Elena Pulvirenti receives M-grant for her innovative research on the metastability of spin systems

News - 28 September 2023 - Communication EWI

The NWO Domain Board Science has announced that Dr. Elena Pulvirenti, from the EEMCS faculty, will receive an M-grant for her impressive research on the metastability of dilute spin models. M-grants are intended for innovative, high-quality, fundamental research and studies involving matters of scientific urgency. Elena will receive 350.000 euros to invest in her research.

Unstable equilibrium

Metastability is a phenomenon where a system, subject to random dynamics, exhibits very different behaviours on different time scales. A metastable state is a state of equilibrium that is not completely stable. A state exists that is energetically more favourable, but the system does not immediately decay to that energetically more favourable state.

An example is boiling delay where water is heated to a temperature above the boiling point without boiling. The gaseous form of the water is thermodynamically (energetically) more favourable, but the microscopic bubbles that form in the liquid do not grow into real bubbles. Only when a bubble reaches a certain size this is sufficiently favourable to allow the bubble to grow through. An external disturbance (e.g., bumping into the pan) can then cause such a sufficiently large bubble, and lead to the sudden occurrence of vigorous boiling. This example shows that while the system quickly reaches a metastable state, it takes a very long time for it to transition to the stable one.

Universal character

The universal character of metastability makes it a phenomenon observed in various systems in physics, chemistry, biology, and economics. Some experimentally observed examples are:

  • Physics: condensation of over-saturated water vapour.
  • Chemistry: mixing of two reactive compounds.
  • Economics: crashing of financial markets.
  • Biology: dynamics of large biomolecules such as proteins.
  • Population dynamics: viruses moving through a complex network causing an epidemic.
  • Material science: anomalous relaxation in disordered media.
  • Climatology: changing in global climate systems.
  • Neuroscience: production of neural oscillation in a cooperative manner in conscious activity.

Identifying a pattern in randomness

The main challenge in the mathematical study of metastability is to identify the characteristics of its random nature, and of its random transition time. With her project Elena wants to understand the characteristics of metastability for dilute spin systems (the Ising, the Hopfield and the block spin model). Spin models are often used in physics to explain magnetism, while dilute models are systems with random interactions. A strong reason to study systems with random interactions is their deep connection with the theory of random graphs (probability distributions over graphs, which can be generated by a random process), which attracted great interest in the last years due to their application to real-world networks.

An example of spin system is the Hopfield model, which models a neural network:  Such a network consists of binary or polar neurons and can serve as an associative memory. Elena is particularly interested in describing the time these systems need to do the metastable transition. This will in turn allow the study of pattern recognition of associative memories. Because there is a relation between the study of associative memories and machine learning, this study can also translate into practical recipes for the optimisation of machines learning. The mathematical theory and tools used in this project will have not only a direct impact on probability theory itself, the branch of mathematics that investigates the probabilities associated with random phenomena, but also on physics and biology.