Generalized <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>f</mml:mi><mml:mo>−</mml:mo><mml:mi>sum</mml:mi></mml:mrow></mml:math> rules and Kohn formulas on nonlinear conductivities
Haruki Watanabe, Masaki Oshikawa
Abstract
The $f$-sum rule and the Kohn formula are well-established general constraints on the electric conductivity in quantum many-body systems. We present their generalization to nonlinear conductivities at all orders of the response in a unified manner by considering two limiting quantum time-evolution processes: a quench process and an adiabatic process. Our generalized formulas are valid in any stationary state, including the ground state and finite-temperature Gibbs states, regardless of the details of the system such as the specific form of the kinetic term, the strength of the many-body interactions, or the presence of disorders.
Topics & Concepts
AlgorithmAdiabatic processMathematicsGeneralizationGibbs stateGround stateMachine learningThermodynamicsPhysicsQuantumComputer scienceQuantum mechanicsMathematical analysisQuantum many-body systemsSpectroscopy and Quantum Chemical StudiesQuantum and electron transport phenomena