Bateman's dual system revisited: I. Quantization, geometric phase and relation with the ground-state energy of the linear harmonic oscillator

量子阻尼谐振子的有效描述： revisit 巴特曼对偶系统

Effective Description of the Quantum Damped Harmonic Oscillator: Revisiting the Bateman Dual System

本文提出基于矩量子力学的阻尼谐振子量子化方案，利用巴特曼对偶模型，所得描述与林德布拉德主方程高度一致，为开放量子系统提供有效且普适的工具。

On quantization of nondispersive wave packets

Canonical commutation relations for the Bateman-Hillion type nondispersive wave packets are constructed

Dissipation and quantization for composite systems

In the framework of 't Hooft's quantization proposal, we show how to obtain from the composite system of two classical Bateman's oscillators a quantum isotonic oscillator. In a specific range of parameters, such a system can be interpreted as a particle in an effective magnetic field, interacting through a spin-orbit interaction term. In the limit of a large separation from the interaction region one can describe the system in terms of two irreducible elementary subsystems which correspond to two independent quantum harmonic oscillators.

Quantization of the Damped Harmonic Oscillator Revisited

We return to the description of the damped harmonic oscillator by means of a closed quantum theory with a general assessment of previous works, in particular the Bateman-Caldirola-Kanai model and a new model recently proposed by one of the authors. We show the local equivalence between the two models and argue that latter has better high energy behavior and is naturally connected to existing open-quantum-systems approaches.

从Caldirola到Bateman阻尼系统的对称性之旅

A symmetry trip from Caldirola to Bateman damped systems

本文从Caldirola-Kanai阻尼谐振子出发，通过幺正扩展对称代数，自然引出Bateman对偶系统，并给出其对称群与量子化方案，实现一阶薛定谔方程。

自旋诱导非马尔可夫时间晶格状动力学与Bateman双振子中的分形缩放

Spin-Induced Non-Markovian Time-Crystal-Like Dynamics and Fractal Scaling in the Bateman Dual Oscillator

该研究通过Bateman双振子框架展示了一个封闭量子系统可以在没有外部驱动的情况下产生持久的时间晶格状动力学，其核心方法是利用自旋诱导的空间变形生成有效的Bateman振子结构，并通过非马尔可夫减少动力学揭示了自相似分形缩放与非平衡子系统动力学之间的联系。

Quantum damped oscillator I: dissipation and resonances

Quantization of a damped harmonic oscillator leads to so called Bateman's dual system. The corresponding Bateman's Hamiltonian, being a self-adjoint operator, displays the discrete family of complex eigenvalues. We show that they correspond to the poles of energy eigenvectors and the corresponding resolvent operator when continued to the complex energy plane. Therefore, the corresponding generalized eigenvectors may be interpreted as resonant states which are responsible for the irreversible quantum dynamics of a damped harmonic oscillator.

关于一个经典动力系统及其量子化的注记

A note on a classical dynamical system and its quantization

本文研究修改版Bateman系统，发现其量子化后不必然耗散，Hamiltonian随参数关系可表现为标准谐振子或包含倒置振子，并用阶梯算符分析了两种情况。

A no-go result for the quantum damped harmonic oscillator

In this letter we show that it is not possible to set up a canonical quantization for the damped harmonic oscillator using the Bateman lagrangian. In particular, we prove that no square integrable vacuum exists for the {\em natural} ladder operators of the system, and that the only vacua can be found as distributions. This implies that the procedure proposed by some authors is only formally correct, and requires a much deeper analysis to be made rigorous.

Precanonical quantization and the Schrödinger wave functional revisited

We address the issue of the relation between the canonical functional Schrödinger representation in quantum field theory and the approach of precanonical field quantization proposed by the author, which requires neither a distinguished time variable nor infinite-dimensional spaces of field configurations. We argue that the standard functional derivative Schrödinger equation can be derived from the precanonical Dirac-like covariant generalization of the Schrödinger equation under the formal limiting transition $γ^0\varkappa\rightarrowδ(\mathbf{0})$, where the constant $\varkappa$ naturally appe…

The Hopfield model revisited: Covariance and Quantization

There are several possible applications of quantum electrodynamics in dielectric media which require a quantum description for the electromagnetic field interacting with matter fields. The associated quantum models can refer to macroscopic electromagnetic fields or, in alternative, to mesoscopic fields (polarization fields) describing an effective interaction between electromagnetic field and matter fields. We adopt the latter approach, and focus on the Hopfield model for the electromagnetic field in a dielectric dispersive medium in a framework in which space-time dependent mesoscopic paramet…

重新审视电磁激发的量子振子模型

The quantum oscillator model of electromagnetic excitations revisited

本文重新考察电磁场的量子振子模型，阐明实Maxwell场二次量子化所得Hermitian算符描述局域耦合于费米子物质的光子-反光子对，并指出单光子场应解释为概率幅。

Three Photon Entanglement from Ortho-Positronium Revisited

Entanglement of three photons from the decay of ortho-positronium is re-analyzed. We use the full three body phase space to write down the entangled states classified according to the spin directions of the ortho-positronium. Even in the case when the spin is perpendicular to the decay plane, we find non-negligible phases entering the entangled state. This has not been noticed before. We advocate a fixed quantization axis of the spin for the sake of generality. A brief discussion of a three dimensional formalism for photons, including correlations, versus a two dimensional one is given.

Dirac's Method for the Two-Dimensional Damped Harmonic Oscillator in the Extended Phase Space

The system of two-dimensional damped harmonic oscillator is revisited in the extended phase space. It is an old problem already addressed by many authors that we present here in some fresh points of view and carry on smoothly a whole discussion. We show that the system is singular. The classical Hamiltonian is proportional to the first-class constraint. We pursue with the Dirac's canonical quantization procedure by fixing the gauge and provide a reduced phase space description of the system. As result the quantum system is simply modeled by the original quantum Hamiltonian.