In this paper we introduce and analyze a class of diffusion type equations related to certain non-Markovian stochastic processes. We start from the forward drift equation which is made non-local in time by the introduction of a suitable chosen memory kernel K(t). The resulting non-Markovian...

The evolution of open systems, subject to both Hamiltonian and dissipative forces, is studied by writing the nm element of the time (t) dependent density matrix in the formρnm(t)=1A∑α=1Aγnα(t)γmα*(t).The so called “square-root factors”, the γ(t)'s, are non-square matrices and are...

The method of stochastic quantization for a scalar field theory is reviewed. A brief survey for the case of self-interacting scalar field, implementing the stochastic perturbation theory up to the one-loop level, is presented. Then, it is introduced a colored random noise in the Einstein's...

We consider the non-Markovian Langevin evolution of a dissipative dynamical system in quantum mechanics in the path integral formalism. After discussing the role of the frequency cutoff for the interaction of the system with the heat bath and the kernel and noise correlator that follow from the...

We address the question as to what extent individuals, when given information in marketing polls on the decisions made by the previous Nr individuals questioned, are likely to change their original choices. The processes can be formulated in terms of a Cost function equivalent to a Hamiltonian,...

An important class of random walks includes those in which the random increment at time step t depends on the complete history of the process. We consider a recently proposed discrete-time non-Markovian random walk process characterized by a memory parameter p. We numerically calculate the first...

A 1D bosonic many-body system, related to the Bose–Einstein condensation in atomic traps and periodic optical lattices, is described by a coherent state path integral of the grand canonical partition function. Since the interaction is given by a contact potential, as commonly applied in atomic...

We present a perturbation theory by extending a prescription due to Feynman for computing the probability density function for the random flight motion. The method can be applied to a wide variety of otherwise difficult circumstances. The series for the exact moments, if not the distribution...

Spatial transfer-matrices are constructed for 1D su(2)-spin and h4-bosonic many-body systems in external magnetic fields B(x) or potentials V(x). In the case of the spin system, generalized coherent states are applied to derive a path integral which can be reordered according to the spatial...

General stochastic dynamics, developed in a framework of Feynman path integrals, have been applied to Lewinian field-theoretic psychodynamics [K. Lewin, Field Theory in Social Science, University of Chicago Press, Chicago, 1951; K. Lewin, Resolving Social Conflicts, and, Field Theory in Social...