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arXiv:1210.8108 · Brazilian Journal of Physics

Response Function Theory for Many-Body Systems Away from Equilibrium: Conditions of Ultrafast-Time and Ultrasmall-Space Experimental Resolution

Clóves Gonçalves Rodrigues, Aurea Rosas Vasconcellos, J. G. G. S. Ramos, Roberto Luzzi

Published Nov 19, 2014• 3 citations
arXivHTMLPDF
DOI
10.1007/s13538-014-0280-0

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A response function theory for many-body systems arbitrarily away from equilibrium is presented. It is based on the n onequilibrium statistical operator method fully described in a previous article (~ev. Brasil .Fis.15, 106 (1985)l. We present a formal theory for evaluation of transition probabilties and the average values of dynamical quan- tities in far - from - equilibrium many-body systems under the action of externa1 perturbations. We also derive a n onequilibrium thermodynamic Green's functions algorithm appropriate for the calculation of response functions and scattering cross sections in terms ofa generalized fluc- tuation - dissipation theorem for far - from - equilibrium systems.
Quasiparticles are fundamental in describing the complex many-body interactions underlying single-particle excitations, playing a key role in understanding the macroscopic properties of quantum materials. Recent advancements in ultrafast laser technology, combined with various detection methods, have enabled precise monitoring and manipulation of quantum states and their dynamic processes. These developments not only enhance our comprehension of quasiparticle excitation mechanisms but also facilitate driving materials into non-equilibrium states, uncovering novel physical phenomena and advancing the design and application of innovative functional materials. The computational approach based on real-time time-dependent density functional theory (rt-TDDFT) transcends the limitations of linear response theory, enabling first-principles simulations of the dynamic response of strongly coupled quasiparticles under non-equilibrium conditions. The proposed method provides accurate predictions of highly nonlinear phenomena induced by strong laser fields, offering deeper insights into the underlying physical mechanisms. These theoretical insights are crucial for optimizing the performance of optoelectronic devices. This paper introduces the theoretical foundations of Ehrenfest dynamics within the framework of rt-TDDFT and presents case studies on the evolution of various quasiparticles under laser excitation. The results demonstrate the significant potential of ultrafast lasers for probing and controlling the properties of quantum materials, while also underscoring the vital role of dynamic simulations for studying non-equilibrium states and their time-domain characteristics.
While new light sources allow for unprecedented resolution in experiments with X-rays, a theoretical understanding of the scattering cross-section is lacking. In the particular case of strongly correlated electron systems, numerical techniques are quite limited, since conventional approaches rely on calculating a response function (Kramers-Heisenberg formula) that is obtained from a perturbative analysis of scattering processes in the frequency domain. This requires a knowledge of a full set of eigenstates in order to account for all intermediate processes away from equilibrium, limiting the applicability to small tractable systems. In this work, we present an alternative paradigm, recasting the problem in the time domain and explicitly solving the time-dependent Schrödinger equation without the limitations of perturbation theory: a faithful simulation of the scattering processes taking place in actual experiments, including photons and core electrons. We show how this approach can yield the full time and momentum resolved Resonant Inelastic X-Ray Scattering (RIXS) spectrum of strongly interacting many-body systems. We demonstrate the formalism with an application to Mott insulating Hubbard chains using the time-dependent density matrix renormalization group method, which does not require a priory knowledge of the eigenstates and can solve very large systems with dozens of orbitals. This approach can readily be applied to systems out of equilibrium without modification and generalized to other spectroscopies.