THE SUPERCONFORMAL MASTER EQUATION

Entrainment in the Master Equation

The master equation plays an important role in many scientific fields including physics, chemistry, systems biology, physical finance, and sociodynamics. We consider the master equation with periodic transition rates. This may represent an external periodic excitation like the 24h solar day in biological systems or periodic traffic lights in a model of vehicular traffic. Using tools from system...

Numerical analysis of the master equation.

Applied to the master equation, the usual numerical integration methods, such as Runge-Kutta method, become inefficient when the rates associated with various transitions differ by several orders of magnitude. We introduce an integration scheme that remains stable with much larger time increments than can be used in standard methods. When only the stationary distribution is required, a direct i...

On the quantum master equation for fermions

A quantum master equation is obtained for identical fermions by including a relaxation term in addition to the mean-field Hamiltonian. [Huang C F and Huang K N 2004 Chinese J. Phys. 42 221; Gebauer R and Car R 2004 Phys. Rev. B 7

Numerical Methods for the Chemical Master Equation

Approximate probability distributions of the master equation.

Master equations are common descriptions of mesoscopic systems. Analytical solutions to these equations can rarely be obtained. We here derive an analytical approximation of the time-dependent probability distribution of the master equation using orthogonal polynomials. The solution is given in two alternative formulations: a series with continuous and a series with discrete support, both of wh...