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Generalized Pentagon Equations
Generalized Pentagon Equations
Drinfeld defined the Knizhnik–Zamolodchikov (KZ) associator $$\Phi _}$$ by considering the regularized holonomy of t...
Prethermalization for Deformed Wigner Matrices
Prethermalization for Deformed Wigner Matrices
We prove that a class of weakly perturbed Hamiltonians of the form $$H_\lambda = H_0 + \lambda W$$ , with W being a Wigner...
Relative Entropy and Mutual Information in Gaussian Statistical Field Theory
Relative Entropy and Mutual Information in Gaussian Statistical Field Theory
Relative entropy is a powerful measure of the dissimilarity between two statistical field theories in the continuum. In th...
Quantum Observables of Quantized Fluxes
Quantum Observables of Quantized Fluxes
While it has become widely appreciated that defining (higher) gauge theories requires, in addition to ordinary phase space...
Typical Macroscopic Long-Time Behavior for Random Hamiltonians
Typical Macroscopic Long-Time Behavior for Random Hamiltonians
We consider a closed macroscopic quantum system in a pure state $$\psi _t$$ evolving unitarily and take for granted that d...
Immersed figure-8 Annuli and Anyons
Immersed figure-8 Annuli and Anyons
Immersion (i.e., local embedding) is relevant to the physics of topologically ordered phases through entanglement bootstra...
Modular Hamiltonian for Fermions of Small Mass
Modular Hamiltonian for Fermions of Small Mass
We consider the algebra of massive fermions restricted to a diamond in two-dimensional Minkowski spacetime, and in the Min...
Averaging Theorems for Slow–Fast Systems in $$\mathbb {Z}$$ -extensions (Discrete Time)
Averaging Theorems for Slow–Fast Systems in $$\mathbb {Z}$$ -extensions (Discrete Time)
We study the averaging method for flows perturbed by a dynamical system preserving an infinite measure. Motivated by the c...
Hofstadter Butterflies and Metal/Insulator Transitions for Moiré Heterostructures
Hofstadter Butterflies and Metal/Insulator Transitions for Moiré Heterostructures
We consider a tight-binding model recently introduced by Timmel and Mele (Phys Rev Lett 125:166803, 2020) for strained moi...
From Orbital Magnetism to Bulk-Edge Correspondence
From Orbital Magnetism to Bulk-Edge Correspondence
By extending the gauge covariant magnetic perturbation theory to operators defined on half-planes, we prove that for 2d ra...
Extensions of Lorentzian Hawking–Page Solutions with Null Singularities, Spacelike Singularities, and Cauchy Horizons of Taub–NUT Type
Extensions of Lorentzian Hawking–Page Solutions with Null Singularities, Spacelike Singularities, and Cauchy Horizons of Taub–NUT Type
Starting from the Hawking–Page solutions of [14], we consider the corresponding Lorentzian cone metrics. These repre...
Asymptotics of Solutions to Silent Wave Equations
Asymptotics of Solutions to Silent Wave Equations
We study the asymptotics of solutions to a particular class of systems of linear wave equations, namely, of silent equatio...
Point Potentials on Euclidean Space, Hyperbolic Space and Sphere in Any Dimension
Point Potentials on Euclidean Space, Hyperbolic Space and Sphere in Any Dimension
In dimensions $$d=1,2,3$$ , the Laplacian can be perturbed by a point potential. In higher dimensions, the Laplacian with ...
Fine Structure of Flat Bands in a Chiral Model of Magic Angles
Fine Structure of Flat Bands in a Chiral Model of Magic Angles
We analyse symmetries of Bloch eigenfunctions at magic angles for the Tarnopolsky–Kruchkov–Vishwanath chiral m...
Magnetic Response Properties of Twisted Bilayer Graphene
Magnetic Response Properties of Twisted Bilayer Graphene
In this article, we analyze the Bistritzer–MacDonald model (also known as the continuum model) of twisted bilayer gr...
