SubsidieMeestersQuantum Ergodicity: Stability and Transitions
Develop methods to analyze and manipulate quantum ergodicity in many-body systems, aiming to understand stability and transitions for broad applications in physics.
Projectdetails
Introduction
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.
Importance of Ergodicity
Ergodicity is a cornerstone of statistical mechanics and a key manifestation of many-body quantum chaos. Manipulating ergodicity and engineering ergodicity-breaking transitions will have immense applications, such as:
- Scarred states in Rydberg arrays
- Heating transitions in Floquet systems
- Time crystalline phases of matter
Proposed Methods
The Principal Investigator (PI) proposed groundbreaking methods for establishing quantum ergodicity by rigorous analysis of:
- Spectral statistics
- Correlation functions
- Dynamical complexity indicators
- Entanglement on the basis of space-time duality
Most of the current understanding of many-body physics or quantum fields is based on perturbative expansions around free, integrable, or localized models.
Paradigm Shift
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 the 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.
Order Parameters and Goals
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 the construction of exactly solvable models in which the eigenstate thermalization hypothesis can be proven.
Expected Applications
Being of fundamental importance in mathematical and statistical physics, the results are expected to have widespread applications across fields, including:
- Studying localization transitions in disordered systems
- Benchmarking quantum simulators and certifying quantum supremacy
- Rigorous proofs of chaos in holographic models of black holes
Financiële details & Tijdlijn
Financiële details
| Subsidiebedrag | € 1.944.625 |
| Totale projectbegroting | € 1.944.625 |
Tijdlijn
| Startdatum | 1-4-2024 |
| Einddatum | 31-3-2029 |
| Subsidiejaar | 2024 |
Partners & Locaties
Projectpartners
- UNIVERZA V LJUBLJANIpenvoerder
Land(en)
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