Title :

The quantum Loschmidt echo on flat tori

Author(s) :

Rivière, Gabriel [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Ueberschaer, Henrik [Auteur]
Institut de Mathématiques de Jussieu - Paris Rive Gauche [IMJ-PRG (UMR_7586)]

English keyword(s) :

semiclassical analysis
completely integrable systems
quantum fidelity

HAL domain(s) :

Mathématiques [math]/Physique mathématique [math-ph]
Mathématiques [math]/Equations aux dérivées partielles [math.AP]

English abstract : [en]

The Quantum Loschmidt Echo is a measurement of the sensitivity of a quantum system to perturbations of the Hamiltonian. In the case of the standard 2-torus, we derive some explicit formulae for this quantity in the transition ...
Show more >The Quantum Loschmidt Echo is a measurement of the sensitivity of a quantum system to perturbations of the Hamiltonian. In the case of the standard 2-torus, we derive some explicit formulae for this quantity in the transition regime where it is expected to decay in the semiclassical limit. The expression involves both a two-microlocal defect measure of the initial data and the form of the perturbation. As an application, we exhibit a non-concentration criterium on the sequence of initial data under which one does not observe a macroscopic decay of the Quantum Loschmidt Echo. We also apply our results to several examples of physically relevant initial data such as coherent states and plane waves.Show less >

Language :

Anglais

Comment :

34 pages

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL