Project description
A new approach to study how quantum systems reach equilibrium
Ergodicity is a fundamental concept in statistical mechanics describing how systems evolve over time to explore all accessible states, ensuring equilibrium properties emerge. The ERC-funded QUEST project will further understanding of quantum ergodicity in many-body systems, proving its stability against small perturbations, and study transitions where ergodicity breaks owing to diverse factors such as integrability, disorder and impurities. QUEST will examine weak perturbations in specific types of systems already well understood and chaotic like dual-unitary quantum circuits. This method differs from traditional approaches that often rely on simpler, less chaotic systems. Furthermore, QUEST will create special models where the eigenstate thermalisation hypothesis – explaining how systems reach equilibrium – can be proven. Project advancements could boost quantum simulations and chaos theory, with applications spanning from quantum technologies to black hole physics.
Objective
We shall develop methods and models for analyzing quantum ergodicity in many-body systems, proving its stability against small perturbations, and studying ergodicity-breaking transitions due to integrability, disorder, or localized impurities. Ergodicity is a cornerstone of statistical mechanics and a key manifestation of many-body quantum chaos, while manipulating ergodicity and engineering ergodicity-breaking transitions will have immense applications (cf.scarred states in Rydberg arrays, heating transitions in Floquet systems, time crystalline phases of matter). PI proposed groundbreaking methods for establishing quantum ergodicity by rigorous analysis of spectral statistics, correlation functions, dynamical complexity indicators and entanglement on the basis of space-time duality. Most of current understanding of many-body physics or quantum fields is based on perturbative expansions around free, integrable or localized models. Here we propose a twist of paradigm: We shall study weak perturbations of statistically exactly solvable ergodic models, such as dual-unitary chaotic quantum circuits proposed by PI. An intuitive expectation of structural stability of ergodic dynamics (in analogy to rigorous results in classical ergodic theory) implies that such expansions typically have, unlike expansions around free/integrable models, finite radii of convergence. Various order parameters of the ergodic phase shall be developed and compared in their utility to signal and characterize ergodicity-breaking transitions. A related goal is a construction of exactly solvable models in which the eigenstate thermalization hypothesis can be proven. Being of fundamental importance in mathematical and statistical physics, the results are expected to have widespread applications across fields: from studying localization transitions in disordered systems, benchmarking quantum simulators and certifying quantum supremacy, to rigorous proofs of chaos in holographic models of black holes.
Fields of science (EuroSciVoc)
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CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
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Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
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Multi-annual funding programmes that define the EU’s priorities for research and innovation.
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HORIZON.1.1 - European Research Council (ERC)
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Topic(s)
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Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
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Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
HORIZON-ERC - HORIZON ERC Grants
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Call for proposal
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Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
(opens in new window) ERC-2022-ADG
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1000 Ljubljana
Slovenia
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