# Valentin Bruch

I am a PhD candidate in theoretical physics at RWTH Aachen University. My interests lie in the field of open quantum systems, focussing on general analytic insights and semi-analytic renormalization group methods.

## Publications

• V. B., K. Nestmann, J. Schulenborg and M. R. Wegewijs Fermionic duality: General symmetry of open systems with strong dissipation and memory, SciPost Phys. 11, 053 (2021)
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.
• K. Nestmann, V. B. and M. R. Wegewijs How quantum evolution with memory is generated in a time-local way, Phys. Rev. X 11, 021041 (2021)
Two widely used but distinct approaches to the dynamics of open quantum systems are the Nakajima-Zwanzig and time-convolutionless quantum master equation, respectively. Although both describe identical quantum evolutions with strong memory effects, the first uses a time-nonlocal memory kernel 𝒦, whereas the second achieves the same using a time-local generator 𝒢. Here we show that the two are connected by a simple yet general fixed-point relation: $\mathcal{G}=\hat{\mathcal{K}}[\mathcal{G}]$. This allows one to extract nontrivial relations between the two completely different ways of computing the time-evolution and combine their strengths. We first discuss the stationary generator, which enables a Markov approximation that is both nonperturbative and completely positive for a large class of evolutions. We show that this generator is not equal to the low-frequency limit of the memory kernel, but additionally “samples” it at nonzero characteristic frequencies. This clarifies the subtle roles of frequency dependence and semigroup factorization in existing Markov approximation strategies. Second, we prove that the fixed-point equation sums up the time-domain gradient / Moyal expansion for the time-nonlocal quantum master equation, providing nonperturbative insight into the generation of memory effects. Finally, we show that the fixed-point relation enables a direct iterative numerical computation of both the stationary and the transient generator from a given memory kernel. For the transient generator this produces non-semigroup approximations which are constrained to be both initially and asymptotically accurate at each iteration step.
→ Press releases by RWTH Aachen, FZ Jülich and JARA

## CV

• 2019–2022 (planned): PhD student in the research training group 1995 with Prof. Dante Kennes (RWTH Aachen University) and Prof. Maarten Wegewijs (FZ Jülich)
• 2019: Master of Science, RWTH Aachen University, thesis on Fermionic duality: dissipative symmetry for open system dynamics beyond weak coupling in the group of Prof. Maarten Wegewijs
• 2017: Bachelor of Science, RWTH Aachen University, thesis on Density oscillations in one-dimensional many-body systems with spin

### Awards

• 2020: Springorum-Denkmünze, awarded by RWTH Aachen University
• 2018: Scholarship awarded by RWTH Education Fund, funded by Robert Bosch GmbH and the German Ministry for Education and Science
• 2018: Schöneborn Prize for outstanding results in the Bachelor studies by the Department of Computer Science at RWTH Aachen University