Comparison of quantization of charge transport in periodic and open pumps

高阶 Berry 曲率与高阶 Thouless 泵的量子化

Quantization of the higher Berry curvature and the higher Thouless pump

本文研究可逆相晶格系统族中的高阶拓扑不变量，证明高阶 Berry 曲率和高阶 Thouless 泵分别可加细为参数空间上的整值三次类与二次类，并将二维泵识别为磁通插入的超额曲率。

托勒密泵与多滑动准周期晶格中的通用几何诱导漂移速度

Thouless pumps and universal geometry-induced drift velocity in multi-sliding quasi-periodic lattices

本文提出了一种通用框架，用于研究多滑动准周期晶格中的托勒密泵，揭示了拓扑漂移与准布里渊区几何之间的普遍关系，并通过模拟验证了其有效性。

Semi-classical quantization rules for a periodic orbit of hyperbolic type

Determination of periodic orbits for a Hamiltonian system together with their semi-classical quantization has been a long standing problem. We consider here resonances for a $h$-Pseudo-Differential Operator $H(y,hD_y;h)$ induced by a periodic orbit of hyperbolic type at energy $E_0$. We generalize the framework of [GéSj], in the sense that we allow for both hyperbolic and elliptic eigenvalues of Poincaré map, and show that all resonances in $W=[E_0-\varepsilon_0,E_0+\varepsilon_0]-i]0,h^δ]$, $0<δ<1$, are given by a generalized Bohr-Sommerfeld quantization rule.

Periodic orbit quantization of a Hamiltonian map on the sphere

In a previous paper we introduced examples of Hamiltonian mappings with phase space structures resembling circle packings. It was shown that a vast number of periodic orbits can be found using special properties. We now use this information to explore the semiclassical quantization of one of these maps.

Quantization of Conductance in Quasi-Periodic Quantum Wires

We study charge transport in the Peierls-Harper model with a quasi-periodic cosine potential. We compute the Landauer-type conductance of the wire. Our numerical results show the following: (i) When the Fermi energy lies in the absolutely continuous spectrum that is realized in the regime of the weak coupling, the conductance is quantized to the universal conductance. (ii) For the regime of localization that is realized for the strong coupling, the conductance is always vanishing irrespective of the value of the Fermi energy. Unfortunately, we cannot make a definite conclusion about the case w…

Geometry, Statistics and Asymptotics of Quantum Pumps

We give a pedestrian interpretation of a formula of Buttiker et. al. (BPT) relating the adiabatically pumped current to the S matrix and its (time) derivatives. We relate the charge in BPT to Berry's phase and the corresponding Brouwer pumping formula to curvature. As applications we derive explicit formulas for the joint probability density of pumping and conductance when the S matrix is uniformly distributed; and derive a new formula that describes hard pumping when the S matrix is periodic in the driving parameters.