Talks

Biological evolution is a complex blend of ever changing structural stability, variability and emergence of new phenotypes, niches, ecosystems. We wish to argue that the evolution of life marks the end of a physics world view of law entailed dynamics.

The detection of coalescing neutron stars via gravitational waves (GW170817) has revolutionized our understanding of the equation of state at supranuclear densities. The equation of state determines how neutron stars interact in a variety of astrophysical contexts, from rapidly rotating millisecond pulsars, to accreting X-ray sources, and, of course, coalescing binaries radiating gravitational waves. I will review the state of the field, including commonly adopted parametrizations of the neutron star equation of state in the context of theoretical expectations, before introducing a nonparametric inference scheme based on Gaussian processes. Nonparametric inference provides much greater functional freedom than parametrized analyses, allowing for the direct inference of neutron star composition and the existence of possible phase transtions above nuclear density. Additionally, I will review the search for predicted secular fluid instabilities within neutron star cores and their possible impact on gravitational-wave signals. This instability couples pressure-supported (p-mode) and gravity supported (g-mode) oscillations within the star, and I will show how GW170817 rules out only the most extreme theoretical predictions for how the instability could saturate. As the advanced LIGO and Virgo detectors gear-up for the second half of their third observing run, we will conclude by discussing the outlook for these measurements with future detections and the implications for broader astrophysical populations.

Black Hole Entropy is a well established concept and arises naturally once one realises that black holes are characterised by a temperature. Boltzmann established that entropy can be regarded as the logarithm of the density of states function. However, black hole uniqueness theorems appeared to indicate that black holes have no hair. I will describe a loophole in the no-hair theorems and how black holes can have an infinite set of charges related to "large" gauge transformations. I will then use these ideas to show that on sections of the horizon there is a holographic conformal field theory. The temperature of this conformal theory means that it has a statistical entropy that reproduces the Hawking formula. The implications of this for the black hole information paradox will be briefly described.
 

The mixing time of Markovian dissipative evolutions of open quantum many-body systems can be bounded using optimal constants of certain quantum functional inequalities, such as the logarithmic Sobolev constant. For classical spin systems, the positivity of such constants follows from a mixing condition for the Gibbs measure, via quasi-factorization results for the entropy.

Inspired by the classical case, we present a strategy to derive the positivity of the logarithmic Sobolev constant associated to the dynamics of certain quantum systems from some clustering conditions on the Gibbs state of a local, commuting Hamiltonian. In particular we address this problem for the heat-bath dynamics in 1D and the Davies dynamics, showing that the first one is positive under the assumptions of a mixing condition on the Gibbs state and a strong quasi-factorization of the relative entropy, and the second one under some strong clustering of correlations.

Global symmetries and gauge symmetries have played a crucial role in physics.  The idea of duality demonstrates that gauge symmetries can be emergent and might not be fundamental.  During the past decades it became clear that the circle of ideas about emergent gauge symmetries and duality is central in different branches of physics including Condensed Matter Physics, Quantum Field Theory, and Quantum Gravity.   We will review these developments, which highlight the unity of physics.

Thanks to the Lanczos algorithm, the Hamiltonian dynamics of any operator can be written as a hopping problem on a semi-infinite one-dimensional chain. Our hypothesis states that the hopping strength grows linearly down the chain, with a universal growth rate $\alpha$ that is an intrinsic property of the system. This leads to an exponential motion of the operator down the chain, capturing the irreversible process of simple operators inevitably evolving into complex ones. This exponential growth exists for generic quantum systems, even away from large-$N$ or semiclassical limits. In fact, $\alpha$ gives an upper bound for the exponential growth rate of a large class of operator complexity measures, including out-of-time-order correlations. As a result, we conjecture a new bound on Lyapunov exponents $\lambda_L \leq 2 \alpha$, which generalizes the known universal low-temperature bound $\lambda_L \leq 2 \pi T$. We illustrate the hypothesis in paradigmatic examples such as non-integrable spin chains, the $q$-SYK model, and chaotic coupled top models, and show that some of them saturate the conjectured bound.