Symmetric Functions from the Six-Vertex Model in Half-Space
Symmetric Functions from the Six-Vertex Model in Half-Space
We study the stochastic six-vertex model in half-space with generic integrable boundary weights, and define two families o...
A Lower Semicontinuous Time Separation Function for $$C^0$$ Spacetimes
A Lower Semicontinuous Time Separation Function for $$C^0$$ Spacetimes
The time separation function (or Lorentzian distance function) is a fundamental tool used in Lorentzian geometry. For smoo...
A Construction of Approximately Self-Similar Naked Singularities for the Spherically Symmetric Einstein-Scalar Field System
A Construction of Approximately Self-Similar Naked Singularities for the Spherically Symmetric Einstein-Scalar Field System
In this work, we identify stable perturbations of k-self-similar naked singularities, in the full parameter range $$k^2 \i...
A New Gauge for Gravitational Perturbations of Kerr Spacetimes I: The Linearised Theory
A New Gauge for Gravitational Perturbations of Kerr Spacetimes I: The Linearised Theory
We propose a new geometric framework to address the stability of the Kerr solution to gravitational perturbations in the f...
Boundary Structure of the Standard Model Coupled to Gravity
Boundary Structure of the Standard Model Coupled to Gravity
In this article a description of the reduced phase space of the standard model coupled to gravity is given. For space or t...
The Asymptotic Expansion of the Spacetime Metric at the Event Horizon
The Asymptotic Expansion of the Spacetime Metric at the Event Horizon
Hawking’s local rigidity theorem, proven in the smooth setting by Alexakis-Ionescu-Klainerman, says that the event h...
Schur Function Expansion in Non-Hermitian Ensembles and Averages of Characteristic Polynomials
Schur Function Expansion in Non-Hermitian Ensembles and Averages of Characteristic Polynomials
We study k-point correlators of characteristic polynomials in non-Hermitian ensembles of random matrices, focusing on the ...
Kac–Ward Solution of the 2D Classical and 1D Quantum Ising Models
Kac–Ward Solution of the 2D Classical and 1D Quantum Ising Models
We give a rigorous derivation of the free energy of (i) the classical Ising model on the triangular lattice with translati...
Anisotropic Ising Model in $$d+s$$ Dimensions
Anisotropic Ising Model in $$d+s$$ Dimensions
In this note, we consider the asymmetric nearest neighbor ferromagnetic Ising model on the $$(d+s)$$ -dimensional unit cub...
Graph Hörmander Systems
Graph Hörmander Systems
This paper extends the Bakry-Émery criterion relating the Ricci curvature and logarithmic Sobolev inequalities to the...
The Sobolev Wavefront Set of the Causal Propagator in Finite Regularity
The Sobolev Wavefront Set of the Causal Propagator in Finite Regularity
Given a globally hyperbolic spacetime $$M=}\times \Sigma $$ of dimension four and regularity $$C^\tau $$ , we estimate the...
Time Functions on Lorentzian Length Spaces
Time Functions on Lorentzian Length Spaces
In general relativity, time functions are crucial objects whose existence and properties are intimately tied to the causal...
Almost Optimal Upper Bound for the Ground State Energy of a Dilute Fermi Gas via Cluster Expansion
Almost Optimal Upper Bound for the Ground State Energy of a Dilute Fermi Gas via Cluster Expansion
We prove an upper bound on the energy density of the dilute spin- $$\frac$$ Fermi gas capturing the leading correction to ...
The Double Semion State in Infinite Volume
The Double Semion State in Infinite Volume
We describe in a simple setting how to extract a braided tensor category from a collection of superselection sectors of a ...
Ergodic Theorems for Continuous-Time Quantum Walks on Crystal Lattices and the Torus
Ergodic Theorems for Continuous-Time Quantum Walks on Crystal Lattices and the Torus
We give several quantum dynamical analogs of the classical Kronecker–Weyl theorem, which says that the trajectory of...
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