采用自适应储器模式窗口的含受控全态误差的长时费米子量子输运
Long-time fermionic quantum transport with controlled full-state error using an adaptive reservoir-mode window
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中文总结 AI 辅助
该研究提出磁带记录仪粗粒化方法，通过自适应储器模式窗口控制全态误差，实现了相互作用费米子输运中全器件-储器态的长时模拟，经多类基准测试验证有效。
中文摘要 AI 辅助
耦合到费米子储器的相互作用纳米结构的实时模拟，往往需要不断增加环境自由度以保留长时关联。我们引入了磁带记录仪粗粒化方法，该方法将每个非相互作用引线重新组织为入射模式、活动模式和出射模式。器件随活动模式传播，而出射模式则被随机采样并在其剩余积分耦合降至规定阈值以下时移除。对于每个出射模式截断，我们推导了精确和截断的全器件-储器态在任意规定有限区间内的非微扰保真度上界，该上界取决于模式的剩余耦合权重和有限区间响应因子。数值计算表明，在固定相对阈值下，活动模式数量随时间趋于饱和，而当阈值降低时，活动模式数量呈对数增长。我们在零温度和最大偏压下的两位置量子点接触上对该方法进行了基准测试：对于洛伦兹型储器，其动力学与收敛的HEOM计算结果一致，稳态电流与Landauer–Büttiker结果一致；对于具有代数衰减关联的平带储器，其在有限尺寸重现前与直接薛定谔演化结果一致，且能重现Landauer–Büttiker稳态电流，而有限指数HEOM分解则未收敛；对于相互作用接触，该方法能产生库仑阻塞峰分裂；在非相互作用驱动极限下，其与精确的Floquet格林函数计算结果一致，且能重现周期驱动下的相干电流抑制，该抑制在有限库仑排斥下仍存在。这些基准测试共同表明，磁带记录仪粗粒化方法可实现相互作用费米子输运中全器件-储器态的实用长时模拟。
英文摘要
Real-time simulations of interacting nanostructures coupled to fermionic reservoirs can require a growing number of environmental degrees of freedom to retain long-lived correlations. We introduce tape-recorder coarse graining, which reorganizes each noninteracting lead into incoming, active, and outgoing modes. The device is propagated with the active modes, while outgoing modes are stochastically sampled and removed once their remaining integrated coupling falls below a prescribed threshold. For each outgoing-mode truncation, we derive a nonperturbative upper bound on the infidelity between the exact and truncated full device-reservoir states over any prescribed finite interval. The bound depends on the mode's remaining coupling weight and finite-interval response factors. Numerically, the active-mode count saturates in time at fixed relative threshold and grows logarithmically as the threshold is reduced. We benchmark the method on a two-site quantum point contact at zero temperature and maximal bias. For Lorentzian reservoirs, the dynamics agrees with converged HEOM calculations and the steady-state current with the Landauer-Büttiker result. For flat-band reservoirs with algebraically decaying correlations, it agrees with direct Schrödinger evolution before finite-size recurrences and reproduces the Landauer-Büttiker stationary current, while finite exponential HEOM decompositions remain unconverged. For interacting contacts, the method yields Coulomb-blockade peak splitting. In the noninteracting driven limit, it agrees with an exact Floquet Green-function calculation and reproduces coherent current suppression under periodic driving, which persists at finite Coulomb repulsion. Together, these benchmarks show that tape-recorder coarse graining enables practical long-time simulations of the full device-reservoir state in interacting fermionic transport.
