On the general properties of non-linear optical conductivities

Abstract

The optical conductivity is the basic defining property of materials characterizing the current response toward time-dependent electric fields. In this work, following the approach of Kubo's response theory, we study the general properties of the nonlinear optical conductivities of quantum many-body systems both in equilibrium and non-equilibrium. We obtain an expression of the second- and the third-order optical conductivity in terms of correlation functions and present a perturbative proof of the generalized Kohn formula proposed recently. We also discuss a generalization of the $f$-sum rule to a non-equilibrium setting by focusing on the instantaneous response.

arXiv comment17 pages, 1 figure, 1 table; v2: Introduction expanded. To appear in JSP

References in corpus (14)

• Nonequilibrium dynamical mean-field theory and its applications
• The Quantum-Mechanical Position Operator in Extended Systems
• Topological nature of nonlinear optical effects in solids
• Polarization and localization in insulators: generating function approach
• Integrability and ideal conductance at finite temperatures
• Diagrammatic approach to nonlinear optical response with application to Weyl semimetals
• A many-body index for quantum charge transport
• A proof of the Bloch theorem for lattice models
• Quantum Quench and $f$-Sum Rules on Linear and Non-linear Conductivities
• Generalized $f$-Sum Rules and Kohn formulas on Non-linear Conductivities
• General properties of response functions of nonequilibrium steady states
• Two No-Go Theorems on Superconductivity
• Universal Properties of Nonlinear Response Functions of Nonequilibrium Steady States
• Sum Rules and Asymptotic Behaviors for Optical Conductivity of Nonequilibrium Many-Electron Systems

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• Spectral Density and Sum Rules for Second-Order Response Functions
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• Energy-twisted boundary condition and response in one-dimensional quantum many-body systems
• Non-linear Transport by Bethe Bound States
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• Drude weights in one-dimensional systems with a single defect
• Hydrodynamic non-linear response of interacting integrable systems
• Patchwork Conditions for Holographic Nonlinear Responses: A Computational Method for Electric Conductivity and Friction Coefficient
• Long-time divergences in the nonlinear response of gapped one-dimensional many-particle systems
• Imaginary Time Formalism for Causal Nonlinear Response Functions