AI 中文总结
研究石墨烯量子态，通过选择展开系数使级数在二维空间特定圆内收敛，解析延拓得到反常波函数，探讨了反常电子等概念，指出反常真空形成是集体量子现象，且石墨烯薄膜边缘的反常态具高导电性。
AI 中文摘要
量子力学波动方程的一个定态解是本征函数的叠加。它们中的每一个都对应于希尔伯特空间中的一个向量。在石墨烯样本中，可以选择展开系数以使级数仅在二维空间中的某个圆内收敛。在这个圆之外，需要以不同级数的形式进行解析延拓。精确的波函数被称为反常的。它不是传统本征函数的叠加，并且超出了希尔伯特空间。反常电子和反电子是可能的。反电子不是传统价带中的空位。反常电子 - 反电子对是从反常真空中产生的，就像电子 - 正电子对是从电子 - 正电子真空中产生的一样。反常真空的形成不是单电子效应，而是集体量子现象。在石墨烯薄膜中，反常态位于薄膜边缘，预计具有高导电性。
英文摘要
A stationary solution of quantum mechanical wave equation is the superposition of eigenfunctions. Each of them corresponds to a vector in the Hilbert space. In a graphene sample one can choose expansion coefficients to get the series convergent solely within the certain circle in the two-dimensional space. Outside this circle the analytic continuation is required in the form of a different series. The exact wave function is referred to as anomalous. It is not a superposition of conventional eigenfunctions and gets ouside the Hilbert space. Anomalous electron and antielectron are possible. The antielectron is not a vacancy in the conventional valence band. The anomalous electron-antielectron pair is created from the anomalous vacuum like the electron-positron pair is created from the electron-positron vacuum. Formation of the anomalous vacuum is not a single electron effect but the collective quantum phenomenon. In the film of graphene the anomalous states are located at the film edge and are expected to be of high conductivity.
