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Zhongguo kexue. Wulixue Lixue Tianwenxue

量子非平衡态与输运计算物理

Youqi Ke, Sheng Meng, Ke Xia, Suhuai Wei

Published Feb 1, 2024• 0 citations
Publisher

Abstract

Under external driving forces, the system deviates from the equilibrium distribution and enters a non-equilibrium state, resulting in transport phenomena of both charge and energy and the emergence of many novel non-equilibrium phases. The transport of charge and energy through a quantum many-body material system is a fundamental process in the conversion and storage of energy and information, and material properties can undergo significant changes at the far-from-equilibrium conditions. A deep understanding and accurate calculation of non-equilibrium states in materials and devices, including transport properties, are essential for enhancing the control of material properties and advancing the related manufacturing technologies, constituting a key aspect of condensed matter physics and computational physics.

DOI
10.1360/sspma-2024-0037

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Under external driving forces, the system deviates from the equilibrium distribution and enters a non-equilibrium state, resulting in transport phenomena of both charge and energy and the emergence of many novel non-equilibrium phases. The transport of charge and energy through a quantum many-body material system is a fundamental process in the conversion and storage of energy and information, and material properties can undergo significant changes at the far-from-equilibrium conditions. A deep understanding and accurate calculation of non-equilibrium states in materials and devices, including transport properties, are essential for enhancing the control of material properties and advancing the related manufacturing technologies, constituting a key aspect of condensed matter physics and computational physics.
Condensed matter physics is a rich field with a wide variety of phenomena. In condensed matter, we consider systems composed of many electrons and nuclei, with the only fundamental interaction being electromagnetism. Nuclei of a given charge and mass are considered as point particles. The relevant fundamental physics that we use as our foundations is the quantum many-body problem. That is, just standard many-body quantum mechanics, but formulated in terms of a useful second quantized field theory, which can deal with an arbitrary number of particles within a single Hilbert space. In general, this many-body problem is essentially intractable for numbers of particles as large as those we must consider for materials. Thus we must look for simplifications and look at easily measurable aspects which allow us to make predictions still. We employ the trick of phrasing the questions differently. Rather than look at the time evolution of an arbitrary many-body wavefunction for the fundamental degrees of freedom, we look at transport in scenarios where the starting point is a relatively simple assumed equilibrium state of the material, consisting of a ground state with postulated quasiparticle excitations.
Among of the ultimate goals of modern science is the understanding of emergent complex properties of matter in the strongly interacting regime from simple constituents and their interactions. This understanding can lead towards the development of new materials and devices with novel functionalities both at the level of basic research and for numerous technological applications. Richard Feynman’s pioneering ideas of quantum simulation [1] constitute a promising path to reach such goals. A major push to implement them has been possible thanks to advances in cooling and trapping atoms in optical lattices [2]. These systems are not only a defect-free replica of electrons in crystalline lattices but, in addition satisfy the requirement of full controllability.
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.
The physics of non-equilibrium many-body systems is a rapidly expanding area of theoretical physics. Traditionally employed in laser physics and superconducting kinetics, these techniques have more recently found applications in the dynamics of cold atomic gases, mesoscopic and nano-mechanical systems, and quantum computation. This book provides a detailed presentation of modern non-equilibrium field-theoretical methods, applied to examples ranging from biophysics to the kinetics of superfluids and superconductors. A highly pedagogical and self-contained approach is adopted within the text, making it ideal as a reference for graduate students and researchers in condensed matter physics. In this Second Edition, the text has been substantially updated to include recent developments in the field such as driven-dissipative quantum systems, kinetics of fermions with Berry curvature, and Floquet kinetics of periodically driven systems, among many other important new topics. Problems have been added throughout, structured as compact guided research projects that encourage independent exploration.
This paper explores the application of real-time Feynman diagrammatics as a powerful theoretical framework for understanding and predicting emergent topological phenomena in quantum materials under non-equilibrium conditions. Traditional approaches, primarily focused on equilibrium systems, often fall short in describing the rich dynamics and transient phases induced by external drives or sudden quenches. We delve into the intricacies of the Keldysh formalism, a crucial tool for non-equilibrium quantum field theory, and detail how it can be combined with diagrammatic expansions to capture time-dependent correlations and interactions. The methodology presented allows for the analysis of phenomena such as Floquet topological insulators, dynamically induced topological phase transitions, and the evolution of topological invariants in time-dependent settings. Through this framework, we aim to uncover novel topological states that emerge far from equilibrium, offering pathways for their experimental realization and manipulation. The discussion highlights the unique insights provided by a real-time perspective, contrasting it with static descriptions and emphasizing its potential to drive advancements in both fundamental condensed matter physics and the engineering of quantum devices.