Effective mass of the polaron -- revisited

Fröhlich极化子的有效质量与Landau-Pekar-Spohn猜想

Effective Mass of the Fröhlich Polaron and the Landau-Pekar-Spohn Conjecture

本文证明Fröhlich极化子有效质量满足$m(α)\geq\overline C α^4$，证实了Landau-Pekar-Spohn猜想，并进一步得到有效质量严格单调性及广义极化子型相互作用的四次发散结果。

High Density Limit of the Fermi Polaron with Infinite Mass

We analyze the ground state energy for $N$ identical fermions in a two-dimensional box of volume $L^2$ interacting with an external point scatterer. Since the point scatterer can be considered as an impurity particle of infinite mass, this system is a limit case of the Fermi polaron. We prove that its ground state energy in the limit of high density $N/L^2 \gg 1$ is given by the polaron energy. The polaron energy is an energy estimate based on trial states up to first order in particle-hole expansion, which was proposed by F. Chevy in the physics literature. The relative error in our result is…

声学极化子基态能量的不可忽略的上界估计

Infinitely Improvable Upper Bound Estimates for Acoustical Polaron Ground State Energy

结果表明，利用广义变分法可以得到一个无限收敛的序列，该序列改进了慢运动声学极化子基态能量的非增上界。所提出的方法是特别适合于大量的分析和数值计算的实验测量性能的现实极化子，可以进一步阐述，没有重大的改动，以允许治疗各种极化子类型的模型。

Weak coupling limit for the ground state energy of the 2D Fermi polaron

We analyze the ground state energy for N fermions in a two-dimensional box interacting with an impurity particle via two-body point interactions. We allow for mass ratios M > 1.225 between the impurity mass and the mass of a fermion and consider arbitrarily large box sizes while keeping the Fermi energy fixed. Our main result shows that the ground state energy in the limit of weak coupling is given by the polaron energy. The polaron energy is an energy estimate based on trial states up to first order in particle-hole expansion, which was proposed by Chevy in the physics literature. For the pro…

The Polaron at Strong Coupling

We review old and new results on the Fröhlich polaron model. The discussion includes the validity of the (classical) Pekar approximation in the strong coupling limit, quantum corrections to this limit, as well as the divergence of the effective polaron mass.

Renewal approach for the energy-momentum relation of the Fröhlich polaron

We study the qualitative behaviour of the energy-momentum relation of the Fröhlich polaron at fixed coupling strength. Among other properties, we show that it is non-decreasing and that the correction to the quasi-particle energy is negative. We give a proof that the effective mass lies in $(1, \infty)$ that does not need the validity of a central limit theorem for the path measure.

强耦合下极化子有效质量的Landau-Pekar公式的证明

Proof of the Landau-Pekar Formula for the effective Mass of the Polaron at strong coupling

该研究针对强耦合区Fröhlich极化子，证明了有效质量的渐近严格下界，结合已有的上界结果，证实了1948年提出的Landau-Pekar公式的有效性，解决了Spohn于1987年提出的相关猜想。

移动费米极化子的质量间隙泛函行列式方法

Mass-gap functional determinant approach for mobile Fermi polarons

该研究将泛函行列式方法（FDA）扩展到有限质量移动杂质情形，利用质量间隙模型实现移动杂质多体谱与拉姆齐动力学的精确计算，为移动杂质量子动力学提供了高效框架。

Feynman极化子路径积分处理中的最佳二次近似

On the Best Quadratic Approximation in Feynman's Path Integral Treatment of the Polaron

对Adamowski { \it et al.}和Saitoh的数值研究了广泛的耦合常数。用一种有效的方法迭代求解非线性变分方程，得到极化子的基态能量和有效质量。为了检验数值结果的高精度，我们采用了维里定理和大小耦合的展开式。仅观察到比费曼（非最优）结果小的改进。对于一个运动的极化子，它示出，最一般的二次审判行动可能包含各向异性条款，然而，不导致改善的基态能量和有效质量。

二维费米极化子的稳定性

Stability of the two-dimensional Fermi polaron

考虑了由N个费米子组成的理想气体与杂质粒子在二维空间相互作用的系统。杂质和费米子之间的相互作用是用两体点相互作用来表示的，其强度由两体结合能决定，结合能是模型的一个自由参数。如果杂质的质量比费米子的质量大1.225倍，则表明能量在费米子的数量N下均匀地有界。这一结果改善了以前的，N-依赖的下限，它补充了最近的，类似的约束费米极化子在三维空间。

极化子能量 - 动量关系的下界

Lower bound on the energy-momentum relation of the polaron

针对一类极化子型模型，通过真空重叠和总动量为零哈密顿量的谱隙建立能量 - 动量关系下界，证明重标平均平方位移收敛到有效质量倒数，推导大总动量时无基态的概率准则。

Polaron models with regular interactions at strong coupling

We study a class of polaron-type Hamiltonians with sufficiently regular form factor in the interaction term. We investigate the strong-coupling limit of the model, and prove suitable bounds on the ground state energy as a function of the total momentum of the system. These bounds agree with the semiclassical approximation to leading order. The latter corresponds here to the situation when the particle undergoes harmonic motion in a potential well whose frequency is determined by the corresponding Pekar functional. We show that for all such models the effective mass diverges in the strong coupl…

费米气体中重杂质的质量隙描述

Mass-gap description of heavy impurities in Fermi gases

本文通过算符重排引入“质量隙”概念，统一描述费米极化子与安德森正交灾难，揭示隙内态在极化子-分子转变中的关键作用，并推导准粒子权重的幂律标度。