett. 99 190601), a symmetric exclusion process with time-dependent hopping rates was introduced. Using simulations and a perturbation theory, it was shown that if the hopping rates at two neighboring sites of a closed ring vary periodically in time and have a relative phase difference, there is a net DC current which decreases inversely with the system size. In this work, we simplify and generalize our earlier treatment. We study a model where hopping rates at all sites vary periodically in time, and show that for certain choices of relative phases, a DC current of order unity can be obtained. Our results are obtained using a perturbation theory in the amplitude of the time-dependent part of the hopping rate. We also present results obtained in a sudden approximation that assumes large modulation frequency.Comment: 17 pages, 2 figure