• Corpus ID: 248887276

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

@inproceedings{Reginatto2022MeasurementOA,
  title={Measurement of a quantum system with a classical apparatus using ensembles on configuration space},
  author={Marcel Reginatto and S. Ulbricht},
  year={2022}
}
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… 

Figures from this paper

References

SHOWING 1-10 OF 41 REFERENCES
Interaction between classical and quantum systems: A new approach to quantum measurement.I
We introduce an unconventional approach to the measurement problem in quantum mechanics: we treat the apparatus as a classical system belonging to the macroworld. To describe the quantum measurement
Interacting classical and quantum ensembles
A consistent description of interactions between classical and quantum systems is relevant to quantum measurement theory and to calculations in quantum chemistry and quantum gravity. A solution is
Interaction between classical and quantum systems; a new approach to quantum measurement. II. Theoretical considerations
A new approach to the quantum measurement process is developed further. In this approach, the apparatus is treated as a classical system; however, the classical apparatus is directly coupled to the
Koopman wavefunctions and classical states in hybrid quantum-classical dynamics
We deal with the reversible dynamics of coupled quantum and classical systems. Based on a recent proposal by the authors, we exploit the theory of hybrid quantum–classical wavefunctions to devise a
Linear dynamics of quantum-classical hybrids
A formulation of quantum-classical hybrid dynamics is presented, which concerns the direct coupling of classical and quantum mechanical degrees of freedom. It is of interest for applications in
Interaction between classical and quantum systems: A new approach to quantum measurement. III. Illustration
Following the approach to quantum measurement, proposed in an earlier paper, in which the apparatus is treated as a purely classical instrument to be described by the laws of classical mechanics we
Koopman wavefunctions and classical–quantum correlation dynamics
TLDR
This paper addresses the long-standing problem of formulating a dynamical theory of classical–quantum coupling using the exactly solvable model of a degenerate two-level quantum system coupled to a classical harmonic oscillator.
Madelung transform and probability densities in hybrid quantum–classical dynamics
This paper extends the Madelung–Bohm formulation of quantum mechanics to describe the time-reversible interaction of classical and quantum systems. The symplectic geometry of the Madelung transform
Interaction between classical and quantum systems and the measurement of quantum observables
Quantum mechanics presumes classical measuring instruments with which they interact. The problem of measurement interaction between classical and quantum systems is posed and solved. The restriction
Classical behaviour in quantum systems: the case of straight tracks in a cloud chamber
The aim of this paper is to discuss in a pedagogical way the problem of the emergence of classical behaviour in certain physical systems which, in principle, are correctly described by quantum
...
...