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Squeezed states of a particle in magnetic field
Umeå University, Faculty of Science and Technology, Department of Physics.
1998 (English)In: Physics of the solid state, ISSN 1063-7834, E-ISSN 1090-6460, Vol. 40, no 8, 1276-1282 p.Article in journal (Refereed) Published
Abstract [en]

For a charged particle in a homogeneous magnetic field, we construct stationary squeezed states which are eigenfunctions of the Hamiltonian and the non-Hermitian operator (X) over cap(Phi) = (X) over cap cos Phi + (Y) over cap sin Phi, (X) over cap and (Y) over cap being the coordinates of the Larmor circle center and Phi is a complex parameter. In the family of the squeezed states, the quantum uncertainty in the Larmor circle position is minimal. The wave functions of the squeezed states in the coordinate representation are found and their properties are discussed. Besides, for arbitrary gauge of the vector potential we derive the symmetry operators of translations and rotations.

Place, publisher, year, edition, pages
1998. Vol. 40, no 8, 1276-1282 p.
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:umu:diva-91465DOI: 10.1134/1.1130543ISI: 000075726400004OAI: oai:DiVA.org:umu-91465DiVA: diva2:736434
Available from: 2014-08-06 Created: 2014-08-05 Last updated: 2017-12-05Bibliographically approved
In thesis
1. Mesoscopic superconductivity: quasiclassical approach
Open this publication in new window or tab >>Mesoscopic superconductivity: quasiclassical approach
2001 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This Thesis is concerned with the quasiclassical theory of meso-scopic superconductivity. The aim of the Thesis is to introduce the boundary conditions for a quasiclassical Green’s function on partially transparent interfaces in mesoscopic superconducting structures and to analyze the range of applicability of the quasiclassical theory. The linear boundary conditions for Andreev amplitudes, factoring the quasiclassical Green’s function, are presented.  The quasiclassical theory on classical trajectories is reviewed and then generalized to include knots with paths intersections.  The main focus of the Thesis is on the range of validity of the quasiclassical theory. This goal is achieved by comparison of quasiclassical and exact Green’s functions.  The exact Gor’kov Greens function cannot be directly used for the comparison because of its strong microscopic variations on the length-scale of λF. It is the coarse-grain averaged exact Green’s function which is appropriate for the comparison. In most of the typical cases the calculations show very good agreement between both theories. Only for certain special situations, where the classical trajectory contains loops, one encounters discrepancies. The numerical and analytical analysis of the role of the loop-like structures and their influence on discrepancies between both exact and quasiclassical approaches is one of the main results of the Thesis. It is shown that the terms missing in the quasiclassical theory can be attributed to the loops formed by the interfering paths.  In typical real samples any imperfection on the scale larger than the Fermi wavelength disconnects the loops and the path is transformed into the tree-like graph. It is concluded that the quasiclassical theory is fully applicable in most of real mesoscopic samples. In the situations where the conventional quasiclassical theory is inapplicable due to contribution of the interfering path, one can use the modification of the quasiclassical technique suggested in the Thesis.

Place, publisher, year, edition, pages
Umeå: Umeå universitet, 2001. 56 p.
Keyword
mesoscopic superconductivity, quasiclassical theory, boundary conditions, multi-layer structures, Gor'kov equations, quasiclassical Green's function, Green's function on classical trajectories
National Category
Physical Sciences
Identifiers
urn:nbn:se:umu:diva-91484 (URN)91-7305-161-6 (ISBN)
Public defence
2001-12-10, Naturvetarhuset, N320, Umeå universitet, Umeå, 10:30 (English)
Opponent
Supervisors
Available from: 2014-08-06 Created: 2014-08-06 Last updated: 2014-08-19Bibliographically approved

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Ozana, MarekShelankov, Andrei L
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