Instituto de Física, Universidade de São Paulo, Rua do Matão 1371, 05508-090 São Paulo, São Paulo, Brazil.
Phys Rev E. 2018 Jan;97(1-1):012105. doi: 10.1103/PhysRevE.97.012105.
The transport properties of a bosonic chain have been calculated by placing the ends of the chain in contact with thermal and particle reservoirs at different temperatures and chemical potentials. The contact with the reservoirs is described by the use of a quantum Fokker-Planck-Kramers equation, which is a canonical quantization of the classical Fokker-Planck-Kramers equation. From the quantum equation we obtain equations for the covariances of the creation and annihilation boson operators and solve them in the stationary state for small interactions. From the covariances we determine the Onsager coefficients and in particular the conductance, which was found to be finite for any chain size leading to an infinite conductivity and the absence of Fourier's law.
通过将链的两端与处于不同温度和化学势的热和粒子储库接触，计算了玻色链的输运性质。通过使用量子福克-普朗克-克莱默斯方程来描述与储库的接触，该方程是经典福克-普朗克-克莱默斯方程的正则量子化。从量子方程中，我们得到了产生和湮灭玻色子算符协方差的方程，并在小相互作用下在定态下求解它们。从协方差中，我们确定了昂萨格系数，特别是电导率，对于任何链尺寸，电导率都是有限的，导致无限电导率和不存在傅里叶定律。
