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

Abstract

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.

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“…Such equations find fruitful applications in the theory of strongly-interacting quantum fluids, and have been successfully applied to laboratory superfluids [10,43,49]. We note that, in principle, one is not precluded from adding other types of nonlinearity, such as polynomial ones, into the condensate wave equations, but the role of logarithmic nonlinearity is crucial.…”

“…One of underlying reasons for such phenomenological success is that the ground-state wavefunction of free (trapless) logarithmic liquid is not a de Broglie plane wave, but a spatial Gaussian modulated by a de Broglie plane wave. This explains the liquid's inhomogenization followed by the formation of fluid elements or parcels; which indicates that such models do describe fluids, rather than gaseous matter [44][45][46][47][48][49].…”

“…For example, changing the sign of the field-theoretical potential; or, alternatively, the overall sign of the nonlinear coupling b; switches between the topologically trivial, which is considered in this paper, and the topologically non-trivial sectors. In a logarithmic liquid model with constant nonlinear coupling, switching to the topologically non-trivial sector of the theory means that wavefunction changes from a droplet-like non-topological soliton type to a bubble-like topological soliton type, as discussed in [47,49]. Consequently, the forms of a trial wavefunction and induced potential in Section 3 would also change.…”

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“…Further, other stages in this research program have experimentally demonstrated the existence repulsion force between water droplets and the Earth, and that the time-of-fall of a water-droplet in still air increases with the temperature of the droplet [1,2]. A similar idea has been predicted for a hypothetical quantum fluid: "that the temperature difference creates a direction in space in which quantum liquids can flow, even against the force of gravity" [45] p1950184-1.…”

“…The total kinetic energy of particles bounded by potential forces over time in virial theorem [44] assuming that average kinetic energy of a system is proportional to the average potential energy is another concept of energy in a system. Virial theorem also discusses some possible mechanisms [45] dominating stellar contraction due to the gravitational attraction. Our discussion, however, is grounded on a repulsive force dependent on thermal energy which is based only on its potential energy and therefore further engagement with kinetic energy is disregarded in this paper.…”