Completely mixing quantum open systems and quantum fractals

Blanchard, Ph.; Jadczyk, Arkadiusz; Olkiewicz, Robert

doi:10.1016/s0167-2789(00)00175-5

Cited by 6 publications

(2 citation statements)

References 39 publications

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“…Such a generalization is necessary in considering quantum measurements because the state transformation associated with a given measurement outcome cannot be defined on the states with zero probability of producing this outcome, see (2.3). IFSs acting on the set of pure quantum states have been examined in the framework of Event Enhanced Quantum Theory (EEQT) [12,13,14]; in particular, IFSs acting on the Bloch sphere were investigated in [31,35], see also [32,33,34]. A generalization to systems that act in the space of all quantum states was proposed in [39].…”

Section: Partial Iterated Function Systemsmentioning

confidence: 99%

Eight types of qutrit dynamics generated by unitary evolution combined with 2+1 projective measurement

Szczepanek¹

2021

Preprint

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We classify the Markov chains that can be generated on the set of quantum states by a unitarily evolving 3-dim quantum system (qutrit) that is repeatedly measured with a projective measurement (PVM) consisting of one rank-2 projection and one rank-1 projection. The dynamics of such a system can be visualized as taking place on the union of a Bloch ball and a single point, which correspond to the respective projections. The classification is given in terms of the eigenvalues of the 2 × 2 matrix that describes the dynamics arising on the Bloch ball, i.e., on the 2-dim subsystem. We also express this classification as the partition of the numerical range of the unitary operator that governs the evolution of the system. As a result, one can easily determine which of the eight possible chain types can be generated with the help of any given unitary.

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Section: Partial Iterated Function Systemsmentioning

confidence: 99%

Eight types of qutrit dynamics generated by unitary evolution combined with 2+1 projective measurement

Szczepanek¹

2021

Preprint

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“…Details of the dynamics of our model has been described elsewhere [51]. Here we will describe only the resulting non-linear iterated function system, with point dependent probabilities.…”

Section: Tetrahedral Spin Modelmentioning

confidence: 99%

How events come into being: EEQT, particle tracks, quantum chaos and tunnelling time

Blanchard

Jadczyk

Ruschhaupt

2000

Journal of Modern Optics

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In sections 1 and 2 we review Event Enhanced Quantum Theory (EEQT). In section 3 we discuss applications of EEQT to tunneling time, and compare its quantitative predictions with other approaches, in particular with Büttiker-Larmor and Bohm trajectory approach. In section 4 we discuss quantum chaos and quantum fractals resulting from simultaneous continuous monitoring of several non-commuting observables. In particular we show self-similar, nonlinear, iterated function system-type, patterns arising from quantum jumps and from the associated Markov operator. Concluding remarks pointing to possible future development of EEQT are given in section 5.

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On the pertinence to Physics of random walks induced by random dynamical systems: a survey

Petritis

2016

J. Phys.: Conf. Ser.

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Completely mixing quantum open systems and quantum fractals

Cited by 6 publications

References 39 publications

Eight types of qutrit dynamics generated by unitary evolution combined with 2+1 projective measurement

Eight types of qutrit dynamics generated by unitary evolution combined with 2+1 projective measurement

How events come into being: EEQT, particle tracks, quantum chaos and tunnelling time

On the pertinence to Physics of random walks induced by random dynamical systems: a survey

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