Theory of Non-Equilibirum States Driven by Constant Electromagnetic Fields : Non-Commutative Quantum Mechanics in the Keldysh Formalism(Condensed Matter and Statistical Physics)

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概要

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• We develop a general theory of non-equilibrium states based on the Keldysh formalism, in particular, for charged-particle systems under static uniform electromagnetic fields. The Dyson equation for the uniform stationary state is rewritten in a compact gauge-invariant form by using the Moyal product in the phase space of energy-momentum variables, whcich originally do not commute in the case of the conventional operator algebra. Expanding the Dyson equation in electromagnetic fields, a systematic method for the order-by-order calculation of linear and non-linear responses from the zeroth-order Green's functions is obtained. In particular, we find that for impurity problems, up to linear order in the electric field, the present approach provides a diagrammatic method for the Streda formula. This approach also generalizes the semi-classical Boltzmann transport theory to fully quantum-mechanical and/or multi-component systems. In multi-component systems and/or for Hall transport phenomena, however, this quantum Boltzmann transport theory, constructed from the anti-symmetric combination of two different representations for the Dyson equation, does not uniquely specify the non-equilibrium state, but the symmetric combination is required. We demonstate the formalism to calculate longitudinal and Hall electric conductivities in an isotropic single-band electron system in the clean limit. It is found that the results are fully consistent with those obtained by Mott and Ziman in terms of the semi-classical Boltzmann transport theory.

• 理論物理学刊行会の論文
• 2006-07-25

著者

• Nagaosa Naoto

  Crest Department Of Applied Physics University Of Tokyo:correlated Electron Research Center National

• Nagaosa Naoto

  Crest Department Of Applied Physics University Of Tokyo:correlated Electron Research Center (cerc) N

• SUGIMOTO Naoyuki

  Department of Applied Physics, University of Tokyo

• ONODA Shigeki

  Spin Superstructure Project, ERATO, Japan Science and Technology Agency, c o Department of Applied P

• Nagaosa Naoto

  Crest Japan Science And Technology Agency (jst) Aist:crest Department Of Applied Physics The Univers

• Onoda Shigeki

  Crest Department Of Applied Physics University Of Tokyo

• Sugimoto Naoyuki

  Department Of Applied Physics University Of Tokyo

• NAGAOSA Naoto

  CREST, Department of Applied Physics, University of Tokyo:Correlated Electron Research Center, National Institute of Advanced Industrial Science and Technology

• ONODA Shigeki

  Spin Superstructure Project, ERATO, Japan Science and Technology Agency, c o Department of Applied Physics, University of Tokyo

関連論文

• Spin Currents in Semiconductors, Metals, and Insulators(Advances in Spintronics)
• Gauge Covariant Formulation of the Wigner Representation through Deformation Quantization : Application to Keldysh Formalism with an Electromagnetic Field(Condensed Matter and Statistical Physics)
• Theory of Non-Equilibirum States Driven by Constant Electromagnetic Fields : Non-Commutative Quantum Mechanics in the Keldysh Formalism(Condensed Matter and Statistical Physics)
• Theory of Excitation Spectra of Electron-Phonon Coupled Systems(Photo-Induced Phase Transitions and their Dynamics)
• Non-commutative quantum mechanics and deformation quantization in condensed-matter physics(Fundamental Problems and Applications of Quantum Field Theory-Topological Aspects of Quantum Field Theory-)

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