Sign Flip in the Casimir Force for Interacting Fermion Systems

Abstract

In this work we consider a fermionic chain of finite length ℓ. Fermions are allowed to interact and are forced to obey boundary conditions, thus altering the process of condensation. Our goal is to explore how this affects the quantum vacuum energy for this system. We approach this problem by using a self-consistent method and observe a nontrivial behavior in the Casimir force, displaying a switch from an attractive to a repulsive regime. This flip stems from the competition between the attractive contribution from the usual fermionic Casimir effect and a repulsive one coming from the condensate.

Self-consistent large-N analytical solutions of inhomogeneous condensates in quantum ℂPN − 1 model

“…Such analogies in the CP N −1 model may imply a possibility of a crystaline phase. While our periodic soliton lattice can be put on a ring, an extension to an interval [34][35][36] is also possible to calculate a Casimir force [90], since the exact solutions in the GN model on an interval have been found recently [86]. Another relation between the CP N −1 model and the GN model in 2 + 1 dimensions has recently been found in ref.…”

“…More generally, multiple twisted kinks with arbitrary phase and positions [75,76] can be further constructed systematically due to the integrable structure behind the model known as the Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy for the nonlinear Schrödinger equation [77][78][79]. Recent developments include time-dependent soliton scatterings [80,81], multi-component condensates [82][83][84], a ring geometry [85], and an interval with a Casimir force [86].…”

Confining solitons in the Higgs phase of ℂP N −1 model: self-consistent exact solutions in large-N limit

“…Self-consistent analytic solutions for this case was obtained in refs. [61,62]. A similar problem in a two-dimensional disk was discussed in refs.…”

“…A superconducting ring with a Zeeman magnetic field and magnetic flux penetrating the ring exhibits similar configurations [37]. Inhomogeneous configurations also appear in a finite interval with the Dirichlet boundary condition [38]. Apart from inhomogeneous ground states, solitons as excited states have been constructed as self-consistent analytic solutions, such as a kink [39,40], kink-anti-kink [39,41,42], kink-anti-kink-kink [43][44][45] for the real GN model, and twisted kink [46] and multiple twisted kinks with arbitrary separations [47,48] in the chiral GN model.…”

“…In the case of a finite interval with the Dirichlet boundary condition, it is inevitable that the Higgs field and mass gap function are inhomogeneous [59][60][61][62][63]. Self-consistent analytic solutions for this case was obtained in refs.…”