Theory of one-dimensional electronic Casimir effect in terms of complex eigenvalue problem of Hamiltonian and Liouvilian

2014 Fiscal Year Final Research Report

• Project/Area Number: 24540327
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Condensed matter physics I
• Research Institution: Osaka Prefecture University
• Principal Investigator: TANAKA Satoshi 大阪府立大学, 理学(系)研究科(研究院), 教授 (80236588)
• Co-Investigator(Kenkyū-buntansha): KANKI Kazuki 大阪府立大学, 大学院理学系研究科, 准教授 (10264821)
• Research Collaborator: TOMIO Petrosky
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 量子光学 / 非平衡統計力学

Outline of Final Research Achievements

Electronic Casimir effect between impurities in a quantum wire has been theoretically investigated in terms of complex eigenvalue problem of Hamiltonian. We have revealed that a mechanism of a force between the impurities caused by an electron transfer through a one-dimensional conduction band is essentially the same as a ordinary Casimir force between atoms mediated by a virtual photon. In this electronic system, a finite effective band-mass of an electron leads the Casimir force to decay exponentially in the distance of the impurities, in contrast to a power law decay in an ordinary Casimir force. It is found out that the electronic Casimir force extends to a very long range due to the Van Hove singularity characteristic to a one-dimensional system. We have further clarified that virtual cloud, key element of the Casimir force, disappears when the atom is in the excited state as a result of the nonlinear dispersion relation of the electronic band.

Free Research Field

物性理論