Condensation phenomena with distinguishable particles

We study real-space condensation phenomena in a type of classical stochastic processes (site-particle system), such as zero-range processes and urn models. We here study a stochastic process in the Ehrenfest class, i.e., particles in a site are distinguishable. In terms of the statistical mechanical analogue, the Ehrenfest class obeys the Maxwell-Boltzmann statistics. We analytically clarify conditions for condensation phenomena in disordered cases in the Ehrenfest class. In addition, we discuss the preferential urn model as an example of the disordered urn model. It becomes clear that the quenched disorder property plays an important role in the occurrence of the condensation phenomenon in the preferential urn model. It is revealed that the preferential urn model shows three types of condensation depending on the disorder parameters.Comment: 7 pages, 4 figure

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

One-parameter extension of the Doi-Peliti formalism and relation with orthogonal polynomials

An extension of the Doi-Peliti formalism for stochastic chemical kinetics is proposed. Using the extension, path-integral expressions consistent with previous studies are obtained. In addition, the extended formalism is naturally connected to orthogonal polynomials. We show that two different orthogonal polynomials, i.e., Charlier polynomials and Hermite polynomials, can be used to express the Doi-Peliti formalism explicitly.Comment: 10 page

Optimization in the design of a 12 gigahertz low cost ground receiving system for broadcast satellites. Volume 1: System design, performance, and cost analysis

The technical and economical feasibility of using the 12 GHz band for broadcasting from satellites were examined. Among the assigned frequency bands for broadcast satellites, the 12 GHz band system offers the most channels. It also has the least interference on and from the terrestrial communication links. The system design and analysis are carried out on the basis of a decision analysis model. Technical difficulties in achieving low-cost 12 GHz ground receivers are solved by making use of a die cast aluminum packaging, a hybrid integrated circuit mixer, a cavity stabilized Gunn oscillator and other state-of-the-art microwave technologies for the receiver front-end. A working model was designed and tested, which used frequency modulation. A final design for the 2.6 GHz system ground receiver is also presented. The cost of the ground-terminal was analyzed and minimized for a given figure-of-merit (a ratio of receiving antenna gain to receiver system noise temperature). The results were used to analyze the performance and cost of the whole satellite system

Optimization in the design of a 12 gigahertz low cost ground receiving system for broadcast satellites. Volume 2: Antenna system and interference

The antenna characteristics are analyzed of a low cost mass-producible ground station to be used in broadcast satellite systems. It is found that a prime focus antenna is sufficient for a low-cost but not a low noise system. For the antenna feed waveguide systems are the best choice for the 12 GHz band, while printed-element systems are recommended for the 2.6 GHz band. Zoned reflectors are analyzed and appear to be attractive from the standpoint of cost. However, these reflectors suffer a gain reduction of about one db and a possible increase in sidelobe levels. The off-axis gain of a non-auto-tracking station can be optimized by establishing a special illumination function at the reflector aperture. A step-feed tracking system is proposed to provide automatic procedures for searching for peak signal from a geostationary satellite. This system uses integrated circuitry and therefore results in cost saving under mass production. It is estimated that a complete step-track system would cost only $512 for a production quantity of 1000 units per year

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

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

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

Duality in interacting particle systems and boson representation

In the context of Markov processes, we show a new scheme to derive dual processes and a duality function based on a boson representation. This scheme is applicable to a case in which a generator is expressed by boson creation and annihilation operators. For some stochastic processes, duality relations have been known, which connect continuous time Markov processes with discrete state space and those with continuous state space. We clarify that using a generating function approach and the Doi-Peliti method, a birth-death process (or discrete random walk model) is naturally connected to a differential equation with continuous variables, which would be interpreted as a dual Markov process. The key point in the derivation is to use bosonic coherent states as a bra state, instead of a conventional projection state. As examples, we apply the scheme to a simple birth-coagulation process and a Brownian momentum process. The generator of the Brownian momentum process is written by elements of the SU(1,1) algebra, and using a boson realization of SU(1,1) we show that the same scheme is available.Comment: 13 page