相关论文: Proximality of multidimensional $\mathscr{B}$-free…
The review studies connections between integrable many-body systems and gauge theories. It is shown how the degrees of freedom in integrable systems are related with topological degrees of freedom in gauge theories. The relations between…
Let $(M,d)$ be a complete metric space and let $\mathcal{F}(M)$ denote the Lipschitz-free space over $M$. We develop a ``Choquet theory of Lipschitz-free spaces'' that draws from the classical Choquet theory and the De Leeuw representation…
Self-consistent dynamical approximations for strongly correlated fermion systems are particularly successful in capturing the dynamical competition of local correlations. In these, the effect of spatially extended degrees of freedom is…
Based on a fairly precise approximation to the lattice discrepancy of a Lame disc, an asymptotic formula is established for the number of lattice points in a related three-dimensional body, linearly dilated by a large real parameter x.…
The study of nonlinear phenomena in systems with many degrees of freedom often relies on complex numerical simulations. In trying to model realistic situations, these systems may be coupled to an external environment which drives their…
We construct an analytic theory of many-body localization (MBL) in random spin chains. The approach is based on a first quantized perspective in which MBL is understood as a localization phenomenon on the high dimensional lattice defined by…
Many-body localization for a system of bosons trapped in a one dimensional lattice is discussed. Two models that may be realized for cold atoms in optical lattices are considered. The model with a random on-site potential is compared with…
We give algebraic conditions about a finite algebra $B$ over a perfect field of positive characteristic, which are equivalent to the companionability of the theory of fields with "$B$-operators" (i.e. the operators coming from homomorphisms…
We construct a canonical extension for strong proximity lattices in order to give an algebraic, point-free description of a finitary duality for stably compact spaces. In this setting not only morphisms, but also objects may have distinct…
We prove that the Lipschitz free space over a certain type of discrete metric space has the Radon-Nikod\'ym property. We also show that the Lipschitz free space over a complete, locally compact metric space has the Schur or approximation…
In this paper, we study a classical construction of lattices from number fields and obtain a series of new results about their minimum distance and other characteristics by introducing a new measure of algebraic numbers. In particular, we…
We survey recent progress on three relevant instances of free objects related to Banach spaces: Lipschitz free spaces generated by metric spaces, holomorphic free spaces generated by open sets and free Banach lattices generated by Banach…
For purposes of regularization as well as numerical simulation, the discretization of Lorentz invariant continuum field theories on a space-time lattice is often convenient. In general, this discretization destroys the rotational or…
In this paper we address the problem of finding well approximating lattices for a given finite set $A$ of points in ${\mathbb R}^n$. More precisely, we search for $\v{o},\v{d_1}, \dots,\v{d_n}\in \mathbb{R}^n$ such that $\v{a}-\v{o}$ is…
By relating the two-dimensional U(N) Principal Chiral Model to a simple linear system we obtain a free-field parametrisation of solutions. Obvious symmetry transformations on the free-field data give symmetries of the model. In this way all…
We report about a mechanism for surface localization, present in finite defect-free polyatomic lattices described by a tight binding model. Numerical diagonalization and degenerated perturbation theory show that there is a minimum number of…
We explore quantitative descriptors that herald when a many-particle system in $d$-dimensional Euclidean space $\mathbb{R}^d$ approaches a hyperuniform state as a function of the relevant control parameter. We establish quantitative…
Graphity models are characterized by configuration spaces in which states correspond to graphs and Hamiltonians that depend on local properties of graphs such as the degrees of vertices and numbers of short cycles. As statistical systems,…
We show that finite rank perturbations of certain random matrices fit in the framework of infinitesimal (type B) asymptotic freeness. This can be used to explain the appearance of free harmonic analysis (such as subordination functions…
Matter interacting classically with gravity in 3+1 dimensions usually gives rise to a continuum of degrees of freedom, so that, in any attempt to quantize the theory, ultraviolet divergences are nearly inevitable. Here, we investigate…