GENERALIZED WEAK WEYL RELATION AND DECAY OF QUANTUM DYNAMICS

DOI10.1142/S0129055X05002479zbMath1111.81053MaRDI QIDQ5711050

Asao Arai

Publication date: 9 December 2005

Published in: Reviews in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

HamiltonianSchrödinger operatorDirac operatorsecond quantizationFock spacesurvival probabilityquantum dynamicscanonical commutation relationtime operatortime-energy uncertainty relationdecay in timegeneralized weak Weyl relation

Mathematics Subject Classification ID

Applications of operator theory in the physical sciences (47N50) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10)

Related Items (18)

Spectrum of time operators ⋮ Hilbert space representations of generalized canonical commutation relations ⋮ Ultra-weak time operators of Schrödinger operators ⋮ Representations of the weak Weyl commutation relation ⋮ Time operators for quantum walks ⋮ Remarks on Infinite-Dimensional Representations of the Heisenberg Algebra ⋮ TIME DELAY AND CALABI INVARIANT IN CLASSICAL SCATTERING THEORY ⋮ Generalized uncertainty relations ⋮ A Hardy's uncertainty principle lemma in weak commutation relations of Heisenberg-Lie algebra ⋮ TIME OPERATORS OF A HAMILTONIAN WITH PURELY DISCRETE SPECTRUM ⋮ Construction of a Weyl representation from a weak Weyl representation of the canonical commutation relation ⋮ Necessary and sufficient conditions for a Hamiltonian with discrete eigenvalues to have time operators ⋮ Strong time operators associated with generalized Hamiltonians ⋮ On the uniqueness of weak Weyl representations of the canonical commutation relation ⋮ A New Formula Relating Localisation Operators to Time Operators ⋮ Weak commutation relations of unbounded operators and applications ⋮ Weak commutation relations of unbounded operators: Nonlinear extensions ⋮ Time operators and time crystals: self-adjointness by topology change

Cites Work

• Unnamed Item
• Unnamed Item
• Characterization of anticommutativity of self-adjoint operators in connection with Clifford algebra and applications
• Die Eindeutigkeit der Schrödingerschen Operatoren
• On the Heisenberg commutation relation. I
• A generalized Weyl relation approach to the time operator and its connection to the survival probability
• Time in the Quantum Theory and the Uncertainty Relation for Time and Energy
• Significance of Electromagnetic Potentials in the Quantum Theory
• Representation-theoretic aspects of two-dimensional quantum systems in singular vector potentials: Canonical commutation relations, quantum algebras, and reduction to lattice quantum systems
• Time in Quantum Mechanics
• The various power decays of the survival probability at long times for a free quantum particle
• On the Relation $PQ -QP = -iI$.

This page was built for publication: GENERALIZED WEAK WEYL RELATION AND DECAY OF QUANTUM DYNAMICS