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arXiv · 1812.10718

Quantum time delay for unitary operators: general theory

Diomba Sambou·Rafael Tiedra de Aldecoa
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Abstract

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.

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Diomba Sambou, Rafael Tiedra de Aldecoa. 2018-12-27. Quantum time delay for unitary operators: general theory. https://doi.org/10.1142/s0129055x19500181

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