局域增益费米子晶格中全计数统计的量子动力学
Quantum Dynamics of Full Counting Statistics in Fermionic Lattices with Localized Gain
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中文总结 AI 辅助
本文研究一维无相互作用费米子晶格在局域增益下的全计数统计动力学，通过GKSL方程和Schwinger-Keldysh路径积分推导出累积量生成函数，证明所有累积量随时间线性增长，并建立通用理论框架。
中文摘要 AI 辅助
我们研究了在一维无相互作用晶格中，总费米子数增长的全计数统计（FCS）的动力学，该晶格在一端受到局域粒子增益（源）的作用。该设置的动力学由Gorini--Kossakowski--Sudarshan--Lindblad（GKSL）量子主方程建模。我们将涉及在每个格点计数粒子数的计数问题，转化为仅涉及局域注入点的问题。我们在GKSL框架内采用Schwinger-Keldysh路径积分形式，推导出任意时刻累积量生成函数的解析表达式，并在长时间极限下获得了Levitov-Lesovik型公式，该公式此前是针对稳态边界驱动设置推导的。对于具有短程或长程跳跃、支持单粒子离域本征态的清洁晶格，我们证明在渐近区域所有累积量随时间线性增长。我们的解析结果与直接数值模拟高度吻合。这些发现为表征具有局域粒子注入的驱动开放费米子系统中的FCS和量子涨落建立了一个通用框架。
英文摘要
We investigate the dynamics of full counting statistics (FCS) of the growth of the total number of fermions in a one-dimensional non-interacting lattice subjected to a localized particle gain (source) at one edge. The dynamics of the setup is modeled by the Gorini--Kossakowski--Sudarshan--Lindblad (GKSL) quantum master equation. We recast the counting problem that involves counting particle number at every lattice site to a problem where only the local injected site is involved. We employ the Schwinger-Keldysh path integral formalism within the GKSL framework and derive an analytical expression for the cumulant generating function at arbitrary times and obtain a Levitov-Lesovik type formula in the long-time limit, earlier derived for boundary driven setups in the steady-state. For clean lattices with either short- or long-range hopping, supporting single-particle delocalized eigenstates, we show that all cumulants grow linearly with time in the asymptotic regime. Our analytical results are in excellent agreement with direct numerical simulations. These findings establish a general framework for characterizing FCS and quantum fluctuations in driven open fermionic systems with localized particle injection.
发表机构
- Indian Institute of Science Education and Research Pune（印度科学教育研究所浦那分校）
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research（塔塔基础研究院国际理论科学中心）
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