Quasiclassical equations of motion for nonlinear Brownian systems

Quasiclassical equations of motion for nonlinear Brownian systems.

Following the formalism of Gell-Mann and Hartle, phenomenological equations of motion are derived from the decoherence functional of quantum mechanics, using a path-integral description. This is done explicitly for the case of a system interacting with a “bath” of harmonic oscillators whose individual motions are neglected. The results are compared to the equations derived from the purely class...

ABS methods for nonlinear systems of algebraic equations

 Abstract    This paper gives a survey of the theory and practice of nonlinear ABS methods including various types of generalizations and computer testing. We also show three applications to special problems, two of which are new.

Dynamical peculiarities of the nonlinear quasiclassical systems

The quantum-classical correspondence for dynamics of the nonlinear classically chaotic systems is analysed. The problem of quantum chaos consists of two parts: the quasiclassical quantisation of the chaotic systems and attempts to understand the classical chaos in terms of quantum mechanics. The first question has been partially solved by the Gutzwiller semiclassical trace formula for the eigen...

Stochastic Differential Equations for Sticky Brownian Motion

dXt = 12 d` 0 t (X) + I(Xt >0) dBt I(Xt =0) dt = 1 2μ d` 0 t (X) for reflecting Brownian motion X in IR+ sticky at 0 , where X starts at x in the state space, μ ∈ (0,∞) is a given constant, `(X) is the local time of X at 0 , and B is a standard Brownian motion. We prove that both systems (i) have a jointly unique weak solution and (ii) have no strong solution. The latter fact verifies Skorokhod...

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion