Langevin Equations with Grassmann Variables

Elimination of fast variables in chemical Langevin equations.

Internal and external fluctuations are ubiquitous in cellular signaling processes. Because biochemical reactions often evolve on disparate time scales, mathematical perturbation techniques can be invoked to reduce the complexity of stochastic models. Previous work in this area has focused on direct treatment of the master equation. However, eliminating fast variables in the chemical Langevin eq...

Supersymmetry without Grassmann variables

Supersymmetry transformations may be represented by unitary operators in a formulation of supersymmetry without numbers that anti-commute. The physical relevance of this formulation hinges on whether or not one may add states of even and odd fermion number, a question which soon may be settled by experiment.

Supersymmetry without Grassmann variables

Path Integrals with Generalized Grassmann Variables

We construct path integral representations for the evolution operator of q-oscillators with root of unity values of q-parameter using BargmannFock representations with commuting and non-commuting variables, the differential calculi being q-deformed in both cases. For q = −1 we obtain a new form of Grassmann-like path integral. on leave of absence from Nuclear Physics Institute, Moscow State Uni...

Lattice Boltzmann-Langevin Equations

Intrinsic fluctuations around the solution of the lattice Boltzmann equation are described or modeled by addition of a white Gaussian noise source. For stationary states a fluctuation-dissipation theorem relates the variance of the fluctuations to the linearized Boltzmann collision operator and the pair correlation function.