### Abstract

Muñoz, Seidel, and Muga [Phys. Rev. A79, 012108 (Year: 2009)10.1103/PhysRevA.79.012108], following an earlier proposal by Pollak and Miller [Phys. Rev. Lett.53, 115 (Year: 1984)10.1103/PhysRevLett.53.115] in the context of a theory of a collinear chemical reaction, showed that suitable moments of a two-flux correlation function could be manipulated to yield expressions for the mean quantum dwell time and mean square quantum dwell time for a structureless particle scattering from a time-independent potential energy field between two parallel lines in a two-dimensional spacetime. The present work proposes a generalization to a charged, nonrelativistic particle scattering from a transient, spatially confined electromagnetic vector potential in four-dimensional spacetime. The geometry of the spacetime domain is that of the slab between a pair of parallel planes, in particular, those defined by constant values of the third (*z*) spatial coordinate. The mean *N*th power, *N* = 1, 2, 3, …, of the quantum dwell time in the slab is given by an expression involving an *N*-flux-correlation function. All these means are shown to be nonnegative. The *N* = 1 formula reduces to an *S*-matrix result published previously [G. E. Hahne, J. Phys. A36, 7149 (Year: 2003)10.1088/0305-4470/36/25/316]; an explicit formula for *N* = 2, and of the variance of the dwell time in terms of the *S*-matrix, is worked out. A formula representing an incommensurability principle between variances of the output-minus-input flux of a pair of dynamical variables (such as the particle's time flux and others) is derived.

Received 23 April 2012
Accepted 02 January 2013
Published online 24 January 2013

Article outline:

I. INTRODUCTION
II. SINGLE-PARTICLE, MULTIPLE-POINT-CURRENT CORRELATION FUNCTIONS
III. MEAN POWERS OF THE DWELL TIME
IV. VARIANCE OF THE DWELL TIME

Commenting has been disabled for this content