The Linear Response Function of a Many-Body System

Xiao-Yue Gu, Gabor J. Kalman, Z. C. Tao

Xiaotian Nie, Wei Zheng

Adiabatic theorem and non-adiabatic corrections have been widely applied in modern quantum technology. Recently, non-adiabatic linear response theory has been developed to probe the many-body correlations in closed systems. In this work, we generalize the non-adiabatic linear response theory to open quantum many-body systems. We show that, similar to the closed case, the first-order deviation from the instantaneous steady state is memoryless—it depends only on the final parameters and not on the initial state or ramping path. When ramping the Hamiltonian, the linear response of observables is governed by the derivative of the retarded Green’s function, as in closed systems. In contrast, ramping the dissipation gives rise to a different response, characterized by a high-order correlation function defined in the steady state. Our results offer a compact and physically transparent formulation of non-adiabatic response in open systems, and demonstrate that ramping dynamics can serve as a versatile tool for probing many-body correlations beyond equilibrium.

Gianluca Stefanucci, Robert van Leeuwen

Shiwei Li, Jerome K. Percus

The one-body density matrix of a noninteracting Fermion system is expressed in terms of a contour integral, and expanded about that of the free particle system. High-order k-space linear response functions of this in an external potential are calculated for one and three dimensions via a functional expansion formulation. The results are compared with those given by the inverse Laplace transform (ILT) method. It is shown that the k-space linear responses in one dimension have a much simpler structure than those in the real space, and can be evaluated systematically. Two special one-body Hamiltonians are used to illustrate the one-dimensional results. The validity of the linear response expansion is addressed in the discussion of these examples.

Arnold J. Glick

Gabor J. Kalman, J. M. Rommel

While the theory of linear response functions in many body theory has developed into a substantial lore over the past decades, rather little is known about the properties and behavior of higher order (quadratic, etc.) response functions of many body systems. In this poster we first review essential elements of quadratic response theory such as the quadratic fluctuation dissipation theorems and sum rules for the quadratic density response function. Next we show how the correlational local field G(k,ω) in the linear response is fundamentally linked to the quadratic response function which opens a way to a non-perturbational analysis of the former. We proceed to present the results of the explicit calculation of the quadratic density response of 2D and 3D electron gas. Both, real and imaginary part of the latter reveal an extremely rich behavior. Of particular interest is the comparison between the two- and the three-dimensional case.