Motion-driven quantum dissipation in an open electronic system with nonlocal interaction

TL;DR

The paper addresses motion-induced excitations and quantum dissipation in a pair of parallel metallic plates modeled by 1+2D Dirac fermions coupled via a nonlocal interaction. By integrating out the R-plate and employing a perturbative expansion in the coupling $g$, it derives an effective action for the L-plate and computes the vacuum occupation number $n_L(\mathbf{k})$, which is isotropic at $v=0$ and becomes anisotropic for $v>0$. It then analyzes the imaginary part of the quantum action $\mathrm{Im}\Gamma$ and the resulting dissipative force $F_{\mathrm{diss}}$, finding a threshold at $v>2v_F$ and a linear friction regime at small speeds, consistent with a Schwinger-like dissipation mechanism. The results highlight how nonlocal interplate coupling and Galilean motion drive dissipation in open quantum systems and suggest extensions to other nonperturbative regimes or nonlocal couplings in condensed matter contexts.

Abstract

In this paper, we study excitations and dissipation in two infinite parallel metallic plates undergoing relative motion. The degrees of freedom of the electrons in both plates are modeled using the 1+2 dimensional Dirac field, and a nonlocal potential is selected to describe the interaction between the two plates. The internal relative motion is introduced via a Galilean boost, with one plate assumed to slide relative to the other. We then calculate the effective action of the system and derive the vacuum occupation number in momentum space using a perturbative method. Numerical plots reveal that the vacuum occupation number, as a function of momentum, is isotropic for a motion speed $v = 0$ and anisotropic for nonzero $v$. The relative motion induces energy transfer between the plates, leading to on-shell excitations in a manner analogous to the dissipative process of the Schwinger effect. Consequently, we study the motion-induced dissipation effects and the dissipative forces through the quantum action. Numerical results demonstrate that both the imaginary part of the quantum action due to the motion boost and the dissipative force exhibit a threshold as functions of $v$, and both are positively correlated with $v$.

Figures (4)

• Figure 1: Schematic picture of the system.
• Figure 2: 3D and Contour-plot of the vacuum occupation number, for the case $v_\mathrm{F}=0.001$, $m=10$, in the order of $g^2$. Here (a) and (b) for $v=0$; (c) and (d) for $v=7$.
• Figure 3: The imaginary part of quantum action as a function of $v$, for the case $v_\mathrm{F}=0.001$, $m=10$, in units of $g^2TV$.
• Figure 4: The dissipative force as a function of $v$, for the case $v_\mathrm{F}=0.001$, $m=10$, in units of $g^2$.