Anisotropic Lavine's formula and symmetrised time delay in scattering theory

Abstract

We consider, in quantum scattering theory, symmetrised time delay defined in terms of sojourn times in arbitrary spatial regions symmetric with respect to the origin. For potentials decaying more rapidly than $|x{|}^{-4}$ at infinity, we show the existence of symmetrised time delay, and prove that it satisfies an anisotropic version of Lavine's formula. The importance of an anisotropic dilations-type operator is revealed in our study.

arXiv comment19 pages, 2 figures

References in corpus (3)

• Time delay for one-dimensional quantum systems with steplike potentials
• Generalized definition of time delay in scattering theory
• Time delay and short-range scattering in quantum waveguides

Cited by in corpus (5)

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• On a new formula relating localisation operators to time operators
• Quantum time delay for unitary operators: general theory
• Time delay is a common feature of quantum scattering theory
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