Time-dependent scattering theory in exterior domains

1975 ◽  
pp. 76-83
Author(s):  
Calvin H. Wilcox
Keyword(s):  
Scattering Theory ◽  
Time Dependent ◽  
Exterior Domains

scholarly journals Large Time Decay of Solutions to a Linear Nonautonomous System in Exterior Domains

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 841
Author(s):  
Toshiaki Hishida
Keyword(s):  
Evolution Operator ◽  
Large Time ◽  
Rigid Motion ◽  
Time Dependent ◽  
Energy Relation ◽  
Exterior Domains ◽  
Decay Properties ◽  
Decay Of Solutions ◽  
Whole Space ◽  
Expository Paper

In this expository paper, we study Lq-Lr decay estimates of the evolution operator generated by a perturbed Stokes system in n-dimensional exterior domains when the coefficients are time-dependent and can be unbounded at spatial infinity. By following the approach developed by the present author for the physically relevant case where the rigid motion of the obstacle is time-dependent, we clarify that some decay properties of solutions to the same system in whole space Rn together with the energy relation imply the desired estimates in exterior domains provided n≥3.

scholarly journals Time-dependent scattering theory on manifolds

2019 ◽  
Vol 277 (5) ◽  
pp. 1423-1468
Author(s):  
K. Ito ◽  
E. Skibsted
Keyword(s):  
Scattering Theory ◽  
Time Dependent

scholarly journals Stochastic scattering theory for excitation-induced dephasing: Time-dependent nonlinear coherent exciton lineshapes

2020 ◽  
Vol 153 (16) ◽  
pp. 164706
Author(s):  
Ajay Ram Srimath Kandada ◽  
Hao Li ◽  
Félix Thouin ◽  
Eric R. Bittner ◽  
Carlos Silva
Keyword(s):  
Scattering Theory ◽  
Time Dependent ◽  
Dephasing Time

scholarly journals SPECTRAL ANALYSIS AND TIME-DEPENDENT SCATTERING THEORY ON MANIFOLDS WITH ASYMPTOTICALLY CYLINDRICAL ENDS

2013 ◽  
Vol 25 (02) ◽  
pp. 1350003 ◽  
Author(s):  
S. RICHARD ◽  
R. TIEDRA DE ALDECOA
Keyword(s):  
Spectral Analysis ◽  
Time Delay ◽  
Hilbert Spaces ◽  
Scattering Theory ◽  
Asymptotic Completeness ◽  
Time Dependent ◽  
Resolvent Estimates ◽  
Wave Operators ◽  
Use Of Time ◽  
Stationary Scattering

We review the spectral analysis and the time-dependent approach of scattering theory for manifolds with asymptotically cylindrical ends. For the spectral analysis, higher order resolvent estimates are obtained via Mourre theory for both short-range and long-range behaviors of the metric and the perturbation at infinity. For the scattering theory, the existence and asymptotic completeness of the wave operators is proved in a two-Hilbert spaces setting. A stationary formula as well as mapping properties for the scattering operator are derived. The existence of time delay and its equality with the Eisenbud–Wigner time delay is finally presented. Our analysis mainly differs from the existing literature on the choice of a simpler comparison dynamics as well as on the complementary use of time-dependent and stationary scattering theories.

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