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Stochastic Behaviour of the Magnetisation in a Classically Integrable Quantum System
Europhysics Letters (EPL), 1991We present a two-dimensional model of noninteracting electrons in an external magnetic field. This model is of common use in the study of the Hall effect. In the classical limit the system is integrable. Nevertheless at the quantum level, the magnetisation as a function of the number of electrons exhibits a chaotic behaviour.
K. REZAKHANLOU +2 more
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Algebraic theory of product integrals in quantum stochastic calculus
Journal of Mathematical Physics, 2000Motivated by the search for solutions of the quantum Yang–Baxter equation, an algebraic theory of quantum stochastic product integrals is developed. The product integrators are formal power series in an indeterminate h whose coefficients are elements of the Lie algebra ℒ labelling the usual integrators of a many-dimensional quantum stochastic calculus.
Hudson, R. L., Pulmannová, S.
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Stochastic Integration and Quantum Ito’s Formula
1992In Section 21 we have already seen how the classical stochastic processes with independent increments can be realised as suitable linear combinations of the creation, conservation and annihilation operators in the boson Fock space Γs (ℋ) over a Hilbert space ℋ. This includes, in particular, the Brownian motion and Poisson process.
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On Solutions of Quantum Stochastic Integral Equations
1986Throughout the discussion, we employ the notation and concepts already introduced in [1]. Thus, we also adopt here the partial *-algebraic setting of that paper.
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Quantum Stochastic Processes and Quantum non-Markovian Phenomena
PRX Quantum, 2021Kavan Modi, Simon Milz
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Stochastic integral representations of quantum martingales on multiple Fock space
Proceedings of the Indian Academy of Sciences - Section A, 2006Un Çig Ji
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Efficient stochastic thermostatting of path integral molecular dynamics
Journal of Chemical Physics, 2010Parrinello Michele +2 more
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