Dr. Valentin Bruch

• valentin.bruch@rwth-aachen.de
• stiglers-eponym
• 0000-0001-5562-9285
• ITMS Project
• Deutscher Wetterdienst
• RWTH Aachen University
• Institute for Theory of Statistical Physics
• Research Training Group 1995

I am a physicist who started in theoretical condensed matter research and now works on estimating greenhouse gas emission based on atmospheric observations. My interests lie in the fields of open quantum systems, renormalization group methods, and inverse problems in mathematics.

Research interests

• Estimating greenhouse gas emissions
• Inverse problems in mathematics
• Kondo physics
• Renormalization group methods for open quantum systems
• Exact analytic properties of fermionic open systems
• Applying quantum information methods to condensed matter problems

Publications

• V. B. Renormalization group approach to strongly correlated and coherently driven open quantum systems, PhD thesis (RWTH Aachen University, 2023)

  In this thesis, we study open quantum systems in nonequilibrium with strong correlations and memory effects from two complementary views.

  In the first part, we discuss the so-called fermionic duality relation, which can be used to simplify the description of the dynamics for a large class of fermionic models. Unlike ordinary symmetries, this relation connects the dynamics for different sets of parameters. We provide a new and simpler proof of this duality relation, which is also closer adapted to quantum information formulations of open system dynamics. This derivation highlights what prohibits or limits the generalization of the duality relation to transport observables and systems with time-dependent driving. For systems obeying ordinary symmetries associated with conservation laws, we focus on local states projected onto the symmetry sector. This projection simplifies the description of the dynamics in different formalisms, but excludes states that are entangled with some ancilla system. Applying the projection to the noninteracting resonant level model, we illustrate how it can significantly simplify the Kraus operator sum form and how the combination with fermionic duality leads to further restrictions on the dynamics.

  The main part of this thesis discusses the concrete solution of the strongly correlated problem of the isotropic spin-1/2 Kondo model with time-periodic bias voltage at zero temperature. We use a recent nonequilibrium renormalization group (RG) method combined with Floquet theory to incorporate the interplay of strong correlations and coherent driving. We show in line with an experiment that such an approach is necessary for a quantitative description of transport properties by comparing our results to the simple phenomenological picture of photon-assisted tunneling, which underestimates decoherence, and to the adiabatic limit. Our findings show excellent quantitative agreement with experiments, which find side peaks of the Kondo resonance in the differential conductance. These side peaks are not completely washed out by the decoherence induced by the driving except at low driving frequency, and we predict these peaks to be sharper when the coupling to the reservoirs is asymmetric. To analyze memory effects for strong and fast harmonic driving in detail, we discuss the response to short voltage pulses. The time-resolved current after such pulses shows memory effects that arise from correlations between the two reservoirs, which are generated through the coupling to a quantum dot in the Kondo limit.

  This solution of the driven Kondo model is based on the E-flow scheme of the real-time RG method, which we combine with a Floquet representation. This method is applicable to small open quantum systems with time-periodic external driving. Based on a perturbative expansion in the coupling between the system and the reservoirs, the real-time RG sums up large classes of terms in the coupling expansion in a self-consistent way. We provide a detailed derivation of the RG equations for a general fermionic cotunneling Hamiltonian before applying these equations to the isotropic spin 1/2 Kondo model up to next-to-leading order in the renormalized coupling. We also discuss the convergence of the expansion in the coupling, numerical approximations, and subtleties arising in calculations with Floquet matrices.

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• V. B., M. Pletyukhov, H. Schoeller and D. M. Kennes Floquet Renormalization Group Approach to the Periodically Driven Kondo Model, Phys. Rev. B 106, 115440 (2022)

  We study the interplay of strong correlations and coherent driving by considering the strong-coupling Kondo model driven by a time-periodic bias voltage. Combining a recent nonequilibrium renormalization group method with Floquet theory, we find that by the coherent dressing of the driving field side-replicas of the Kondo resonance emerge in the conductance, which are not completely washed out by the decoherence induced by the driving. We show that to accurately capture the interplay of driving and strong correlations one needs to go beyond simple phenomenological pictures, which underestimate decoherence, or adiabatic approximations, highlighting the relevance of non-Markovian memory effects. Within our method the differential conductance shows good quantitative agreement with experimental data in the full crossover regime from weak to strong driving. We analyze memory effects in detail based on the response to short voltage pulses.

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• 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.

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• 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: 𝒢 = 𝒦 ^ [ 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.

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  → Press releases by RWTH Aachen, FZ Jülich and JARA

CV

• 2023 – expected 2026: Researcher at Deutscher Wetterdienst (German Meteorological Service), working on an Integrated Greenhouse Gas Monitoring System for Germany (ITMS)
• 2019 – 2023: PhD student in the RTG 1995, thesis on Renormalization group approach to strongly correlated and coherently driven open quantum systems, supervised by Prof. Dante M. Kennes (RWTH Aachen University and MPI for the Structure and Dynamics of Matter) and Prof. Maarten R. Wegewijs (FZ Jülich and RWTH Aachen University)
• 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 R. Wegewijs
• 2017: Bachelor of Science, RWTH Aachen University, thesis on Density oscillations in one-dimensional many-body systems with spin
• Awards: Springorum-Denkmünze (RWTH, 2021), Scholarship by RWTH Education Fund (2018), Schöneborn Prize (RWTH, 2018)