Conjoint spectral asymptotics for the families of commuting operators and for operators with the periodic hamiltonian flow
Eigenvalue asymptotics for Schrödinger and Dirac operators with the constant magnetic field and with electric potential decreasing at infinity
Accurate Spectral Asymptotics for periodic operators
Asymptotics with sharp remainder estimates are recovered for number of eigenvalues of operator crossing level as runs from to , . Here is periodic matrix operator, matrix is positive, periodic with respect to first copy of and decaying as second copy of goes to infinity, either belongs to a spectral gap of or is one its ends. These problems are first treated in papers of M. Sh. Birman, M. Sh. Birman-A. Laptev and M. Sh. Birman-T. Suslina.
Around Scott correction term(s)
Heavy molecules in the strong magnetic field
Estimates for a number of negative eigenvalues of the Schrödinger operator with intensive magnetic field
Eigenvalue asymptotics for Neumann Laplacian in domains with ultra-thin cusps
Asymptotics with sharp remainder estimates are recovered for number of eigenvalues of the generalized Maxwell problem and for related Laplacians which are similar to Neumann Laplacian. We consider domains with ultra-thin cusps (with ) width ; ) and recover eigenvalue asymptotics with sharp remainder estimates.
Magnetic Schrödinger Operator: Geometry, Classical and Quantum Dynamics and Spectral Asymptotics
I study the Schrödinger operator with the strong magnetic field, considering links between geometry of magnetic field, classical and quantum dynamics associated with operator and spectral asymptotics. In particular, I will discuss the role of short periodic trajectories.
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