Nonequilibrium pervades nature, from the expanding universe to climate dynamics, living cells and molecular machines. Key to nonequilibrium states is the entropy production rate σ at which energy is dissipated to the environment. Despite its importance, σ remains challenging to measure, especially in nanoscale systems with limited access to microscopic variables. Here I present a recently introduced variance sum rule for displacement and force variances that permits to measure σ by constraining energetics through modelling. We apply it to measure the first heat map of human red blood cells in experiments with laser optical tweezers and ultrafast life-imaging microscopy. We find a spatially heterogeneous σ with finite-correlation length of half a micron ξ~0.5μm and global σ~106 kBT/s per single cell, in agreement with calorimetry estimates. The variance sum rule sets a new resource for nonequilibrium systems, from measuring entropy production rates in active and living matter to machine learning.
Integrable unitary circuits can be seen as a Trotter formulation of certain integrable continuous-time Hamiltonians. Their importance lies in the potential to use analytical methods to compute physical observables, such as correlation functions and mean particle current. In this talk, I will explain the different terms in the title and explore their connections.
I will begin with an introduction to integrability, which is the property of a physical system having an infinite number of commuting conserved charges. Then, I will discuss the discrete dynamical evolution of a quantum system and explain how a quantum circuit can be integrable. Using this construction, I will build different quantum circuits with open boundary conditions and address the question of under which conditions the structure of the boundary gate factorizes. In continuous-time evolution, this question corresponds to understanding when we can interpret the boundary terms as a Lindbladian: the effective action of a Markovian environment on the system. I will show how, for specific parameter choices, these solutions correspond to Lindbladians that inject or remove particles at the boundaries of the spin chain.
Based on arXiv:2406.12695 with T. Prosen.
The past three decades of exoplanet discovery have revealed a bewildering diversity of planetary systems, as well as tantalizing correlations between their features and other properties such as the mass of the host stars. To understand the origin of these patterns, we must study the emergence of planets from circumstellar disks of gas and dust, and the prior evolution of those disks. These too exhibit remarkable differences in structure, evolution, and lifetime which are poorly understood. The dissipation of disks under the influence of high-energy emission from the central star is considered important; I show how the interaction of the partially ionized disk with the stellar magnetic field will modulate that emission and can explain observations. This suggests that the outcome of planet formation is significantly influenced by the large-scale magnetic field of the star, among other variables. Future observations by ground- and space-telescopes of the fields of very young stars, the structures and compositions of their disks, and the planets that form from them will more fully explore this connection. In a real way, the ancient Sun’s magnetic field could be one reason these words are written on a world that orbits it.
