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arXiv:1704.04918 · Physical Review Letters

Sign Flip in the Casimir Force for Interacting Fermion Systems

Antonino Flachi, Muneto Nitta, Satoshi Takada, Ryosuke Yoshii

Published Jul 21, 2017• 43 citations
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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.

DOI
10.1103/physrevlett.119.031601

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This paper explores how magnetic fields affect the Casimir effect within the context of a simple quasi-1D interacting fermionic system. A novel phenomenon emerges, resulting from the interaction between external magnetic fields and boundary conditions, which alters the ground state in complex ways and leads to first-order phase transitions among various ground states, specifically inhomogeneous solutions with differing node counts. We calculate the Casimir force, which exhibits discontinuities (jumps) at the transition points between the different ground states.
We demonstrate quantum levitation controlled by Casimir forces acting between a polystyrene surface and a Teflon-coated metallic substrate immersed in a mixture of Toluene and magnetite particles. This system experiences repulsion-attraction transitions in the Casimir interaction for distances where the effect is measurable. This Casimir trapping can be controlled by clever choices of metallic and ferrofluid materials, which are directly linked to the emergence of the trapping effect. Thermal and quantum contributions are investigated in detail, showing how the optical and magnetic properties of the ferrofluid and other materials affect the magnitude of the trapping and its distance range of observability.
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We consider the Bose gas on a ddd-dimensional anisotropic lattice employing the imperfect (mean-field) gas as a prototype example. We study the dimensional crossover arising as a result of varying the dispersion relation at finite temperature TTT. We analyze in particular situations where one of the relevant effective dimensionalities is located at or below the lower critical dimension, so that the Bose-Einstein condensate becomes expelled from the system by anisotropically modifying the lattice parameters controlling the kinetic term in the Hamiltonian. We clarify the mechanism governing this phenomenon. Subsequently we study the thermodynamic Casimir effect occurring in this system. We compute the exact profile of the scaling function for the Casimir energy. As an effect of strongly anisotropic scale invariance, the Casimir force below or at the critical temperature Tc{T}_{c}Tc​ may be repulsive even for periodic boundary conditions. The corresponding Casimir amplitude is universal only in a restricted sense, and the power law governing the decay of the Casimir interaction becomes modified. We also demonstrate that, under certain circumstances, the scaling function is constant for sufficiently large values of the scaling variable, and in consequence is not an analytical function. At T>TcT>{T}_{c}T>Tc​ the Casimir-like interactions reflect the structure of the correlation function, and, for certain orientations of the confining walls, show exponentially damped oscillatory behavior so that the corresponding force is attractive or repulsive depending on the distance.