Physical equivalence based on the experimental uncertainties is shown to be described as the equivalence of eigenstates based on free ultra-filters on $*\mathcal{H}$ .The coarse-graining is realized by means of the equivalent treatment with respect to the equivalent eigenstates.Two different types of decoherence between quantum states are simultaneously derived in the coarse-graining process.One represents the decoherence for realizing microcanonical ensemble of statistical mechanics and the other is that required in quantum theory of measurements.Physical equivalence based on the experimental uncertainties is shown to be described as the equivalence of eigenstates based on free ultra-filters on $*\mathcal{H}$ .The coarse-graining is realized by means of the equivalent treatment with respect to the equivalent eigenstates.Two different types of decoherence between quantum states are simultaneously derived in the coarse-graining process.One represents the decoherence for realizing microcanonical ensemble of statistical mechanics and the other is that required in quantum theory of measurements.

Oct 1, 19980 citations

Decoherence and Classical Behaviour in Quantum Mechanics

Gianfausto Dell’Antonio, Rodolfo Figari, Alessandro Teta

Springer eBooksJan 1, 20030 citations

Constrained quantum dynamics and coarse-grained description of a quantum system of nonlinear oscillators

Milan Radonjić, Slobodan Prvanović, Nikola Burić

Constrained Hamiltonian dynamics is exploited to provide the mathematical framework of a coarse-grained description of the quantum system of nonlinear interacting oscillators. The coarse graining is treated as an equivalence relation on the set of quantum states resulting in the emergence of classical phase space. The equivalence relation imposes constraints on the Hamiltonian dynamics of the quantum system. It is seen that the evolution of the coarse-grained system preserves constant and minimal quantum fluctuations of the fundamental observables. This leads to the emergence of the corresponding classical system on a sufficiently large scale.Constrained Hamiltonian dynamics is exploited to provide the mathematical framework of a coarse-grained description of the quantum system of nonlinear interacting oscillators. The coarse graining is treated as an equivalence relation on the set of quantum states resulting in the emergence of classical phase space. The equivalence relation imposes constraints on the Hamiltonian dynamics of the quantum system. It is seen that the evolution of the coarse-grained system preserves constant and minimal quantum fluctuations of the fundamental observables. This leads to the emergence of the corresponding classical system on a sufficiently large scale.

Physica ScriptaApr 27, 20121 citation

Decoherence and the Foundations of Quantum Mechanics

Maximilian Schlosshauer, Arthur I. Fine

Springer eBooksNov 1, 20069 citations

Coarse-grained quantum systems and symmetries

Nikola Burić, Slobodan Prvanović, Milan Radonjić

Constrained Hamiltonian dynamics is exploited to provide the mathematical framework of a coarse-grained description of the quantum system of two interacting qubits and of nonlinear interacting oscillators. The coarse-graining is treated as an equivalence relation on the set of quantum states resulting in the emergence of the classical phase-space. The equivalence relation imposes constraints on the Hamiltonian dynamics of the quantum system. It is seen that the evolution of the coarse-grained system preserves constant and minimal quantum fluctuations of the fundamental observables. This leads to the emergence of typical classical properties, like the relation between symmetry and integrability, and in the case of oscillators in the macro-limit implies the emergence of the classical system.Constrained Hamiltonian dynamics is exploited to provide the mathematical framework of a coarse-grained description of the quantum system of two interacting qubits and of nonlinear interacting oscillators. The coarse-graining is treated as an equivalence relation on the set of quantum states resulting in the emergence of the classical phase-space. The equivalence relation imposes constraints on the Hamiltonian dynamics of the quantum system. It is seen that the evolution of the coarse-grained system preserves constant and minimal quantum fluctuations of the fundamental observables. This leads to the emergence of typical classical properties, like the relation between symmetry and integrability, and in the case of oscillators in the macro-limit implies the emergence of the classical system.

Journal of Physics Conference SeriesFeb 8, 20120 citations

Physical equivalence based on the experimental uncertainties is shown to be described as the equivalence of eigenstates based on free ultra-filters on

*\mathcal{H}

.The coarse-graining is realized by means of the equivalent treatment with respect to the equivalent eigenstates.Two different types of decoherence between quantum states are simultaneously derived in the coarse-graining process.One represents the decoherence for realizing microcanonical ensemble of statistical mechanics and the other is that required in quantum theory of measurements.