Nonequilibrium Energy Transport in Nanostructures
Theoretical Condensed Matter Physics
Final Report Abstract
Before we formally extended QUAPI to treat the dynamics of quantum systems subject to various non-commuting noise sources, we studied the influence of a single noise source treated within a system-bath approach when a second noise source, i.e. a dephasing noise, is treated phenomenologically. The phenomenological dephasing is described by a dephasing rate resulting in a Liouvillian dynamics for the statistical operator of the system dynamics. This effective system is then treated within a system-bath approach to deal with the first noise source. For this situation, we develop a path integral approach, which allows to treat the systemenvironment coupling numerically exact, and additionally we extend standard perturbative approaches. We observe strong deviations between the numerical exact and the perturbative results even for weak system-bath coupling. This shows that standard perturbative approaches fail for additional, even weak, system-bath couplings if the system dynamics is already dissipative. In charge and also flux qubits pure dephasing noise is notoriously difficult to characterize and, thus, typically treated phenomenologically whereas the other noise sources are most often perturbatively treated. We should point out that typically the first noise source is treated perturbatively resulting in weak coupling rate expressions and only then the phenomenological rate is added to the dynamic equations. Our perturbative approach goes beyond this approximation by extending the system by including the dephasing before perturbatively treating the first noise source. Nevertheless our result shows that both approaches fail when the phenomenological dissipative behaviour is sizeable (which is typically the case in qubit systems and photosynthetic energy transfer systems). In this work we extend the quasi-adiabatic path integral approach to treat multiple noncommuting environmental noise sources. We determine the time discrete influence functional and by modify the propagation scheme accordingly. We then test the extended quasi-adiabatic path integral approach by determining the time evolution of a quantum two-level system coupled to two independent bath via non-commuting operators. In detail, we focus on a case with one bath inducing relaxation and a second independent dephasing noise source. We show that convergent results can be obtained and agreement with analytical weak coupling results is achieved in the respective limits. In this work we focussed on achieving active control of energy currents through a quantum system subject to various reservoirs. For this, we propose a rocking ratchet design where a single periodic harmonic force creates transport through a symmetric quantum two-state system if it is influenced symmetrically by thermal fluctuations. We show that the necessary broken symmetry can dynamically be achieved by a thermal environment from a single bath which couples to the energy difference between the two states and the dipolar coupling between them. The quantum two-state system is driven by the harmonic periodic drive through its avoided crossing. The according driven dissipative quantum dynamics results on average in a finite population difference between both states. This, then, causes directed transport. Importantly, two non-commuting uncorrelated baths creating the necessary fluctuations in the energy difference and the dipolar coupling can not achieve this. Thus, the current is a measure of correlations among fluctuations.
Publications
- Environmental rocking ratchet: Environmental rectification by a harmonically driven avoided crossing. Phys. Rev. E 96, 042134 (2017)
P. Nalbach, N. Klinkenberg, T. Palm and N. Müller
(See online at https://doi.org/10.1103/PhysRevE.96.042134) - Nonperturbative environmental influence on dephasing. Phys. Rev. A 96, 032105 (2017)
T. Palm and P. Nalbach
(See online at https://doi.org/10.1103/PhysRevA.96.032105) - Quasi-adiabatic path integral approach for quantum systems under the influence of multiple non-commuting fluctuations. J. Chem. Phys. 149, 214103 (2018)
T. Palm and P. Nalbach
(See online at https://doi.org/10.1063/1.5051652)
