量子场论中的量子运动方程与量子诺特定理

运动方程和诺特定理是经典场论中的核心概念。然而在实际的量子场论中,需要使用量子运动方程和量子诺特定理来研究一系列与物理观测量相关的关联函数或者矩阵元。经典场论中的运动方程和诺特定理与其量子版本之间具有非常微妙,但却十分重要的联系与区别。透析这一点,无论对于前沿工作者,抑或是初学场论的研究生,都具有非常重要的意义。它揭示了经典物理与量子物理之间的本质差别。本文利用路径积分量子化方法,从第一性原理出发,基于泛函计算体系,推导出了量子版本的运动方程与诺特定理,详细探讨了其与经典版本之间的联系与区别。这对于量子物理的前沿计算具有重要的指导和规范作用,也为初学场论的研究生快速进入前沿领域的研究,提供了一条脉络清晰,可操作性很强的道路。Equation of motion and Noether’s theorem are core concepts in classical field theory. However, in practical quantum field theory, it is necessary to use quantum equation of motion and quantum Noether’s theorem to study a series of correlation functions or matrix elements related to physical observables. There is a very subtle yet crucial connection and difference between the classical and quantum versions of the equation of motion and Noether’s theorem. Analyzing this is of great importance not only for researchers at the forefront but also for graduate students new to field theory. It reveals the fundamental differences between classical and quantum physics. This paper utilizes the path integral quantization method, starting from first principles, based on functional calculation, to derive the quantum versions of the equations of motion and Noether’s theorem, and it thoroughly discusses their connections and differences with the classical versions. This serves as an important guide and standard for frontier calculations in quantum physics and also provides a clear and practical path for graduate students new to field theory to quickly engage in forefront research.

Adiabatic Terminator for Fermionic Hierarchical Equations of Motion

The hierarchical equation of motion method has become one of the most popular numerical methods for describing the dissipative dynamics of open quantum systems linearly coupled to environment.However,its applications to systems with strong electron correlation are largely restrained by the computational cost,which is mainly caused by the high truncation tier L required to accurately characterize the strong correlation effect.In this work,we develop an adiabatic terminator by decoupling the principal dissipation mode with the fastest dissipation rate from the slower ones.The adiabatic terminator leads to substantially enhanced convergence with respect to L as demonstrated by the numerical tests carried out on a single impurity Anderson model.Moreover,the adiabatic terminator alleviates the numerical instability problems in the long-time dissipative dynamics.

Classical Mechanics and Quantum Mechanics

The Newton equation of motion is derived from quantum mechanics.

Kondo-Fano Effect in T-shaped Double Quantum Dots Coupled to Ferromagnetic Leads

Using an equation-of-motion technique, we theoretically study the Kondo-Fano effect in the T-shaped double quantum dots coupled to two ferromagnetic leads by the Anderson Hamiltonian. We calculate the density of states in this system by solving Green function. Our results reveal that the density of states show some noticeable characteristics not only depending upon the interdot coupling tab, the energy level eal of the side coupled quantum dot QDb, and the relative angle θ of magnetic moment M, but also the asymmetry parameter a in ferromagnetic leads and so on. All these parameters greatly influence the density of states of the eentral quantum dot QDa. This system is a possible candidate for spin valve transistors and may have potential applications in the spintronies.

Quantum Transport Theory for Fusion Plasmas

Fundamental quantum transport equation for impact-ionization processes in fusion plasmas is formulated in the actor-spectator description. The density-matrix formulism is adopted to treat both coherent and incoherent effects in a unified fashion. Quantum electrodynamic effects are also considered for high-temperature scenarios. Electron-impact ionization of uranium ion U91＋ and proton-impact ionization of hydrogen are given as examples.