Transients with time-independent currents

TL;DR

This paper demonstrates that in quantum systems with initial discontinuities in particle density, currents emerge instantaneously and can be experimentally observed, revealing non-equilibrium effects in finite-width gradients.

Contribution

It introduces the concept that time-independent initial densities with discontinuities lead to immediate current formation, supported by experimental feasibility.

Findings

Currents appear instantaneously at density discontinuities.

Finite-width gradients can be used to measure these effects.

Non-equilibrium currents are observable in real experiments.

Abstract

It is shown that when the initial particles probability density is discontinuous the emerging currents appear instantaneously, and although the density beyond the discontinuity is initially negligible the currents there have a finite value. It is shown that this non-equilibrium effect can be measured in real experiments (such as cooled Rubidium atoms), where the discontinuity is replaced with finite width (hundreds of nanometers) gradient.