The dynamics of the spin–boson Hamiltonian is considered in the stochastic approximation. The Hamiltonian describes a two–level system coupled to an environment and is widely used in physics, chemistry and the theory of quantum measurement. We demonstrate that the method of the stochastic approximation which is a general method of consideration of dynamics… (More)
We prove that the locality condition is irrelevant to Bell in equality. We check that the real origin of the Bell's inequality is the assumption of applicability of classical (Kol-mogorovian) probability theory to quantum mechanics. – Inequalities among numbers – The Bell inequality – Implications of the Bell's inequalities for the singlet correlations –… (More)
We propose a model of an approximatively two–dimensional electron gas in a uniform electric and magnetic field and interacting with a positive background through the Fröhlich Hamiltonian. We consider the stochastic limit of this model and we find the quantum Langevin equation and the generator of the master equation. This allows us to calculate the explicit… (More)
Motivated by the work of Segal and Segal in  on the Black-Scholes pricing formula in the quantum context, we study a quantum extension of the Black-Scholes equation within the context of Hudson-Parthasarathy quantum stochastic calculus,. Our model includes stock markets described by quantum Brownian motion and Poisson process. An option is a ticket… (More)
There exists an important problem whether there exists an algorithm to solve an NP-complete problem in polynomial time. In this paper, a new concept of quantum adaptive stochastic systems is proposed, and it is shown that it can be used to solve the problem above.
We analyze, from the point of view of quantum probability, statistical data from two interesting experiments, done by Shafir and Tversky [1, 2] in the domain of cog-nitive psychology. These are gambling experiments of Prisoner Dilemma type. They have important consequences for economics, especially for the justification of the Savage " Sure Thing Principle… (More)
In this report we discuss some results of non–commutative (quantum) probability theory relating the various notions of statistical independence and the associated quantum central limit theorems to different aspects of mathematics and physics including: q–deformed and free central limit theorems; the description of the master (i.e. central limit) field in… (More)
We investigate the necessary and sufficient conditions in order that a uni-tary operator can amplify a pre-assigned component relative to a particular basis of a generic vector at the expence of the other components. This leads to a general method which allows, given a vector and one of its components we want to amplify, to choose the optimal unitary… (More)