Sum rules for response functions represent some of the few exact results in many-body physics, relating the dynamical response functions to equilibrium ground state properties. To date, however, sum rules have been examined primarily for linear response functions. In this work, the authors introduce a spectral density representation for second-order response functions, using it to systematically derive families of sum rules, including a nonlinear extension of the well-known $f$ -sum rule. This work places important constraints on future nonlinear spectroscopic experiments.Sum rules for response functions represent some of the few exact results in many-body physics, relating the dynamical response functions to equilibrium ground state properties. To date, however, sum rules have been examined primarily for linear response functions. In this work, the authors introduce a spectral density representation for second-order response functions, using it to systematically derive families of sum rules, including a nonlinear extension of the well-known $f$-sum rule. This work places important constraints on future nonlinear spectroscopic experiments.

arXiv:2404.16144Physical review. B./Physical review. BDec 18, 202414 citations

Linear Response

Tamás S. Bíró, Antal Jakovác

SpringerBriefs in physicsJan 1, 20190 citations

Linear response theory*

WORLD SCIENTIFIC eBooksJun 27, 20180 citations

f

-sum rule. This work places important constraints on future nonlinear spectroscopic experiments.