Numerical Algorithms for Time-Resolved Quantum Transport

Guillermo Albareda, Damiano Marian, A. Benali +3 more

Tsuneya Ando, 安藤 恒也

Yinyin Qian, Ming Gong, Chuanwei Zhang

We numerically investigate, using the time evolving block decimation algorithm, the quantum transport of ultracold bosonic atoms in a double-well optical lattice through slow and periodic modulation of the lattice parameters (intra- and inter-well tunneling, chemical potential, etc.). The transport of atoms does not depend on the rate of change of the parameters (as along as the change is slow) and can distribute atoms in optical lattices at the quantized level without involving external forces. The transport of atoms depends on the atom filling in each double well and the interaction between atoms. In the strongly interacting region, the bosonic atoms share the same transport properties as noninteracting fermions with quantized transport at the half filling and no atom transport at the integer filling. In the weakly interacting region, the number of the transported atoms is proportional to the atom filling. We show the signature of the quantum transport from the momentum distribution of atoms that can be measured in the time-of-flight image. A semiclassical transport model is developed to explain the numerically observed transport of bosonic atoms in the noninteracting and strongly interacting limits. The scheme may serve as an quantized battery for atomtronics applications.

Michael Hartung

We numerically study time-dependent quantum transport of an interacting Bose-Einstein condensate based on the Gross-Pitaevskii equation in a two-dimensional correlated disorder potential. The scattering- and transport mean-free-path is numerically calculated and compared with a diagrammatic approach. Furthermore we introduce the phenomenon of coherent backscattering in the context of Bose-Einstein condensates. In the limit of a vanishing atom-atom interaction, a sharp cone in the angle-resolved density of the scattered matter wave is observed, arising from constructive interference between amplitudes propagating along reversed scattering paths. Weak interaction transforms this coherent backscattering peak into a pronounced dip, indicating destructive instead of constructive interference. This agrees with results obtained from a diagrammatic theory of weak localization in the presence of nonlinearity. For intermediate interaction strength we observe intrinsic time-dependent dynamic, which leads to a suppression of coherent backscattering.

Wolfgang Schweizer

Zheng Xiao, Rui‐Xue Xu, Jian Xu +3 more

In this review we give a comprehensive account of a hierarchical equations of motion (HEOM) approach to the characterization of stationary and dynamic properties of open quantum systems. This approach is rooted at the Feynman-Vernon influence functional path integral formalism, but much more implementable numerically and operationally for the study of various complex molecular dynamics and quantum transport in strongly correlated electronic systems. By construction, HEOM resolves nonperturbatively the combined effects of many-particle interaction, system-bath coupling,and non-Markovian memory. Finally the practicality of HEOM to address physical and chemical problems is exemplified with a model simulation of coherent two-dimensional spectroscopy signals of a biological light-harvesting system and a time-dependent quantum transport system involving dynamic Kondo transition.級聯方程已成為研究量子開放系統的穩態性質和動力學過程的重要方法。本文旨在系統綜述量子耗散和量子輸運的級聯方程組方法的建立、發展以及在理論、算法和應用方面的一些最新進展。級聯方程形式理論的建立以影響泛函路徑積分為基礎,并具有數值上的高效性和應用上的靈活性,可用于研究分子體系的復雜動力學過程以及強關聯電子體系中的量子輸運。其級聯耦合結構以非微擾的方式揭示了多體相互作用、體系-環境耦合、非馬爾可夫記憶等的綜合效應。作為應用示例,我們采用級聯方程模擬了生物光富集體系的二維相干動力學光譜以及含時電子輸運過程中的動態近藤效應。