Temperature-driven dynamics of quantum liquids: Logarithmic nonlinearity, phase structure and rising force

We study a large class of strongly interacting condensate-like materials, which can be characterized by a normalizable complex-valued function. A quantum wave equation with logarithmic nonlinearity is known to describe such systems, at least in a leading-order approximation, wherein the nonlinear coupling is related to temperature. This equation can be mapped onto the flow equations of an inviscid barotropic fluid with intrinsic surface tension and capillarity; the fluid is shown to have a nontrivial phase structure controlled by its temperature. It is demonstrated that in the case of a varying nonlinear coupling an additional force occurs, which is parallel to a gradient of the coupling. The model predicts that the temperature difference creates a direction in space in which quantum liquids can flow, even against the force of gravity. We also present arguments explaining why superfluids, be it superfluid components of liquified cold gases or Cooper pairs inside superconductors, can affect closely positioned acceleration-measuring devices.