Related papers: Localization anisotropy and complex geometry in tw…

On a Riemannian manifold with a positive lower bound on the Ricci tensor, the distance of isoperimetric sets from geodesic balls is quantitatively controlled in terms of the gap between the isoperimetric profile of the manifold and that of…

Using the twistor correspondence, we give a classification of toric anti-self-dual Einstein metrics: each such metric is essentially determined by an odd holomorphic function. This explains how the Einstein metrics fit into the…

A quantum model can be mapped to a classical model in one higher dimension. Here we introduce a finite-temperature correlation measure based on a reduced density matrix rho_A obtained by cutting the classical system along the imaginary time…

The verification of whether small-scale turbulence is isotropic remains a grand challenge. The difficulty arises because the presence of small-scale anisotropy is tied to the dissipation tensor, whose components require the full…

We investigate the consequences of reparametrizations in the geometric description of thermodynamics analyzing the effects on the thermodynamic phase space. It is known that the contact and Riemannian structures of the thermodynamic phase…

We revisit the localization tensor (LT) from geometric and probabilistic perspectives and construct extensions that are naturally compatible with periodic boundary conditions (PBC), without redefining the position operator. In open boundary…

The entanglement entropy of a pure quantum state of a bipartite system is defined as the von Neumann entropy of the reduced density matrix obtained by tracing over one of the two parts. Critical ground states of local Hamiltonians in one…

In this book chapter we study the Riemannian Geometry of the density registration problem: Given two densities (not necessarily probability densities) defined on a smooth finite dimensional manifold find a diffeomorphism which transforms…

This work comprises a detailed theoretical and computational study of the boundary value problem for transversely isotropic linear elastic bodies. General conditions for well-posedness are derived in terms of the material parameters. The…

We find all orthogonal metrics where the geodesic Hamilton-Jacobi equation separates and the Riemann curvature tensor satisfies a certain equation (called the diagonal curvature condition). All orthogonal metrics of constant curvature…

Anderson localization is a quantum phenomenon in which disorder localizes electronic wavefunctions. In this work, we propose a new approach to study Anderson localization based on the density matrix formalism. Drawing an analogy to the…

Quantum mechanics is sensitive to the geometry of the underlying space. Here, we present a framework for quantum scattering of a non-relativistic particle confined to a two-dimensional space. When the motion manifold hosts localized…

We propose a covariant definition of an inertia tensor on spatial hypersurfaces in general relativity, constructed via integrals of geodesic distance functions using the exponential map. In the ADM 3+1 decomposition, we consider a spacelike…

We explain the coarse geometric origin of the fact that certain spectral subspaces of topological insulator Hamiltonians are delocalized, in the sense that they cannot admit an orthonormal basis of localized wavefunctions, with respect to…

Within a framework of noncommutative geometry, we develop an analogue of (pseudo) Riemannian geometry on finite and discrete sets. On a finite set, there is a counterpart of the continuum metric tensor with a simple geometric…

The twistor construction for Riemannian manifolds is extended to the case of manifolds endowed with generalized metrics (in the sense of generalized geometry \`a la Hitchin). The generalized twistor space associated to such a manifold is…

We evaluate reflected entropy in certain anisotropic boundary theories dual to nonrelativistic geometries using holography. It is proposed that this quantity is proportional to the minimal area of the entanglement wedge cross section. Using…

We present an analytic theory of quantum criticality in quasi one-dimensional topological Anderson insulators. We describe these systems in terms of two parameters $(g,\chi)$ representing localization and topological properties,…

The topological properties of materials are, until now, associated with the features of their crystalline structure, although translational symmetry is not an explicit requirement of the topological phases. Recent studies of hopping models…

The location of electrons governs phenomena ranging from chemical bonding and electric polarization to the topological classification of band insulators and the emergence of correlated states in quantum matter. While a prescription exists…