538 research outputs found
A stochastic golden rule and quantum Langevin equation for the low density limit
A rigorous derivation of quantum Langevin equation from microscopic dynamics
in the low density limit is given. We consider a quantum model of a microscopic
system (test particle) coupled with a reservoir (gas of light Bose particles)
via interaction of scattering type. We formulate a mathematical procedure (the
so-called stochastic golden rule) which allows us to determine the quantum
Langevin equation in the limit of large time and small density of particles of
the reservoir. The quantum Langevin equation describes not only dynamics of the
system but also the reservoir. We show that the generator of the corresponding
master equation has the Lindblad form of most general generators of completely
positive semigroups
The stochastic limit in the analysis of the open BCS model
In this paper we show how the perturbative procedure known as {\em stochastic
limit} may be useful in the analysis of the Open BCS model discussed by Buffet
and Martin as a spin system interacting with a fermionic reservoir. In
particular we show how the same values of the critical temperature and of the
order parameters can be found with a significantly simpler approach
On Quantum Markov Chains on Cayley tree II: Phase transitions for the associated chain with XY-model on the Cayley tree of order three
In the present paper we study forward Quantum Markov Chains (QMC) defined on
a Cayley tree. Using the tree structure of graphs, we give a construction of
quantum Markov chains on a Cayley tree. By means of such constructions we prove
the existence of a phase transition for the XY-model on a Cayley tree of order
three in QMC scheme. By the phase transition we mean the existence of two now
quasi equivalent QMC for the given family of interaction operators
.Comment: 34 pages, 1 figur
Quantum Markov Fields
The Markov property for quantum lattice systems is investigated in terms of generalized
conditional expectations. General properties of (particular cases of) quantum Markov
elds, i.e. quantum Markov processes with multi-dimensional indices, are pointed out.
In such a way, deep connections with the KMS boundary condition, as well as phenom-
ena of phase transitions and symmetry breaking, naturally emerge
Markov states and chains on the car algebra
We introduce the notion of Markov states and chains on the Canonical Anticommutation Relations algebra over ℤ, emphasizing some remarkable differences with the infinite tensor product case. We describe the structure of the Markov states on this algebra and show that, contrarily to the infinite tensor product case, not all these states are diagonalizable. A general method to construct nontrivial quantum Markov chains on the CAR algebra is also proposed and illustrated by some pivotal examples. This analysis provides a further step for a satisfactory theory of quantum Markov processes
Stock markets and quantum dynamics: a second quantized description
In this paper we continue our descriptions of stock markets in terms of some
non abelian operators which are used to describe the portfolio of the various
traders and other {\em observable} quantities. After a first prototype model
with only two traders, we discuss a more realistic model of market with an
arbitrary number of traders. For both models we find approximated solutions for
the time evolution of the portfolio of each trader. In particular, for the more
realistic model, we use the {\em stochastic limit} approach and a {\em fixed
point like} approximation
Dynamical entropy of generalized quantum Markov chains on gauge invariant -algebras
We prove that the mean entropy and the dynamical entropy are equal for
generalized quantum Markov chains on gauge-invariant -algebras.Comment: 8 page
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