Time Delay for the Dirac Equation

Naumkin, Ivan; Weder, Ricardo

doi:10.1007/s11005-016-0871-5

Cited by 2 publications

(2 citation statements)

References 34 publications

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“…One can find a large literature on the notion of quantum time delay in the setup of scattering theory for self-adjoint operators (see for instance [2,3,5,6,7,13,14,16,17,18,25,27,28,34,35]). But as far as we know, there is no mathematical work on quantum time delay in the setup of scattering theory for unitary operators.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Quantum time delay for unitary operators: General theory

Sambou

Aldecoa

2019

Rev. Math. Phys.

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We present a suitable framework for the definition of quantum time delay in terms of sojourn times for unitary operators in a two-Hilbert spaces setting. We prove that this time delay defined in terms of sojourn times (time-dependent definition) exists and coincides with the expectation value of a unitary analogue of the Eisenbud-Wigner time delay operator (time-independent definition). Our proofs rely on a new summation formula relating localisation operators to time operators and on various tools from functional analysis such as Mackey's imprimititvity theorem, Trotter-Kato Formula and commutator methods for unitary operators. Our approach is general and model-independent. Remark 4.4(b), and we obtain Proof of Propositionwhich implies the first part of the proposition. For the second part, it is sufficient to show that.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Quantum time delay for unitary operators: General theory

Sambou

Aldecoa

2019

Rev. Math. Phys.

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“…Previously, the scientific phenomenon of time-delay has been utilized in applied mathematics, physics, mechanics, computer science, engineering, biology, etc. [4][5][6][7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Noether Symmetry of Multi-Time-Delay Non-Conservative Mechanical System and Its Conserved Quantity

Ji,

Yang,

Zhai

2024

Symmetry

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The study of multi-time-delay dynamical systems has highlighted many challenges, especially regarding the solution and analysis of multi-time-delay equations. The symmetry and conserved quantity are two important and effective essential properties for understanding complex dynamical behavior. In this study, a multi-time-delay non-conservative mechanical system is investigated. Firstly, the multi-time-delay Hamilton principle is proposed. Then, multi-time-delay non-conservative dynamical equations are deduced. Secondly, depending on the infinitesimal group transformations, the invariance of the multi-time-delay Hamilton action is studied, and Noether symmetry, Noether quasi-symmetry, and generalized Noether quasi-symmetry are discussed. Finally, Noether-type conserved quantities for a multi-time-delay Lagrangian system and a multi-time-delay non-conservative mechanical system are obtained. Two examples in terms of a multi-time-delay non-conservative mechanical system and a multi-time-delay Lagrangian system are given.

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Time Delay for the Dirac Equation

Cited by 2 publications

References 34 publications

Quantum time delay for unitary operators: General theory

Quantum time delay for unitary operators: General theory

Noether Symmetry of Multi-Time-Delay Non-Conservative Mechanical System and Its Conserved Quantity

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