The 2D Lorentz-violating fermionic Casimir effect under thermal conditions

TL;DR

This work analyzes a 2D fermionic model with a CPT-even Lorentz-violating higher-derivative term and studies its Casimir effect under MIT bag boundary conditions, deriving exact zero-temperature results and closed-form finite-temperature corrections via the Matsubara formalism. The authors identify a physically consistent spacelike LIV dispersion that yields a standard Casimir energy plus a linear LIV correction, and they extend the analysis to finite temperature, obtaining explicit low- and high-temperature expansions for the Casimir energy, force, and entropy. A condensed-matter SSH lattice analogue is constructed to reproduce the nonlinear LIV-like dispersion and the associated boundary-induced vacuum energy, establishing a concrete bridge between LIV quantum field theory and lattice systems. The results illuminate how LIV corrections enhance vacuum energies at short distances and modify thermal responses, with potential implications for experimental probes of LIV-like effects in controlled settings.

Abstract

In the present work, we study a fermionic Lorentz invariance violation (LIV) theory with a CPT-even extension and analyze its impact on the Casimir effect under the MIT bag boundary condition model in a low-dimensional setting, where results are obtained without any approximations for a null-temperature system. Moreover, the Matsubara formalism is applied to derive closed expressions for the influence of temperature on the physical observables: Casimir energy, Casimir force, and entropy associated with the system in a LIV context. For each thermal observable, the influence of the LIV correction term is considered in the analysis of both low- and high-temperature regimes. Additionally, we construct a condensed matter analogue using the SSH model, where nonlinear fermionic dispersion and boundary-induced vacuum energy emerge, reproducing the analytical structure of the LIV Casimir effect.

Figures (7)

• Figure 1: Plot of the dimensionless energy $aE_{\rm cas}^{\rm low}(T,a)/\hslash c$ in terms of $ak_{\rm B}T/\hslash c$ with a fixed distance $a$.
• Figure 2: Plot of the dimensionless Force $a^2F_{\rm cas}^{\rm low}(T,a)/\hslash c$ in terms of $ak_{\rm B}T/\hslash c$ with a fixed distance $a$.
• Figure 3: Plot of the dimensionless energy $aE_{\rm cas}^{\rm high}(T,a)/\hslash c$ in terms of $ak_{\rm B}T/\hslash c$ with a fixed distance $a$.
• Figure 4: Plot of the dimensionless Force $a^2F_{\rm cas}^{\rm high}(T,a)/\hslash c$ in terms of $ak_{\rm B}T/\hslash c$ with a fixed distance $a$.
• Figure 5: Plot of the dimensionless entropy $S_{\rm cas}^{\rm low}(T,a)/k_{\rm B}$ in terms of $ak_{\rm B}T/\hslash c$ with a fixed distance $a$.