Mathematical Physics
In this work, we investigate the large-scale transport properties of a passive scalar advected by a turbulent fluid, modelled as a superposition of divergence-free vector fields, each weighted by an independent symmetric…
We study a nonrelativistic system made of two quantum particles constrained to move on a line and a spin located at a fixed point of the line. Initially the two particles are in a maximally entangled state and the spin is down. The first…
We consider the transition between short-range entangled (SRE) and long-range ordered (and therefore long-range entangled) states of infinite quantum spin chains, which is induced by local measurements. Specifically, we assume that the…
All isometrically invariant Markov (strictly local) fields on binary assignments are induced by energy functions that can be represented as linear combinations of area, perimeter, and Euler characteristic. This class of model includes the…
Our aim is to introduce a category-theoretic framework sufficiently general to describe a wide variety of open kinematic systems in classical mechanics while uniquely characterizing systems with specified simplest components. The framework…
We prove that the net of localised von Neumann algebras associated with a real scalar field propagating on Minkowski spacetime, in the KMS representation, satisfies a generalised version of Haag duality. Our proof combines ideas from…
We discuss germs of distributions on $d-$dimensional smooth Riemannian manifolds and, in particular, we derive \emph{multi-level Schauder estimates} without making any further assumptions on the underlying geometry. As a preliminary step,…
Our goal is to provide precise effective operators for monolayer graphene at Fermi energy. We consider the microscopic potential created by a lattice, and add a macroscopic potential with the same periodicity but varying at a scale…
Stochastic growth models in the Kardar-Parisi-Zhang (KPZ) universality class exhibit remarkable fluctuation phenomena. While a variety of powerful methods have led to a detailed understanding of their typical fluctuations or large…
The \textit{Teleportation=Translation} conjecture posits that the recovery of information from a black hole is dual to a geometric translation in the emergent spacetime. In this paper, we establish this equivalence for general local quantum…
We develop a systematic framework for constructing (3+1)-dimensional topological orders or topological quantum field theories (TQFTs) that realize specified anomalies of finite symmetries, as encountered in gauge theories with fermions or…
We study the two-dimensional two-component Coulomb gas in the canonical ensemble and at inverse temperature $\beta>2$. In this regime, the partition function diverges and the interaction needs to be cut off at a length scale $\lambda\in…
The theory of the set-theoretic Yang-Baxter equation is reviewed from a purely algebraic point of view. We recall certain algebraic structures called shelves, racks and quandles. These objects satisfy a self-distributivity condition and…
We study the ground state energy of a gas of spin $1/2$ fermions with repulsive short-range interactions. We derive an upper bound that agrees, at low density $\rho$, with the Huang-Yang conjecture. The latter captures the first three terms…
The amplituhedron Ank4 is a geometric object, introduced by Arkani-Hamed and Trnka (2013) in the study of scattering amplitudes in quantum field theories. They conjecture that Ank4 admits a decomposition into images of BCFW positroid cells,…
In this paper, we prove that time-like constant slope surfaces can be reparametrized by using rotation matrices corresponding to unit time-like split quaternions and homothetic motions. Afterwards we give some examples to illustrate our…
We investigate periodic integrable Markov models, constructed from set-theoretical solutions of the Yang-Baxter equation. We first focus on the simplest class of solutions, called Lyubashenko solutions. We show that the resulting models are…
We introduce a class of states of a composite quantum system, the so-called cross states, that turn out to play a major role in the theory of entanglement for a genuinely infinite-dimensional bipartite system. In the case where at least one…
We study the local statistics of orthogonal polynomial ensembles near a hard edge, subject to a multiplicative deformation of the measure. Probabilistically, this deformation corresponds to a position-dependent conditional thinning of the…
In this paper, we consider the parameterization of the spectra of the three-state critical Potts quantum chain with integrable twisted boundary conditions in terms of Bethe ansatz type equations. The Bethe equations are found by…