Coarse-graining of some sort is a fundamental and unavoidable step in any attempt to derive the classical mechan- ical behavior from the quantum formalism. We utilize the two-mode Bose-Hubbard model to illustrate how ...Coarse-graining of some sort is a fundamental and unavoidable step in any attempt to derive the classical mechan- ical behavior from the quantum formalism. We utilize the two-mode Bose-Hubbard model to illustrate how different coarse-grained systems can be naturally associated with a fixed quantum system if it is compatible with different dy- namical algebras. Alternative coarse-grained systems generate different evolutions of the same physical quantities, and the difference becomes negligible only in the appropriate macro-limit.展开更多
Properties of an operator representing the dynamical time in the extended parameterization invariant formulation of quantum mechanics are studied. It is shown that this time operator is given by a positive operator me...Properties of an operator representing the dynamical time in the extended parameterization invariant formulation of quantum mechanics are studied. It is shown that this time operator is given by a positive operator measure analogously to the quantities that are known to represent various measurable time operators. The relation between the dynamical time of the extended formulation and the best known example of the system time operator, i.e., for the free one- dimensional particle, is obtained.展开更多
基金Project supported by the Ministry of Education and Science of the Republic of Serbia(Grant Nos.171017,171028,171038,and III45016)We would like to acknowledge partial support by COST(Action MP1006)
文摘Coarse-graining of some sort is a fundamental and unavoidable step in any attempt to derive the classical mechan- ical behavior from the quantum formalism. We utilize the two-mode Bose-Hubbard model to illustrate how different coarse-grained systems can be naturally associated with a fixed quantum system if it is compatible with different dy- namical algebras. Alternative coarse-grained systems generate different evolutions of the same physical quantities, and the difference becomes negligible only in the appropriate macro-limit.
基金Project supported by the Ministry of Science and Education of the Republic of Serbia (Grant Nos. 171017, 171028, and 171006)
文摘Properties of an operator representing the dynamical time in the extended parameterization invariant formulation of quantum mechanics are studied. It is shown that this time operator is given by a positive operator measure analogously to the quantities that are known to represent various measurable time operators. The relation between the dynamical time of the extended formulation and the best known example of the system time operator, i.e., for the free one- dimensional particle, is obtained.
