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Simple diamagnetic monotonicities for Schroedinger operators with inhomogeneous magnetic fields of constant direction

Hajo Leschke·Rainer Ruder·Simone Warzel
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Abstract

Under certain simplifying conditions we detect monotonicity properties of the ground-state energy and the canonical-equilibrium density matrix of a spinless charged particle in the Euclidean plane subject to a perpendicular, possibly inhomogeneous magnetic field and an additional scalar potential. Firstly, we point out a simple condition warranting that the ground-state energy does not decrease when the magnetic field and/or the potential is increased pointwise. Secondly, we consider the case in which both the magnetic field and the potential are constant along one direction in the plane and give a genuine path-integral argument for corresponding monotonicities of the density-matrix diagonal and the absolute value of certain off-diagonals. Our results complement to some degree results of M. Loss and B. Thaller [Commun. Math. Phys. 186 (1997) 95] and L. Erdos [J. Math. Phys. 38 (1997) 1289].

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Hajo Leschke, Rainer Ruder, Simone Warzel. 2002-07-01. Simple diamagnetic monotonicities for Schroedinger operators with inhomogeneous magnetic fields of constant direction. https://doi.org/10.1088/0305-4470%2F35%2F27%2F311

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