Ángela Capel siiting on the stairs of the LMU Physics foyer.

MCQST Distinguished PostDoc

Technical University of Munich

Mathematical Physics | M5

Boltzmannstrasse 3

85748 Garching

Tel. +49 89 289 18321



I love the beauty of the particular types of abstract patterns involved in my research, feel inspired by the flash of enlightenment I experience when a new idea connects previously unconnected ones and fulfil my expectations by applying them to solve non-trivial problems.


Research focus: Study of the speed of convergence of quantum dissipative evolutions via quantum functional inequalities.

My envisaged project at MCQST concerns the question of how fast a quantum thermal dissipative evolution converges to its equilibrium state. This velocity of thermalization is given by the time that it takes for every initial physical state undergoing a dissipative evolution to be almost indistinguishable from the thermal equilibrium, which can be studied via the optimal constants associated to some quantum functional inequalities. In particular, we are interested in physical systems for which this convergence is fast enough, and thus have nice properties such as stability against external perturbations and satisfy an area law. My goal is to design and implement the necessary mathematical tools to obtain conditions on physical systems that imply rapid mixing on quantum systems and that can be used to estimate the speed of convergence of an algorithm or the noise generated in a quantum circuit.



On the modified logarithmic Sobolev inequality for the heat-bath dynamics for 1D systems

I. Bardet, A. Capel, A. Lucia, D. Pérez-García, C. Rouzé

Journal of Mathematical Physics 62, 61901 (2021).

Show Abstract

The mixing time of Markovian dissipative evolutions of open quantum many-body systems can be bounded using optimal constants of certain quantum functional inequalities, such as the modified logarithmic Sobolev constant. For classical spin systems, the positivity of such constants follows from a mixing condition for the Gibbs measure via quasi-factorization results for the entropy. Inspired by the classical case, we present a strategy to derive the positivity of the modified logarithmic Sobolev constant associated with the dynamics of certain quantum systems from some clustering conditions on the Gibbs state of a local, commuting Hamiltonian. In particular, we show that for the heat-bath dynamics of 1D systems, the modified logarithmic Sobolev constant is positive under the assumptions of a mixing condition on the Gibbs state and a strong quasi-factorization of the relative entropy.

DOI: 10.1063/1.5142186

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