Negative position-momentum covariance and regional momentum distributions

Abstract

We discuss the negative statistical covariance between the position x and momentum p in terms of a conditional momentum distribution (known as the regional momentum distribution) of a free particle in the given region x > 0. Both classical and quantum systems are examined. A negative x-p covariance produces an asymmetry in the regional momentum distribution such that a negative particle momentum is the likely measurement outcome. This effect is enhanced as the x-p covariance becomes more negative.