M. R. Wegewijs's research while affiliated with Bavarian Research Alliance and other places

The description of quantum transport in the strong system-reservoir coupling regime poses a significant theoretical and computational challenge that demands specialized tools for accurate analysis. RealTimeTransport is a new open-source C++ library that enables the computation of both stationary and transient transport observables for generic quantum systems connected to metallic reservoirs. It computes the Nakajima-Zwanzig memory kernels for both dynamics and transport in real-time going beyond traditional expansions in the bare system-reservoir couplings. Currently, several methods are available: (i) A renormalized perturbation theory in leading and next-to-leading order which avoids the low-temperature breakdown that limits the traditional theory. (ii) Starting from this well-behaved reference solution a 2- and 3-loop self-consistent renormalization-group transformation of the memory kernels is implemented. This allows refined quantitative predictions even in the presence of many body resonances, such as the Kondo enhancement of cotunneling. This paper provides an overview of the theory, the architecture of RealTimeTransport and practical demonstrations of the currently implemented methods. In particular, we analyze the stationary transport through a serial double quantum dot and showcase for the $T=0$ interacting Anderson model the complete time-development of single-electron tunneling (SET), cotunneling-assisted SET (CO-SET) and inelastic cotunneling resonances throughout the entire gate-bias stability diagram. We discuss the range of applicability of the implemented methods and benchmark them against other advanced approaches.

We analyze the time evolution of a quantum dot which is proximized by a large-gap superconductor and weakly probed using the charge and heat currents into a wide-band metal electrode. We map out the full time dependence of these currents after initializing the system by a switch. We find that due to the proximity effect there are two simple yet distinct switching procedures which initialize a nonstationary mixture of the gate-voltage-dependent eigenstates of the proximized quantum dot. We find in particular that the ensuing time-dependent heat current is a sensitive two-particle probe of the interplay of strong Coulomb interaction and induced superconducting pairing. The pairing can lead to a suppression of charge and heat current decay which we analyze in detail. The analysis of the results makes crucial use of analytic formulas obtained using fermionic duality, a “dissipative symmetry” of master equations describing this class of open systems.

We analyze the time-dependent solution of master equations by exploiting fermionic duality, a dissipative symmetry applicable to a large class of open systems describing quantum transport. Whereas previous studies mostly exploited duality relations after partially solving the evolution equations, we here systematically exploit the invariance under the fermionic duality mapping from the very beginning when setting up these equations. Moreover, we extend the resulting simplifications -so far applied to the local state evolution- to non-local observables such as transport currents. We showcase the exploitation of fermionic duality for a quantum dot with strong interaction -covering both the repulsive and attractive case- proximized by contact with a large-gap superconductor which is weakly probed by charge and heat currents into a wide-band normal-metal electrode. We derive the complete time-dependent analytical solution of this problem involving non-equilibrium Cooper pair transport, Andreev bound states and strong interaction. Additionally exploiting detailed balance we show that even for this relatively complex problem the evolution towards the stationary state can be understood analytically in terms of the stationary state of the system itself via its relation to the stationary state of a dual system with inverted Coulomb interaction, superconducting pairing and applied voltages.

We analyze the time-evolution of a quantum dot which is proximized by a large-gap superconductor and weakly probed using the charge and heat currents into a wide-band metal electrode. We map out the full time dependence of these currents after initializing the system by a switch. We find that due to the proximity effect there are two simple yet distinct switching procedures which initialize a non-stationary mixture of the gate-voltage dependent eigenstates of the proximized quantum dot. We find in particular that the ensuing time-dependent heat current is a sensitive two-particle probe of the interplay of strong Coulomb interaction and induced superconducting pairing. The pairing can lead to a suppression of charge and heat current decay which we analyze in detail. The analysis of the results makes crucial use of analytic formulas obtained using fermionic duality, a ``dissipative symmetry'' of the master equation describing this class of open systems.

We analyze the time-dependent solution of master equations by exploiting fermionic duality, a dissipative symmetry applicable to a large class of open systems describing quantum transport. Whereas previous studies mostly exploited duality relations after partially solving the evolution equations, we here systematically exploit the invariance under the fermionic duality mapping from the very beginning when setting up these equations. Moreover, we extend the resulting simplifications -- so far applied to the local state evolution- to non-local observables such as transport currents. We showcase the exploitation of fermionic duality for a quantum dot with strong interaction -- covering both the repulsive and attractive case -- proximized by contact with a large-gap superconductor which is weakly probed by charge and heat currents into a wide-band normal-metal electrode. We derive the complete time-dependent analytical solution of this problem involving non-equilibrium Cooper pair transport, Andreev bound states and strong interaction. Additionally exploiting detailed balance we show that even for this relatively complex problem the evolution towards the stationary state can be understood analytically in terms of the stationary state of the system itself via its relation to the stationary state of a dual system with inverted Coulomb interaction, superconducting pairing and applied voltages.

