arXiv subjects

Duc Viet Hoang

Publications and source records attributed to Duc Viet Hoang.

3 recordsLinked to original sources

arXiv2025

Derivation of the time-dependent Hartree equations for strongly interacting dense fermionic systems

The time-dependent Hartree and Hartree-Fock equations provide effective mean-field descriptions for the dynamics of large fermionic systems and play a fundamental role in many areas of physics. In this work, we rigorously derive the time-dependent Hartree equations as the large-$N$ limit of the microscopic Schrödinger dynamics of $N$ fermions confined to a volume of order one and interacting via strong pair potentials. A central step in our analysis is the implementation of time-dependent gauge transformations, which eliminate the dominant contribution from the interaction potential in both the Schrödinger and Hartree evolutions.

math-ph↗

arXiv2025

Effective Polaron Dynamics of an Impurity Particle Interacting with a Fermi Gas

We study the quantum dynamics of a homogeneous ideal Fermi gas coupled to an impurity particle on a three-dimensional box with periodic boundary condition. For large Fermi momentum $k_\text{F}$, we prove that the effective dynamics is generated by a Fröhlich-type polaron Hamiltonian, which linearly couples the impurity particle to an almost-bosonic excitation field. Moreover, we prove that the effective dynamics can be approximated by an explicit coupled coherent state. Our method is applicable to a range of interaction couplings, in particular including interaction couplings of order 1 and time scales of the order $k_\text{F}^{-1}$.

math-ph↗

arXiv2019

A soft-photon theorem for the Maxwell-Lorentz system

For the coupled system of classical Maxwell-Lorentz equations we show that the quantities \begin{equation*} \mathfrak{F}(\hat x, t)=\lim_{|x|\to \infty} |x|^2 F(x,t), \quad \mathcal{F}(\hat k, t)=\lim_{|k|\to 0} |k| \widehat{F}(k,t), \end{equation*} where $F$ is the Faraday tensor, $\hat{F}$ its Fourier transform in space and $\hat{x}:=\frac{x}{|x|}$, are independent of $t$. We combine this observation with the scattering theory for the Maxwell-Lorentz system due to Komech and Spohn, which gives the asymptotic decoupling of $F$ into the scattered radiation $F_{\mathrm{sc},\pm}$ and the soliton field $F_{v_{\pm\infty}}$ depending on the asymptotic velocity $v_{\pm\infty}$ of the electron at large positive (+), resp. negative (-) times. This gives a soft-photon theorem of the form \begin{equation*} \mathcal{F}_{\text{sc},+}(\hat{k}) - \mathcal{F}_{\text{sc},-}(\hat{k})= -( \mathcal{F}_{v_{+\infty}}(\hat{k})-\mathcal{F}_{v_{-\infty}}(\hat{k})), \end{equation*} and analogously for $\mathfrak{F}$, which links the low-frequency part of the scattered radiation to the change of the electron's velocity. Implications for the infrared problem in QED are discussed in the Conclusions.

math-ph↗