Lattice duality for the compact Kardar-Parisi-Zhang equation
Lattice duality for the compact Kardar-Parisi-Zhang equation
复制标题
紧致 Kardar-Parisi-Zhang 方程的格对偶性
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
Sebastian Diehl
中科院分区：
文献类型：
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作者：
L. M. Sieberer;L. M. Sieberer;Gideon Wachtel;Gideon Wachtel;E. Altman;E. Altman;Sebastian Diehl
二维超流体在热平衡状态下的Kosterlitz-Thouless跃迁的综合理论可以在将超流体中的涡旋映射到库仑气体中的电荷的对偶表示中得到发展。在此框架下，涡-反涡对在临界温度下的解离对应于自由电荷等离子体的形成。另一方面，在诸如光流体之类的驱动耗散系统中，旋涡解绑的物理原理却知之甚少。在这里，我们通过推导将描述驱动耗散凝聚物相动力学的紧凑型kardar - paris - zhang （KPZ）方程映射到对偶电动力学理论的变换，迈出了填补这一空白的关键一步。后者是用修正的电磁场麦克斯韦方程和KPZ方程中表示漩涡的电荷的扩散方程来表示的。这种映射利用了对格上紧化KPZ方程的广义Martin-Siggia-Rose泛函积分表示的Villain近似的适应。
A comprehensive theory of the Kosterlitz-Thouless transition in two-dimensional superfluids in thermal equilibrium can be developed within a dual representation which maps vortices in the superfluid to charges in a Coulomb gas. In this framework, the dissociation of vortex-antivortex pairs at the critical temperature corresponds to the formation of a plasma of free charges. The physics of vortex unbinding in driven-dissipative systems such as fluids of light, on the other hand, is much less understood. Here we make a crucial step to fill this gap by deriving a transformation that maps the compact Kardar-Parisi-Zhang (KPZ) equation, which describes the dynamics of the phase of a driven-dissipative condensate, to a dual electrodynamic theory. The latter is formulated in terms of modified Maxwell equations for the electromagnetic fields and a diffusion equation for the charges representing vortices in the KPZ equation. This mapping utilizes an adaption of the Villain approximation to a generalized Martin-Siggia-Rose functional integral representation of the compact KPZ equation on a lattice.