We present the T-flow renormalization group method, which computes the memory kernel for the density-operator evolution of an open quantum system by lowering the physical temperature T of its environment. This has the key advantage that it can be formulated directly in real time, making it particularly suitable for transient dynamics, while automatically accumulating the full temperature dependence of transport quantities. We solve the T-flow equations numerically for the example of the single impurity Anderson model. We benchmark in the stationary limit, readily accessible in real-time for voltages on the order of the coupling or larger using results obtained by the functional renormalization group, density-matrix renormalization group and the quantum Monte Carlo method. Here we find quantitative agreement even in the worst case of strong interactions and low temperatures, indicating the reliability of the method. For transient charge currents we find good agreement with results obtained by the 2PI Green's function approach. Furthermore, we analytically show that the short-time dynamics of both local and non-local observables follow a "universal" temperature-independent behaviour when the metallic reservoirs have a flat wide band.

We present the $T$-flow renormalization group method, which computes the memory kernel for the density-operator evolution of an open quantum system by lowering the physical temperature $T$ of its environment. This has the key advantage that it can be formulated directly in real time, making it particularly suitable for transient dynamics, while automatically accumulating the full temperature dependence of transport quantities. We solve the $T$-flow equations numerically for the example of the single impurity Anderson model. In the stationary limit, readily accessible in real-time for voltages on the order of the coupling or larger, we benchmark using results obtained by the functional renormalization group, density-matrix renormalization group and the quantum Monte Carlo method. Here we find quantitative agreement even in the worst case of strong interactions and low temperatures, indicating the reliability of the method. For transient charge currents we find good agreement with results obtained by the 2PI Green's function approach. Furthermore, we analytically show that the short-time dynamics of both local and non-local observables follow a "universal" temperature-independent behavior when the metallic reservoirs have a flat wide band.

There exist two canonical approaches to describe open quantum systems by a time-evolution equation: the Nakajima-Zwanzig quantum master equation, featuring a time-nonlocal memory kernel K, and the time-convolutionless equation with a time-local generator G. These key quantities have recently been shown to be connected by an exact fixed-point relation [Phys. Rev. X 11, 021041 (2021)]. Here we show that this implies a recursive relation between their perturbative expansions, allowing a series for the kernel K to be translated directly into a corresponding series for the more complicated generator G. This leads to an elegant way of computing the generator using well-developed, standard memory-kernel techniques for strongly interacting open systems. Moreover, it allows for an unbiased comparison of time-local and time-nonlocal approaches independent of the particular technique chosen to calculate expansions of K and G (Nakajima-Zwanzig projections, real-time diagrams, etc.). We illustrate this for leading and next-to-leading-order calculations of K and G for the single impurity Anderson model using both the bare expansion in the system-environment coupling and a more advanced renormalized series. We compare the different expansions obtained, quantify the legitimacy of the generated dynamics (complete positivity) and benchmark with the exact result in the noninteracting limit.

We consider the exact time-evolution of a broad class of fermionic open quantum systems with both strong interactions and strong coupling to wide-band reservoirs. We present a nontrivial fermionic duality relation between the evolution of states (Schrödinger) and of observables (Heisenberg). We show how this highly nonintuitive relation can be understood and exploited in analytical calculations within all canonical approaches to quantum dynamics, covering Kraus measurement operators, the Choi-Jamiołkowski state, time-convolution and convolutionless quantum master equations and generalized Lindblad jump operators. We discuss the insights this offers into the divisibility and causal structure of the dynamics and the application to nonperturbative Markov approximations and their initial-slip corrections. Our results underscore that predictions for fermionic models are already fixed by fundamental principles to a much greater extent than previously thought.

There exist two canonical approaches to describe open quantum systems by a time-evolution equation: the Nakajima-Zwanzig quantum master equation, featuring a time-nonlocal memory kernel $\mathcal{K}$, and the time-convolutionless equation with a time-local generator $\mathcal{G}$. These key quantities have recently been shown to be connected by an exact fixed-point relation [Phys. Rev. X 11, 021041 (2021)]. Here we show that this implies a recursive relation between their perturbative expansions, allowing a series for the kernel $\mathcal{K}$ to be translated directly into a corresponding series for the more complicated generator $\mathcal{G}$. This leads to an elegant way of computing the generator using well-developed, standard memory-kernel techniques for strongly interacting open systems. Moreover, it allows for an unbiased comparison of time-local and time-nonlocal approaches independent of the particular technique chosen to calculate expansions of $\mathcal{K}$ and $\mathcal{G}$ (Nakajima-Zwanzig projections, real-time diagrams, etc.). We illustrate this for leading and next-to-leading order calculations of $\mathcal{K}$ and $\mathcal{G}$ for the single impurity Anderson model using both the bare expansion in the system-environment coupling and a more advanced renormalized series. We compare the different expansions obtained, quantify the legitimacy of the generated dynamics (complete positivity) and benchmark with the exact result in the non-interacting limit.