Physics

We investigate the recently found \cite{migdal2023exact} reduction of decaying turbulence in the Navier-Stokes equation in $3 + 1$ dimensions to a  Number Theory problem of finding the statistical limit of the Euler ensemble.
We reformulate the Euler ensemble as a Markov chain and show the equivalence of this formulation to the quantum statistical theory of free fermions on a ring, with an external field related to the random fractions of $\pi$. 

We find the solution of this system in the statistical limit $N\to \infty$ in terms of a complex trajectory (instanton) providing a saddle point to the path integral over the charge density of these fermions.

This results in an analytic formula for the observable correlation function of vorticity in wavevector space. This is a full solution of decaying turbulence from the first principle without assumptions, approximations, or fitted parameters.
We compute resulting integrals in \Mathematica{} and present effective indexes for the energy decay as a function of time Fig.\ref{fig::NPlot} and the energy spectrum as a function of the wavevector at fixed time Fig.\ref{fig::SPIndex}. 

In particular, the asymptotic value of the effective index in energy decay $n(\infty) = \frac{7}{4}$, but the universal function $n(t)$ is neither constant nor linear.

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Symmetries are fundamental to our understanding of nature. In Quantum Field Theory, they have become the guidelines for the formulation of fundamental theories. In this talk, I will go into the importance of symmetries and the concept of spontaneous symmetry breaking to understand the early Universe. Then, I will discuss gauge symmetries and their fundamental differences with physical symmetries, and the subsequent contradiction in our understanding of the Higgs mechanism as a spontaneously broken gauge symmetry. I will discuss alternative understandings of the Higgs mechanism and the importance of gauge symmetries despite their seemingly redundant nature.

Rich clusters of galaxies are the largest gravitational magnifiers in the Universe. One of the most interesting gravitational lensing phenomena arises when background galaxies overlap with the lensing caustics cast by the cluster lens, such that a portion of it is tremendously magnified by hundreds to even thousands fold. As a result, Nature’s most luminous classes of stars have been individually or collectively detected by space telescopes from cosmological distances. Quantitatively studying their behavior will enable us to probe an impressive hierarchy of fine mass structures inside the lens: from star-free sub-galactic cold dark matter halos, to intracluster stars, and to even minuscule dark matter clumps predicted in many of the particle physics models of the dark matter. I will talk about what we have theoretically understood about the extremely magnified stars, what latest observational advances there are, and what unique constraints on dark matter micro-structures can be derived.

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Quantization of general relativity in four dimensions is not straightforward because Newton's constant carries units of (length)^2 which means the theory is non-renormalizable. Up to now, the only quantum-mechanical approach which has allowed the perturbative computation of graviton scattering at all energy scales is superstring theory. Although it might be a long time before experimental tests of quantum gravity will be able to tell us if superstring theory correctly describes our universe, the theory has other interesting properties such as supersymmetry and duality symmetry whose study has been useful for several branches of physics and mathematics.

Foraging is a ubiquitous behavior performed by all animals and human beings as they search for food needed to survive. Foraging theory has been key to understanding a variety of model systems but it still lacks mechanistic insights that relate it to neurobiological and other physiological mechanisms. In this talk, I will present work that aims to develop a quantitative mechanistic framework of foraging with a specific focus on patch foraging either of an individual agent or in a social context. I will also present a learning model that accounts for how agents learn the structure of the environment

Gravity creates space-time boundaries that limit observables without limiting the flow of energy and information. This means that quantum systems in cosmology are often open systems: to describe them we must include the effects of interaction with an unobservable environment. In many cosmological settings, different observers see different parts of the spacetime; the ensemble of the open systems for each observer makes up the full cosmology. In this talk I will introduce a class of out-of-equilibrium quantum systems constructed to mimic some key features of cosmology and demonstrate the utility of treating the full system as an ensemble of open systems. I will use these models to illustrate the possible connections between cosmological open quantum systems and thermodynamics, as well as open-systems-inspired ways to think about locality.

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