Galilean covariance of quantum-classical hybrid systems of the Sudarshan type

Manjarres, A. D. Bermúdez; Marín-Medina, Nathaly

doi:10.1103/physreva.102.042221

Cited by 6 publications

(8 citation statements)

References 18 publications

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“…In the KvH theory, the unitary transformation associated to space translation and rotations are the same as in Eqs. ( 15) and (19). Galilean boosts and time translation are modified to include a phase factor as follows…”

Section: The Kvn and Kvh Representations Of The Galilei Groupmentioning

confidence: 99%

“…The KvN and KvH theories are also of interest for the formulation of some quantum-classical hybrid theories [9,10,[18][19][20][21][22][23][24][25]. In this last regard, the knowledge of the non-relativistic space-time symmetries of the KvN theory was used to study the viability of quantum-classical hybrids of the Sudarshan type [26]. It was shown there that in Sudarshan hybrids, translational invariance does not equate to the conservation of the total linear momentum.…”

Section: Introductionmentioning

confidence: 99%

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Projective representation of the Galilei group for classical and quantum–classical systems*

Manjarres¹

2021

J. Phys. A: Math. Theor.

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A physically relevant unitary irreducible non-projective representation of the Galilei group is possible in the Koopman–von Neumann formulation of classical mechanics. This classical representation is characterized by the vanishing of the central charge of the Galilei algebra. This is in contrast to the quantum case where the mass plays the role of the central charge. Here we show, by direct construction, that classical mechanics also allows for a projective representation of the Galilei group where the mass is the central charge of the algebra. We extend the result to certain kind of quantum–classical hybrid systems.

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Section: The Kvn and Kvh Representations Of The Galilei Groupmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Projective representation of the Galilei group for classical and quantum–classical systems*

Manjarres¹

2021

J. Phys. A: Math. Theor.

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“…Moreover, tools originally developed for quantum mechanics have been applied to purely classical systems [12][13][14][15][16][17]. The KvN formalism has also received attention in the context of quantum-classical hybrid theories [18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

The Schwinger action principle for classical systems*

Manjarres¹

2021

J. Phys. A: Math. Theor.

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“…Motivated by the measurement problem in quantum mechanics, they proposed a Hilbert space formulation of classical-quantum interactions, which made use of the Koopman-von Neumann description of classical systems [8,19,20,21]. In recent years, this work has been further developed and extended [22,23,24,25,26].…”

Section: Some Aspects Of the Quantum Measurement Problemmentioning

confidence: 99%

Measurement of a quantum system with a classical apparatus using ensembles on configuration space

Reginatto,

Ulbricht

2022

Preprint

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Finding a physically consistent approach to modelling interactions between classical and quantum systems is a highly nontrivial task. While many proposals based on various mathematical formalisms have been made, most of these efforts run into difficulties of one sort or another. One of the first detailed descriptions was given by Sudarshan and his collaborators who, motivated by the measurement problem in quantum mechanics, proposed a Hilbert space formulation of classical-quantum interactions which made use of the Koopman-von Neumann description of classical systems. Here we use the approach of ensembles on configurations space to give a detailed account of a classical apparatus measuring the position of a quantum particle that is prepared in a superposition of two localized states. We show that the probability of the pointer of the classical apparatus is left in a state that corresponds to the probability of the quantum particle. A subsequent observation of the pointer leads to an update of its probability density. From this we can obtain information about the position of the quantum particle, leading to an update of its wave function. Since this formalism incorporates uncertainties and finite measurement precision, it is well suited for metrological applications. Furthermore, it resolves fundamental issues that appear in the case of a quantum description of the apparatus.

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Galilean covariance of quantum-classical hybrid systems of the Sudarshan type

Cited by 6 publications

References 18 publications

Projective representation of the Galilei group for classical and quantum–classical systems*

Projective representation of the Galilei group for classical and quantum–classical systems*

The Schwinger action principle for classical systems*

Measurement of a quantum system with a classical apparatus using ensembles on configuration space

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