Search results for "Quantum probability"

The Dynamical Problem for a Non Self-adjoint Hamiltonian

2012

After a compact overview of the standard mathematical presentations of the formalism of quantum mechanics using the language of C*- algebras and/or the language of Hilbert spaces we turn attention to the possible use of the language of Krein spaces.I n the context of the so-called three-Hilbert-space scenario involving the so-called PT-symmetric or quasi- Hermitian quantum models a few recent results are reviewed from this point of view, with particular focus on the quantum dynamics in the Schrodinger and Heisenberg representations.

Quantum extensions of semigroups generated by Bessel processes

1996

We construct a quantum extension of the Markov semigroup of the classical Bessel process of orderv≥1 to the noncommutative von Neumann algebra s(L2(0, +∞)) of bounded operators onL2(0, +∞).

Entropy production and information fluctuations along quantum trajectories

2013

Employing the stochastic wave function method, we study quantum features of stochastic entropy production in nonequilibrium processes of open systems. It is demonstarted that continuous measurements on the environment introduce an additional, non-thermal contribution to the entropy flux, which is shown to be a direct consequence of quantum fluctuations. These features lead to a quantum definition of single trajectory entropy contributions, which accounts for the difference between classical and quantum trajectories and results in a quantum correction to the standard form of the integral fluctuation theorem.

Governing Survival Probability to Distill Quantum States

2005

A quantum system interacting with a repeatedly measured one undergoes a nonunitary time evolution pushing it into some specific subspaces. We deeply investigate the origin of the relevant selection rule, bringing to the light its connection with the survival probability related with the two-system interaction. The possibility of inducing an effective dynamics in the distilled subspace just during the distillation process is demonstrated.

Steering distillation processes through quantum Zeno dynamics

2005

A quantum system in interaction with a repeatedly measured one undergoes a nonunitary time evolution and is pushed into a subspace substantially determined by the two-system coupling. The possibility of suitably modifying such an evolution through quantum Zeno dynamics (i.e., the generalized quantum Zeno effect) addressing the system toward an a priori decided target subspace is illustrated. Applications and their possible realizations in the context of trapped ions are also discussed.

An Operator-Based Exact Treatment of Open Quantum Systems

2005

"Quantum mechanics must be regarded as open systems. On one hand, this is due to the fact that, like in classical physics, any realistic system is subjected to a coupling to an uncontrollable environment which influences it in a non-negligible way. The theory of open quantum systems thus plays a major role in many applications of quantum physics since perfect isolation of quantum system is not possible and since a complete microscopic description or control of the environment degrees of freedom is not feasible or only partially so" [1]. Practical considerations therefore force one to seek for a simpler, effectively probabilistic description in terms of an open system. There is a close physi…

A quantum statistical approach to simplified stock markets

2009

We use standard perturbation techniques originally formulated in quantum (statistical) mechanics in the analysis of a toy model of a stock market which is given in terms of bosonic operators. In particular we discuss the probability of transition from a given value of the {\em portfolio} of a certain trader to a different one. This computation can also be carried out using some kind of {\em Feynman graphs} adapted to the present context.

Why a Quantum Tool in Classical Contexts?

2012

Geometric Optimal Control of Simple Quantum Systems

2011

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