The high energy asymptotic distribution of the eigenvalues of the scattering matrix

Student thesis: Doctoral ThesisDoctor of Philosophy


We determine the high energy asymptotic density of the eigenvalues of the scat- tering matrix associated with the operators H0 = −∆ and H = (i∇ + A)2 + V (x), where V : Rd → R is a smooth short-range real-valued electric potential and
A = (A1, . . . , Ad) : Rd → Rd is a smooth short-range magnetic vector-potential. Two cases are considered. The first case is where the magnetic vector-potential is non-zero. The spectral density of the associated scattering matrix in this case is expressed as an integral solely in terms of the magnetic vector-potential A. The second case considered is where the magnetic vector-potential is identically zero. Again the spectral density of the scattering matrix is expressed as an integral, this time in terms of the poten- tial V . These results share similar
characteristics to results pertaining to semiclassical asymptotics for pseudodifferential
Date of AwardJun 2013
Original languageEnglish
Awarding Institution
  • King's College London
SupervisorAlexander Pushnitski (Supervisor), Eugene Shargorodsky (Supervisor) & Yuri Safarov (Supervisor)

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