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The Mathematics of Quantum Propagation

Project description

Tackling the mathematics of quantum information propagation

Strongly interacting and highly correlated quantum many-body systems are revolutionising modern quantum physics. Researchers have achieved unprecedented control on the interaction parameters and are able to reliably produce remarkable fundamental phenomena. These groundbreaking advances challenge existing analytical methods and require rigorous mathematical solutions. The ERC-funded MathQuantProp project aims to resolve fundamental mathematical problems for lattice bosons and continuum quantum many-body systems, including the existence of the thermodynamic limit of the dynamics. First, it will establish propagation bounds, including Lieb-Robinson bounds (LRBs), for lattice bosons and identify the true behaviour of information propagation for these systems by building on new analytical techniques. Second, it will develop propagation bounds, including LRBs, for continuum fermions and bosons, taking into account ultraviolet divergences.

Objective

Strongly interacting and strongly correlated quantum many-body systems are at the forefront of modern quantum physics. Experimentalists have obtained unprecedented control on the interaction parameters and are able to reliably produce striking fundamental phenomena. These problems demand a rigorous mathematical treatment, but analytical methods are extremely scarce. Outside of special scaling limits, the gold standard are Lieb-Robinson bounds (LRBs) which provide an a priori bound on the speed of information propagation with broad physical implications. However, for the important classes of (A) lattice bosons and (B) continuum fermions and continuum bosons, the standard derivations of Lieb-Robinson bounds break down because these systems have unbounded interactions.
The first goal of this project is to establish propagation bounds, including LRBs, for lattice bosons and to identify the true behavior of information propagation for these systems. This is the missing puzzle piece to develop a quantum information theory of lattice bosons that is on par with the revolutionary findings for quantum spin systems. The second goal is to develop propagation bounds, including LRBs, for continuum fermions and bosons. These systems present even more fundamental challenges due to ultraviolet divergences. As an application, I aim to close a glaring gap in our understanding of continuum quantum many-body systems: the existence of the thermodynamic limit of the dynamics. I recently developed the ASTLO method which uses bootstrapped differential inequalities, microlocal-inspired resolvent expansions, and multiscale iteration to pioneer particle propagation bounds for the paradigmatic Bose-Hubbard Hamiltonian. This resolved longstanding problems in mathematical physics. My new ASTLO method is a robust proof template. In combination with the technique of truncated dynamics, it enables me to now tackle even more challenging open problems about information propagation.

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(opens in new window) ERC-2024-STG

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Host institution

EBERHARD KARLS UNIVERSITAET TUEBINGEN
Net EU contribution

Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.

€ 1 480 403,00
Address
GESCHWISTER-SCHOLL-PLATZ
72074 Tuebingen
Germany

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Region
Baden-Württemberg Tübingen Tübingen, Landkreis
Activity type
Higher or Secondary Education Establishments
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Total cost

The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.

€ 1 480 403,00

Beneficiaries (1)

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