Pieter Claeys
@pieterclaeys.bsky.social
Physics & Reading & Music. Any permutation of the vowels is acceptable.
Congratulations both!
September 30, 2025 at 9:50 AM
Congratulations both!
Aha, thanks for letting me know!
September 12, 2025 at 3:28 PM
Aha, thanks for letting me know!
All of this suggests that this description of OTOCs and the emergence of free cumulants should hold in more generic quantum systems -- exactly as predicted by ETH. Comments and feedback welcome!
September 11, 2025 at 1:24 PM
All of this suggests that this description of OTOCs and the emergence of free cumulants should hold in more generic quantum systems -- exactly as predicted by ETH. Comments and feedback welcome!
We were able to exactly solve these dynamics by combining tools from free probability with results from dual-unitarity, allowing us to go beyond both. Also, remarkably, we can actually prove that all our predictions are stable even away from this solvable limit! (A rare thing in quantum systems.)
September 11, 2025 at 1:24 PM
We were able to exactly solve these dynamics by combining tools from free probability with results from dual-unitarity, allowing us to go beyond both. Also, remarkably, we can actually prove that all our predictions are stable even away from this solvable limit! (A rare thing in quantum systems.)
In this way we can fully characterize free cumulants and make exact predictions for (higher-order) OTOCs and correlations in matrix elements -- fundamental quantities in ETH.
September 11, 2025 at 1:24 PM
In this way we can fully characterize free cumulants and make exact predictions for (higher-order) OTOCs and correlations in matrix elements -- fundamental quantities in ETH.
Here we introduce a structured model for quantum dynamics, termed boundary scrambling, for which we can exactly solve the OTOC dynamics, and show how our random-bath predictions naturally appears from structured scrambling!
September 11, 2025 at 1:24 PM
Here we introduce a structured model for quantum dynamics, termed boundary scrambling, for which we can exactly solve the OTOC dynamics, and show how our random-bath predictions naturally appears from structured scrambling!
While this clarified the role of free cumulants in quantum dynamics (to me), we were not able to relate these results to ETH: ETH tells us how structured systems lead to random matrix behavior, whereas in that work we used random matrices to obtain random matrix behavior. (Slightly less surprising.)
September 11, 2025 at 1:24 PM
While this clarified the role of free cumulants in quantum dynamics (to me), we were not able to relate these results to ETH: ETH tells us how structured systems lead to random matrix behavior, whereas in that work we used random matrices to obtain random matrix behavior. (Slightly less surprising.)
Extensions of ETH are based on free cumulants from free probability, and it was unclear to me where these came from. In arxiv.org/abs/2506.11197 we made a first step in this direction, showing how coupling a quantum system to a random bath directly returns OTOC dynamics in terms of free cumulants.
Free Probability in a Minimal Quantum Circuit Model
Recent experimental and theoretical developments in many-body quantum systems motivate the study of their out-of-equilibrium properties through multi-time correlation functions. We consider the dynami...
arxiv.org
September 11, 2025 at 1:24 PM
Extensions of ETH are based on free cumulants from free probability, and it was unclear to me where these came from. In arxiv.org/abs/2506.11197 we made a first step in this direction, showing how coupling a quantum system to a random bath directly returns OTOC dynamics in terms of free cumulants.
Such multi-time correlation functions include out-of-time-order correlation functions (OTOCs) and their higher-order generalizations, probes of quantum scrambling, with such higher-order OTOCs recently measured by Google Quantum AI in its 103-qubit quantum processor!
arxiv.org/abs/2506.10191
arxiv.org/abs/2506.10191
Constructive interference at the edge of quantum ergodic dynamics
Quantum observables in the form of few-point correlators are the key to characterizing the dynamics of quantum many-body systems. In dynamics with fast entanglement generation, quantum observables gen...
arxiv.org
September 11, 2025 at 1:24 PM
Such multi-time correlation functions include out-of-time-order correlation functions (OTOCs) and their higher-order generalizations, probes of quantum scrambling, with such higher-order OTOCs recently measured by Google Quantum AI in its 103-qubit quantum processor!
arxiv.org/abs/2506.10191
arxiv.org/abs/2506.10191
I've recently gotten interested in extensions of ETH, which tell us how complicated multi-time correlation functions equilibrate. This theory builds on free probability, extending probability theory and the notion of independent random variables to noncommuting variables (think: random matrices).
September 11, 2025 at 1:24 PM
I've recently gotten interested in extensions of ETH, which tell us how complicated multi-time correlation functions equilibrate. This theory builds on free probability, extending probability theory and the notion of independent random variables to noncommuting variables (think: random matrices).
The eigenstate thermalization hypothesis (ETH) presents the main theoretical framework through which we understand how complex quantum systems can relax to simple equilibrium states. Much of this theory is based on treating highly complex quantum states as essentially random variables.
September 11, 2025 at 1:24 PM
The eigenstate thermalization hypothesis (ETH) presents the main theoretical framework through which we understand how complex quantum systems can relax to simple equilibrium states. Much of this theory is based on treating highly complex quantum states as essentially random variables.
Dit is de droom!
August 30, 2025 at 4:44 PM
Dit is de droom!