Interface potential and line tension for Bose-Einstein condensate mixtures near a hard wall

Abstract

Within Gross-Pitaevskii (GP) theory we derive the interface potential V ( ) which describes the interaction between the interface separating two demixed Bose-condensed gases and an optical hard wall at a distance . Previous work revealed that this interaction gives rise to extraordinary wetting and prewetting phenomena. Calculations that explore nonequilibrium properties by using as a constraint provide a thorough explanation for this behavior. We find that at bulk two-phase coexistence, V ( ) for both complete wetting and partial wetting is monotonic with exponential decay. Remarkably, at the first-order wetting phase transition, V ( ) is independent of . This anomaly explains the infinite continuous degeneracy of the grand potential reported earlier. As a physical application, using V ( ) we study the three-phase contact line where the interface meets the wall under a contact angle θ. Employing an interface displacement model we calculate the structure of this inhomogeneity and its line tension τ . Contrary to what happens at a usual first-order wetting transition in systems with short-range forces, τ does not approach a nonzero positive constant for θ → 0, but instead approaches zero (from below) in the manner τ ∝ −θ as would be expected for a critical wetting transition. This hybrid character of τ is a consequence of the absence of a barrier in V ( ) at wetting. For a typical V ( ) = S exp(− /ξ ), with S the spreading coefficient and ξ a decay length, we conjecture that τ = −2 (1 − ln 2) γ ξ sin θ is exact within GP theory, with γ the interfacial tension and 0 θ π .

Phenomenological Analogy between Gross-Pitaevskii Theory for Bose-Einstein Condensate and Newton Equation for Classical Mechanics

“…al. [9,10], in which the phenomenological analogy was applied for a two-component Bose-Einstein condensate within framwork of the density functional theory, to examine the phenomenological analogy between ( 3) and ( 6) in the dynamic point of view thoughout this work. It is easily seen that these equations have the same mathematical form, this allows us to interpret the GP equation ( 6) as the Newton equation ( 3), which describes a particle with "mass"of 2 /2m moving under of acting force:…”

“…The "equation of motion" (10) shows the "time" z -dependent of the "coordinate"  of the particle with unity "mass" by dimensionless acting force: In dynamic point of view, which is equivelent to Eq. ( 4) of the dynamic mechanics.…”

“…( 4) of the dynamic mechanics. Figure 1 shows graphically the evoluation of (10), in which the solid and dashed lines correspond to "coordinate"  and "velocity" / d dz…”