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We derive equations of motion for higher order density response functions using the theory of thermodynamic Green's functions. We also derive expressions for the higher order generalized dielectric functions and polarization functions.…

Strongly Correlated Electrons · Physics 2024-10-04 Jan Vorberger , Tobias Dornheim , Maximilian P. Böhme , Zhandos Moldabekov , Panagiotis Tolias

This review presents recent breakthroughs in the realm of nonlinear Hall effects, emphasizing central theoretical foundations and recent experimental progress. We elucidate the quantum origin of the second-order Hall response, focusing on…

Mesoscale and Nanoscale Physics · Physics 2024-05-21 Arka Bandyopadhyay , Nesta Benno Joseph , Awadhesh Narayan

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…

Statistical Mechanics · Physics 2020-10-20 Haruki Watanabe , Yankang Liu , Masaki Oshikawa

Nonlinear responses in condensed matters attract recent intensive interest because they provide rich information about the materials and hold the possibility of being applied in diodes or high-frequency optical devices. Nonlinear responses…

Strongly Correlated Electrons · Physics 2022-10-05 Yoshihiro Michishita , Naoto Nagaosa

Nonlinear transport phenomena offer an exciting probe into the band geometry and symmetry properties of a system. While most studies on nonlinear transport have looked at second-order nonreciprocal responses in noncentrosymmetric systems,…

Mesoscale and Nanoscale Physics · Physics 2024-06-04 Debottam Mandal , Sanjay Sarkar , Kamal Das , Amit Agarwal

Nonlinear optical responses provide a powerful way to understand the microscopic interactions between laser fields and matter. They are critical for plenty of applications, such as in lasers, integrated photonic circuits, biosensing and…

The nonlinear optical behavior of quantum systems plays a crucial role in various photonic applications. This study introduces a novel framework for understanding these nonlinear effects by incorporating gauge-covariant formulations based…

General Physics · Physics 2025-03-11 Jingxu Wu , Chenjia Li

Nonlinear effects are omnipresent in thin films of ion conducting materials showing up as a significant increase of the conductivity. For a disordered hopping model general physical mechanisms are identified giving rise to the occurrence of…

Disordered Systems and Neural Networks · Physics 2015-06-18 Andreas Heuer , Lars Luehning

Nonlinear responses in condensed matter are intensively studied because they provide rich information about materials and hold the possibility of being applied in diodes or high-frequency optical devices. While nonlinear responses in…

Strongly Correlated Electrons · Physics 2021-05-26 Yoshihiro Michishita , Robert Peters

We investigate the linear and nonlinear optical responses of dilute anisotropic networks using the Green's-function formalism (GFF)[Gu Y et al. 1999 Phys. Rev. B 59 12847]. For the different applied fields, numerical calculations indicate…

Soft Condensed Matter · Physics 2007-05-23 Y. Gu , K. W. Yu

There are a variety of nonlinear optical effects including higher harmonic generations, photovoltaic effects, and nonlinear Kerr rotations. They are realized by the strong light irradiation to materials that results in nonlinear…

Mesoscale and Nanoscale Physics · Physics 2016-05-26 Takahiro Morimoto , Naoto Nagaosa

One big achievement in modern condensed matter physics is the recognition of the importance of various band geometric quantities in physical effects. As prominent examples, Berry curvature and the Berry curvature dipole are connected to the…

Mesoscale and Nanoscale Physics · Physics 2022-01-26 Huiying Liu , Jianzhou Zhao , Yue-Xin Huang , Xiaolong Feng , Cong Xiao , Weikang Wu , Shen Lai , Wei-bo Gao , Shengyuan A. Yang

We systematically investigate nonlinear Ohmic responses in second-harmonic generation and bilinear magnetoelectric effects within the Matsubara Green's function formalism. The optical nonlinear Ohmic conductivity is shown to consist of a…

Mesoscale and Nanoscale Physics · Physics 2026-05-19 Anwei Zhang , Zheng Cai , C. M. Wang

The nonlinear Hall effect, which is the second-order harmonic charge Hall effect from the Berry curvature dipole in momentum space, has received much attention recently. As the responses to higher harmonics of the driving ac electric field…

Materials Science · Physics 2021-10-14 Zhi-Fan Zhang , Zhen-Gang Zhu , Gang Su

We present a practical scheme to separate the contributions of the electric quadrupole-like and the magnetic dipole-like effects to the forbidden second order optical nonlinear response of graphene, and give analytic expressions for the…

Materials Science · Physics 2017-03-08 J. L. Cheng , N. Vermeulen , J. E. Sipe

In recent years, the investigation of nonlinear electromagnetic responses has received significant attention due to its potential for elucidating the quantum properties of matter. Although remarkable progress has been achieved in developing…

Mesoscale and Nanoscale Physics · Physics 2025-08-28 Anwei Zhang , C. M. Wang

The well-known Green's function method has been recently generalized to nonlinear second order differential equations. In this paper we study possibilities of exact Green's function solutions of nonlinear differential equations of higher…

Mathematical Physics · Physics 2018-10-26 Marco Frasca , Asatur Zh. Khurshudyan

During the past three decades, the advantageous concept of the Green's function has been extended from linear systems to nonlinear ones. At that, there exist a rigorous and an approximate extensions. The rigorous extension introduces the…

Mathematical Physics · Physics 2018-03-28 Asatur Khurshudyan

Intense laser technologies generate light with unprecedented and growing intensities. The possibility emerges that a nucleus responds nonlinearly to an intense light field, pointing to a yet little explored research area of nuclear…

Atomic Physics · Physics 2021-09-01 Tao Li , Xu Wang

We show that Green function methods can be straightforwardly applied to nonlinear equations appearing as the leading order of a short time expansion. Higher order corrections can be then computed giving a satisfactory agreement with…

High Energy Physics - Theory · Physics 2008-11-26 Marco Frasca
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