Microscopic derivation of the Fröhlich Hamiltonian for the Bose polaron in the mean-field limit

Derivation of an effective evolution equation for a strongly coupled polaron

Fröhlich's polaron Hamiltonian describes an electron coupled to the quantized phonon field of an ionic crystal. We show that in the strong coupling limit the dynamics of the polaron is approximated by an effective non-linear partial differential equation due to Landau and Pekar, in which the phonon field is treated as a classical field.

Derivation of Pekar's Polarons from a Microscopic Model of Quantum Crystals

A polaron is an electron interacting with a polar crystal, which is able to form a bound state by using the distortions of the crystal induced by its own density of charge. In this paper we derive Pekar's famous continuous model for polarons (in which the crystal is replaced by a simple effective Coulomb self-attraction) by studying the macroscopic limit of the reduced Hartree-Fock theory of the crystal. The macroscopic density of the polaron converges to that of Pekar's nonlinear model, with a possibly anisotropic dielectric matrix. The polaron also exhibits fast microscopic oscillations whic…

带截断的极化子动力学的半经典极限

Semiclassical limit of polaron dynamics with cutoff

该研究从维格纳测度视角定义并分析了带截断的经典极化子动力学的整体适定性及其从弗罗利希哈密顿量量子动力学的推导，借助格罗斯变换提取发散常数，并探讨了移除截断时定义经典动力学的难点。

Microscopic Derivation of Time-dependent Point Interactions

We study the dynamics of the three-dimensional polaron - a quantum particle coupled to bosonic fields - in the quasi-classical regime. In this case the fields are very intense and the corresponding degrees of freedom can be treated semiclassically. We prove that in such a regime the effective dynamics for the quantum particles is approximated by the one generated by a time-dependent point interaction, i.e., a singular time-dependent perturbation of the Laplacian supported in a point. As a by-product, we also show that the unitary dynamics of a time-dependent point interaction can be approximat…

从非平衡自旋-玻色系统出发，通过Keldysh泛函积分推导一个$\PT$对称的非厄米特正弦-戈登模型

Derivation of a $\PT$-Symmetric Sine-Gordon Model from a Nonequilibrium Spin-Boson System via Keldysh Functional Integrals

本文通过Keldysh泛函积分、Lang-Firsov极化子变换、玻色化和格森 coherent-state 自旋迹，推导出非平衡自旋-玻色系统到$\PT$对称非厄米特正弦-戈登有效理论的微观推导，并给出了自旋-玻色微观参数与非厄米特正弦-戈顿耦合之间的显式字典。