Abstract:
A class of problems connected with the description of the motion of an attracted quantum particle in possibly time-dependent, periodic, external fields is studied on the basis of a development of the method of the inverse problem.
Citation:
S. P. Novikov, “Two-dimensional Schrödinger operators in periodic fields”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat., 23, VINITI, Moscow, 1983, 3–32; J. Soviet Math., 28:1 (1985), 1–20
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Yu. A. Kordyukov, I. A. Taimanov, “Trace formula for the magnetic Laplacian”, Russian Math. Surveys, 74:2 (2019), 325–361
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P. G. Grinevich, A. E. Mironov, S. P. Novikov, “On the non-relativistic two-dimensional purely magnetic supersymmetric Pauli operator”, Russian Math. Surveys, 70:2 (2015), 299–329
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P. G. Grinevich, A. E. Mironov, S. P. Novikov, “Zero level of a purely magnetic two-dimensional nonrelativistic Pauli operator for spin-1/21/2 particles”, Theoret. and Math. Phys., 164:3 (2010), 1110–1127
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P. G. Grinevich, I. A. Taimanov, “Infinitesimal Darboux Transformations of the Spectral Curves of Tori in the Four-Space”, International Mathematics Research Notices, 2007 (2007)
J M Harrison, P Kuchment, A Sobolev, B Winn, “On occurrence of spectral edges for periodic operators inside the Brillouin zone”, J. Phys. A: Math. Theor., 40:27 (2007), 7597
Allal Ghanmi, “Euclidean limit ofL2-spectral properties of the Pauli Hamiltonians on constant curvature Riemann surfaces”, J. Phys. A: Math. Gen., 38:9 (2005), 1917
V. A. Vassiliev, “Spaces of Hermitian operators with simple spectra and their finite-order cohomology”, Mosc. Math. J., 3:3 (2003), 1145–1165
I. A. Taimanov, “On two-dimensional finite-gap potential Schrödinger and Dirac operators with singular spectral curves”, Siberian Math. J., 44:4 (2003), 686–694
J. Brüning, S. Yu. Dobrokhotov, K. V. Pankrashin, “The Asymptotic Form of the Lower Landau Bands in a Strong Magnetic Field”, Theoret. and Math. Phys., 131:2 (2002), 704–728
K. V. Pankrashin, “Locality of Quadratic Forms for Point Perturbations of Schrödinger Operators”, Math. Notes, 70:3 (2001), 384–391
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O. I. Mokhov, “Symplectic and Poisson structures on loop spaces of smooth manifolds, and integrable systems”, Russian Math. Surveys, 53:3 (1998), 515–622
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