A scheme is presented to decompose the exponential of a two-body operator in a discrete sum over exponentials of one-body operators. This discrete decomposition can be used instead of the Hubbard-Stratonovich transformation in auxiliary-field quantum Monte-Carlo methods. As an illustration, the decomposition is applied to the Hubbard model, where it is equivalent to the discrete Hubbard-Straton...

Recently, two different approaches were put forward to extend the supersymmetry method in random matrix theory from Gaussian ensembles to general rotation invariant ensembles. These approaches are the generalized Hubbard– Stratonovich transformation and the superbosonization formula. Here, we prove the equivalence of both approaches. To this end, we reduce integrals over functions of supersymme...

It is shown that a digital simulation of a noise induced phase transition using an algorithm consistent with the Ito stochastic calculus is in agreement with the predictions of that theory, whereas experiments with an analogue simulator yield measured results in agreement with the predictions of the Stratonovich theory.

We consider the Langevin equation with multiplicative noise term which depends on time and space. The corresponding Fokker-Planck equation in Stratonovich approach is investigated. Its formal solution is obtained for an arbitrary multiplicative noise term given by g(x, t) = D(x)T (t), and the behaviors of probability distributions, for some specific functions of D(x), are analyzed. In particula...

Given an integer m, a probability measure ν on [0, 1], a process X and a real function g, we define the m-order ν-integral having as integrator X and as integrand g(X). In the case of the fractional Brownian motion B , for any locally bounded function g, the corresponding integral vanishes for all odd indices m > 1 2H and any symmetric ν. One consequence is an Itô-Stratonovich type expansion fo...

We deduce a nonlinear and inhomogeneous Fokker-Planck equation within a generalized Stratonovich, or stochastic α, prescription (α=0, 1/2, and 1, respectively, correspond to the Itô, Stratonovich and anti-Itô prescriptions). We obtain its stationary state p(st)(x) for a class of constitutive relations between drift and diffusion and show that it has a q-exponential form, p(st)(x)=N(q)[1-(1-q)βV...

Spectral representations of iterated Itô and Stratonovich stochastic integrals arbitrary multiplicity, including from Taylor–Itô Taylor–Stratonovich expansions, are obtained by the spectral method. They required for implementation numerical methods solving differential equations with high orders mean-square strong convergence. The purpose such is modeling nonlinear dynamics in many fields. This...