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Probability Distributions and Hilbert Spaces: Quantum and Classical Systems
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We use the fact that some linear Hamiltonian systems can be considered as ``finite level'' quantum systems, and the description of quantum mechanics in terms of probabilities, to associate probability distributions with this particular class of linear Hamiltonian systems.
Forward citations
Cited by 4 Pith papers
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Quantum observables for probabilistic classical particles
Solutions of the Liouville equation can be rewritten as a Schrödinger equation whose observables are non-commuting 'quantum' operators, reproducing the harmonic oscillator and hydrogen atom spectra as special subsystems.
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Classical probabilistic realisation of quantum double-slit interference
Classical probability distributions over complex scalar fields realize Schrödinger dynamics and double-slit interference for a quantum particle via conserved-charge subsystems.
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Quantum mechanics for classical transport equations
Classical probabilistic transport equations are reformulated as quantum systems whose wave function obeys Schrödinger evolution and whose observables include non-commuting operators for statistical quantities.
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Quantum field theory for classical fields
A classical Klein-Gordon field with random initial conditions, described through specially defined fluctuating observables, obeys the functional-integral rules of a quantum field theory.
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