Duality for open fermion systems: energy-dependent weak coupling and quantum master equations

Open fermion systems with energy-independent bilinear coupling to a fermionic environment have been shown to obey a general duality relation [Phys. Rev. B 93, 81411 (2016)] which allows for a drastic simplification of time-evolution calculations. In the weak-coupling limit, such a system can be associated with a unique dual physical system in which all energies are inverted, in particular the internal interaction. This paper generalizes this fermionic duality in two ways: we allow for weak coupling with arbitrary energy dependence and describe both occupations and coherences coupled by a quantum master equation for the density operator. We also show that whenever generalized detailed balance holds (Kolmogorov criterion), the stationary probabilities for the dual system can be expressed explicitly in terms of the stationary recurrence times of the original system, even at large bias. We illustrate the generalized duality by a detailed analysis of the rate equation for a quantum dot with strong onsite Coulomb repulsion, going beyond the commonly assumed wideband limit. We present predictions for (i) the decay rates for transient charge and heat currents after a gate-voltage quench and (ii) the thermoelectric linear response coefficients in the stationary limit. We show that even for pronouncedly energy-dependent coupling, all nontrivial parameter dependence in these problems is entirely captured by just two well-understood stationary variables, the average charge of the system and of the dual system. Remarkably, it is the latter that often dictates the most striking features of the measurable quantities (e.g., positions of resonances), underscoring the importance of the dual system for understanding the actual one.Comment: 25 pages + 2 pages appendix + 2 pages references, 7 figures. To be submitted to Phys. Rev.

Absence of supercurrent sign reversal in a topological junction with a quantum dot

Experimental techniques to verify Majoranas are of current interest. A prominent test is the effect of Majoranas on the Josephson current between two wires linked via a normal junction. Here, we study the case of a quantum dot connecting the two superconductors and the sign of the supercurrent in the trivial and topological regimes under grand-canonical equilibrium conditions, explicitly allowing for parity changes due to, e.g., quasi-particle poisoning. We find that the well-known supercurrent reversal for odd occupancy of the quantum dot (pi-junction) in the trivial case does not occur in the presence of Majoranas in the wires. However, we also find this to be a mere consequence of Majoranas being zero energy states. Therefore, the lack of supercurrent sign reversal can also be caused by trivial bound states, and is thus not a discriminating signature of Majoranas.Comment: 6 pages + 1 page appendix + 2 pages bibilography, 4 figure

Fermion-parity duality and energy relaxation in interacting open systems

We study the transient heat current out of a confined electron system into a weakly coupled electrode in response to a voltage switch. We show that the decay of the Coulomb interaction energy for this repulsive system exhibits signatures of electron-electron attraction, and is governed by an interaction-independent rate. This can only be understood from a general duality that relates the non-unitary evolution of a quantum system to that of a dual model with inverted energies. Deriving from the fermion-parity superselection postulate, this duality applies to a large class of open systems.Comment: 5 pages + 19 pages of Supplementary Materia

Neuroproteomics as a promising tool in Parkinson's disease research

Despite the vast number of studies on Parkinson's disease (PD), its effective diagnosis and treatment remains unsatisfactory. Hence, the relentless search for an optimal cure continues. The emergence of neuroproteomics, with its sophisticated techniques and non-biased ability to quantify proteins, provides a methodology with which to study the changes in neurons that are associated with neurodegeneration. Neuroproteomics is an emerging tool to establish disease-associated protein profiles, while also generating a greater understanding as to how these proteins interact and undergo post-translational modifications. Furthermore, due to the advances made in bioinformatics, insight is created concerning their functional characteristics. In this review, we first summarize the most prominent proteomics techniques and then discuss the major advances in the fast-growing field of neuroproteomics in PD. Ultimately, it is hoped that the application of this technology will lead towards a presymptomatic diagnosis of PD, and the identification of risk factors and new therapeutic targets at which pharmacological intervention can be aimed