物理学报2026，Vol.75Issue(11)：68-81,14.DOI:10.7498/aps.75.20260182
一维吸引相互作用单自旋翻转费米气体的淬火动力学及量子颤振性质
Quench dynamics and quantum flutter properties of one-dimensional attractive single-spin flipped Fermi gases
摘要
Abstract
The nonequilibrium dynamics of impurities in quantum many-body systems constitute a frontier topic in ultracold-atom physics and are key to uncovering the microscopic mechanisms of polaron physics and collective excitation behavior.Compared with the extensively studied repulsively interacting systems,the dynamical behavior under attractive interactions remains insufficiently explored in a systematic manner,owing to the complex coupling mechanisms among bound states,gas states,and irregular states.We take the ground state of a one-dimensional ideal Fermi gas as the initial state,and add a spin-down impurity particle carrying momentum.The impurity has an attractive interaction with the spin-up fermions.We study the time-evolution behavior of the two-body correlation functions between particles of different spins and the impurity momentum.First,based on the exact solution from the Bethe ansatz(BA),starting from the eigenstate wave functions,we analytically simplify the overlap integrals,the matrix elements of the one-body correlation function of spin-up particles,and the matrix elements of the two-body correlation functions between particles of different spins into finite-sum expressions of simple functions,thereby enabling efficient computations of the occupation probabilities of a large number of eigenstates and the long-time evolution of the correlation functions.Second,in the weakly attractive regime:when the total momentum is less than or equal to the Fermi momentum,the dynamics exhibits features of bound states.The two-body correlation function between particles of different spins shows a stable correlation peak and an outward-propagating correlation hole,and its evolution period agrees with the period corresponding to the energy difference between the two bound states with the highest occupation probabilities.Conversely,when the total momentum is greater than the Fermi momentum,due to the superposition of bound states,gas states,and irregular states,the system exhibits complex oscillatory behavior,alternating between bound-state-like and gas-state-like features.In the strongly attractive regime,regardless of the initial momentum,the system exhibits bound-state-dominated features locally,characterized by a localized correlation peak and Friedel-like oscillations induced by scattering interference.Finally,we rigorously characterize the phenomenon of quantum flutter,namely the periodic oscillation of the impurity momentum,and find that the quantum-flutter period is strictly determined by the chemical potential of the spin-down impurity particle μ↓c,namely τ=2π/|μ↓c|.We obtain consistent results for the chemical potential of the spin-down particle via four approaches:For zero total momentum,it can be obtained by deriving the critical magnetic field and the critical chemical potential at the quantum phase-transition point from the thermodynamic BA equations,and it can also be derived from the discrete BA equations via the energy required to inject a single spin-down particle into the ground state of the ideal Fermi gas;when the total momentum equals the Fermi momentum,the energy difference between the gas-state magnon and the bound-state exciton equals this chemical potential;when the total momentum is greater than the Fermi momentum,by using the relation between the single-particle excitation energy and the dressed energy,we can derive that the energy difference between the bound-state exciton states and the gas-state magnon states,which have relatively high occupation probabilities and form pairwise correspondences,equals this chemical potential.This work investigates the evolution laws of quench dynamics and quantum flutter in systems with attractive interactions,which helps deepen the understanding of nonequilibrium-state properties in quantum many-body physics and provides theoretical support for related ultracold-atom experiments on impurity dynamics.关键词
一维费米气体/关联函数/淬火动力学/量子颤振Key words
one-dimensional Fermi gas/correlation function/quench dynamics/quantum flutter引用本文复制引用
尹相国,赵书龙..一维吸引相互作用单自旋翻转费米气体的淬火动力学及量子颤振性质[J].物理学报,2026,75(11):68-81,14.基金项目
国家自然科学基金(批准号:12461160324)和山西省基础研究计划(批准号:202103021224033)资助的课题. Project supported by the National Natural Science Foundation of China(Grant No.12461160324)and the Research Foundation for Basic Research of Shanxi Province,China(Grant No.202103021224033). （批准号:12461160324）
