实轴最小二乘浴离散化用于量子点约瑟夫森结中的实时输运
Real-axis least-squares bath discretization for real-time transport in quantum-dot Josephson junctions
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中文总结 AI 辅助
本研究提出实轴最小二乘浴离散化方法，用于量子点约瑟夫森结的实时输运模拟，在保持物理精度的同时大幅降低计算成本，并揭示了寿命与展宽参数的关系。
中文摘要 AI 辅助
高效实时方法对于解析驱动超导纳米结构中的瞬态相干性和非线性输运至关重要。此类模拟仍具挑战性，因为BCS连续谱的有限表示会产生递归，而用于抑制递归的阻尼会模糊能隙边缘结构并人为缩短相干寿命；能隙边缘奇点的有限展宽正则化同样施加了寿命分辨率的底线。在此，我们将驱动 Liouville--von Neumann 方法扩展到超导库——一个具有 Bogoliubov--de Gennes 引线的非相互作用量子点——构建一个显式哈密顿框架，该框架容纳一系列浴离散化（均匀和高斯基线以及新的实轴最小二乘方案，其模式能量、谱权重和模式分辨阻尼在能隙感知约束下联合优化）——使展宽成为独立校准的数值参数，其主导长期效应沿联合（$\gamma\to0$, $N_b\to\infty$）细化路径可控外推，同时与高分辨率DLvN参考相比将计算成本降低一个数量级以上。压缩浴重现了已建立的电流-相位关系、多次安德烈夫反射结构、准粒子俘获振荡以及整数和分数夏皮罗锁定；寿命分析得出无参数的首阶关系 $\kappa\simeq w_{\mathrm{bath}}\gamma_{\mathrm{eff}}$，并解析了低于先前有限展宽计算分辨率尺度的阻尼诱导衰减率。作为显式哈密顿库表示，该框架自然推广到多端正常-超导几何结构，并为相互作用杂质求解器提供了一条途径，而有限能隙强驱动锁定幅度标志着其当前的定量边界。
英文摘要
Efficient real-time methods are essential for resolving transient coherence and nonlinear transport in driven superconducting nanostructures. Such simulations remain challenging because finite representations of the BCS continuum generate recurrences, while the damping used to suppress them smears gap-edge structure and artificially shortens coherent lifetimes; finite-broadening regularization of the gap-edge singularity likewise imposes a lifetime-resolution floor. Here we extend the driven Liouville--von Neumann approach to superconducting reservoirs---a noninteracting quantum dot with Bogoliubov--de Gennes leads---building an explicit-Hamiltonian framework that hosts a family of bath discretizations (uniform and Gaussian baselines and a new real-axis least-squares recipe, with mode energies, spectral weights, and mode-resolved dampings optimized jointly under gap-aware constraints)---making the broadening an independently calibrated numerical parameter whose leading long-time effect extrapolates controllably along the joint ($γ\to0$, $N_b\to\infty$) refinement path while cutting computational cost by over an order of magnitude versus the high-resolution DLvN reference. The compressed baths recover established current-phase relations, multiple-Andreev-reflection structure, quasiparticle-trapping oscillations, and integer and fractional Shapiro locking; the lifetime analysis yields the parameter-free leading-order relation $κ\simeq w_{\mathrm{bath}}γ_{\mathrm{eff}}$ and resolves damping-induced decay rates below the resolution scale of a previous finite-broadening calculation. As an explicit Hamiltonian reservoir representation, the framework generalizes naturally to multiterminal normal--superconducting geometries and offers a route toward interacting impurity solvers, while finite-gap strong-drive locking amplitudes mark its present quantitative boundary.
发表机构
- Shanghai Jiaotong University（上海交通大学）
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