- 02-220 Hajo Leschke, Rainer Ruder and Simone Warzel
- Simple diamagnetic monotonicities for Schroedinger operators
with inhomogeneous magnetic fields of constant direction
May 10, 02
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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].