Abstract: Quantum gates are the basic building blocks in the
quantum circuits model. These gates can be implemented using
adiabatic or non adiabatic processes. Adiabatic models can be
controlled using auxiliary qubits, whereas non adiabatic models can
be simplified by using one single-shot implementation. In this paper,
the controlled adiabatic evolutions is combined with the single-shot
implementation to obtain quantum gates with controlled non adiabatic
evolutions. This is an important improvement which can speed the
implementation of quantum gates and reduce the errors due to the
long run in the adiabatic model. The robustness of our scheme to
different types of errors is also investigated.
Abstract: We have investigated statistical properties of the defect turbulence in 1D CGLE wherein many body interaction is involved between local depressing wave (LDW) and local standing wave (LSW). It is shown that the counting number fluctuation of LDW is subject to the sub-Poisson statistics (SUBP). The physical origin of the SUBP can be ascribed to pair extinction of LDWs based on the master equation approach. It is also shown that the probability density function (pdf) of inter-LDW distance can be identified by the hyper gamma distribution. Assuming a superstatistics of the exponential distribution (Poisson configuration), a plausible explanation is given. It is shown further that the pdf of amplitude of LDW has a fattail. The underlying mechanism of its fluctuation is examined by introducing a generalized fractional Poisson configuration.
Abstract: The implementation of single-electron tunneling
(SET) simulators based on the master-equation (ME) formalism
requires the efficient and accurate identification of an exhaustive list
of active states and related tunnel events. Dynamic simulations also
require the control of the emerging states and guarantee the safe
elimination of decaying states. This paper describes algorithms for
use in the stationary and dynamic control of the lists of active states
and events. The paper presents results obtained using these
algorithms with different SET structures.
Abstract: The study of non-equilibrium systems has attracted
increasing interest in recent years, mainly due to the lack of
theoretical frameworks, unlike their equilibrium counterparts.
Studying the steady state and/or simple systems is thus one of the
main interests. Hence in this work we have focused our attention on
the driven lattice gas model (DLG model) consisting of interacting
particles subject to an external field E. The dynamics of the system
are given by hopping of particles to nearby empty sites with rates
biased for jumps in the direction of E. Having used small two
dimensional systems of DLG model, the stochastic properties at nonequilibrium
steady state were analytically studied. To understand the
non-equilibrium phenomena, we have applied the analytic approach
via master equation to calculate probability function and analyze
violation of detailed balance in term of the fluctuation-dissipation
theorem. Monte Carlo simulations have been performed to validate
the analytic results.
Abstract: The paper presented a transient population dynamics of phase singularities in 2D Beeler-Reuter model. Two stochastic modelings are examined: (i) the Master equation approach with the transition rate (i.e., λ(n, t) = λ(t)n and μ(n, t) = μ(t)n) and (ii) the nonlinear Langevin equation approach with a multiplicative noise. The exact general solution of the Master equation with arbitrary time-dependent transition rate is given. Then, the exact solution of the mean field equation for the nonlinear Langevin equation is also given. It is demonstrated that transient population dynamics is successfully identified by the generalized Logistic equation with fractional higher order nonlinear term. It is also demonstrated the necessity of introducing time-dependent transition rate in the master equation approach to incorporate the effect of nonlinearity.
Abstract: Stochastic models of biological networks are well established in systems biology, where the computational treatment of such models is often focused on the solution of the so-called chemical master equation via stochastic simulation algorithms. In contrast to this, the development of storage-efficient model representations that are directly suitable for computer implementation has received significantly less attention. Instead, a model is usually described in terms of a stochastic process or a "higher-level paradigm" with graphical representation such as e.g. a stochastic Petri net. A serious problem then arises due to the exponential growth of the model-s state space which is in fact a main reason for the popularity of stochastic simulation since simulation suffers less from the state space explosion than non-simulative numerical solution techniques. In this paper we present transition class models for the representation of biological network models, a compact mathematical formalism that circumvents state space explosion. Transition class models can also serve as an interface between different higher level modeling paradigms, stochastic processes and the implementation coded in a programming language. Besides, the compact model representation provides the opportunity to apply non-simulative solution techniques thereby preserving the possible use of stochastic simulation. Illustrative examples of transition class representations are given for an enzyme-catalyzed substrate conversion and a part of the bacteriophage λ lysis/lysogeny pathway.