Geometric treatment of electromagnetic phenomena in conducting materials: variational principles
Geometric treatment of electromagnetic phenomena in conducting materials: variational principles
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DOI：
10.1088/0305-4470/39/47/013
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发表时间：
2006-10
期刊：
影响因子：
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通讯作者：
A. Badía–Majós;J. Cariñena;Carlos Monge López
中科院分区：
文献类型：
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作者：
A. Badía–Majós;J. Cariñena;Carlos Monge López
研究了电磁场与导电材料耦合作用下的动力学方程。用时空几何中张量物质定律的经典场论描述了这种相互作用的性质。我们证明了超导响应的主要特征在协方差、规范不变性和变分公式要求内以自然的方式出现。特别是，当考虑到基本对称性时，金兹堡-朗道理论直接遵循伦敦方程。非常规的性质，如超导体与静电场的相互作用，在几何理论中自然地引入了现象学水平。内部对称性的宏观指纹也提示了BCS背景。本文还表明，对于绝热过程，在打破协方差后，耗散导电行为可以近似地用变分框架来处理。因此，非保守的相互作用定律是由一个纯粹的空间变分原理，在准平稳时间离散演化。这一理论证明了一类非功能现象学原理是正确的，这些原理是为处理物质的奇异传导特性而引入的（Badia and Lopez 2001 Phys.）。Rev. Lett. 87 127004)。
The dynamical equations of an electromagnetic field coupled with a conducting material are studied. The properties of the interaction are described by a classical field theory with tensorial material laws in spacetime geometry. We show that the main features of superconducting response emerge in a natural way within the covariance, gauge invariance and variational formulation requirements. In particular, the Ginzburg–Landau theory follows straightforwardly from the London equations when fundamental symmetry properties are considered. Unconventional properties, such as the interaction of superconductors with electrostatic fields are naturally introduced in the geometric theory, at a phenomenological level. The BCS background is also suggested by macroscopic fingerprints of the internal symmetries. It is also shown that dissipative conducting behaviour may be approximately treated in a variational framework after breaking covariance for adiabatic processes. Thus, nonconservative laws of interaction are formulated by a purely spatial variational principle, in a quasi-stationary time discretized evolution. This theory justifies a class of nonfunctional phenomenological principles, introduced for dealing with exotic conduction properties of matter (Badia and Lopez 2001 Phys. Rev. Lett. 87 127004).