scholarly journals Spectral projections for the twisted Laplacian

2007 ◽  
Vol 180 (2) ◽  
pp. 103-110 ◽  
Author(s):  
Herbert Koch ◽  
Fulvio Ricci
Keyword(s):  
Twisted Laplacian ◽  
Spectral Projections

scholarly journals A STRONG OPERATOR TOPOLOGY ADIABATIC THEOREM

2002 ◽  
Vol 14 (06) ◽  
pp. 569-584 ◽  
Author(s):  
ALEXANDER ELGART ◽  
JEFFREY H. SCHENKER
Keyword(s):  
Spectral Data ◽  
Time Scale ◽  
Strong Operator Topology ◽  
Continuous Functions ◽  
Adiabatic Theorem ◽  
Strong Operator ◽  
Intrinsic Time ◽  
Embedded Eigenvalues ◽  
Additive Perturbation ◽  
Spectral Projections

We prove an adiabatic theorem for the evolution of spectral data under a weak additive perturbation in the context of a system without an intrinsic time scale. For continuous functions of the unperturbed Hamiltonian the convergence is in norm while for a larger class functions, including the spectral projections associated to embedded eigenvalues, the convergence is in the strong operator topology.

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