A kinetic description for the electromagnetic response of the charged particles to Chern–Simons gauge fields

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS ACS Applied Bio Materials Pub Date : 2024-10-21 DOI:10.1016/j.physd.2024.134409
Jeongho Kim , Bora Moon , Jinyeong Park
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Abstract

In this paper, we introduce the Vlasov–Chern–Simons (VCS) equation, a Vlasov-type equation that describes the two-dimensional dynamics of charged particles affected by the Chern–Simons electromagnetic potentials. First, we derive the VCS equation from the Chern–Simons–Schrödinger equations, a quantum mechanical model for the particle affected by Chern–Simons gauge fields, via the Wigner transform. Subsequently, we study the local-in-time well-posedness for the strong solution and the global-in-time existence for weak solutions to the VCS equation, respectively. Additionally, we propose a simple semi-Lagrangian numerical scheme for solving the VCS equation and validate the conservation of total moments and Lp-norms through numerical tests.
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带电粒子对切尔诺-西蒙斯量规场的电磁响应的动力学描述
本文介绍了弗拉索夫-切尔恩-西蒙斯(VCS)方程,这是一个描述受切尔恩-西蒙斯电磁势影响的带电粒子二维动力学的弗拉索夫型方程。首先,我们通过维格纳变换从 Chern-Simons-Schrödinger 方程推导出 VCS 方程,该方程是受 Chern-Simons 规量场影响的粒子的量子力学模型。随后,我们分别研究了 VCS 方程强解的局部时间内好求和弱解的全局时间内存在性。此外,我们还提出了求解 VCS 方程的简单半拉格朗日数值方案,并通过数值测试验证了总矩和 Lp 矩的守恒性。
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来源期刊
ACS Applied Bio Materials
ACS Applied Bio Materials Chemistry-Chemistry (all)
CiteScore
9.40
自引率
2.10%
发文量
464
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