相关论文: Geometrically Constrained Statistical Models on Fi…
Certain many-particle Hardy inequalities are derived in a simple and systematic way using the so-called ground state representation for the Laplacian on a subdomain of $\mathbb{R}^n$. This includes geometric extensions of the standard Hardy…
The application of geometry to physics has provided us with new insightful information about many physical theories such as classical mechanics, general relativity, and quantum geometry (quantum gravity). The geometry also plays an…
We study the asymptotic rank of adjacency matrices of a large class of edge-weighted configuration models. Here, the weight of a (multi-)edge can be any fixed non-zero element from an arbitrary field, as long as it is independent of the…
Standard Model determinations of properties of strongly interacting systems of hadrons have become possible with the powerful method of lattice quantum chromodynamics (LQCD), a method with growing applicability and reliability. While growth…
A periodic lattice in Euclidean space is the infinite set of all integer linear combinations of basis vectors. Any lattice can be generated by infinitely many different bases. This ambiguity was only partially resolved, but standard…
The quantum XY, Heisenberg, and transverse field Ising models on hyperbolic lattices are studied by means of the Tensor Product Variational Formulation algorithm. The lattices are constructed by tessellation of congruent polygons with…
Matrix models play an important role in studies of quantum gravity, being candidates for a formulation of M-theory, but are notoriously difficult to solve. In this work, we present a fresh approach by introducing a novel exact model…
We review models of random geometries based on the dynamical lattice approach. We discuss one dimensional model of simplicial complexes (branched polymers), two dimensional model of dynamical triangulations and four dimensional model of…
The random matrix ensembles are applied to the quantum statistical two-dimensional systems of electrons. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The…
The matrix product state formalism is used to simulate Hamiltonian lattice gauge theories. To this end, we define matrix product state manifolds which are manifestly gauge invariant. As an application, we study 1+1 dimensional one flavour…
Complex numbers enter fundamental physics in at least two rather distinct ways. They are needed in quantum theories to make linear differential operators into Hermitian observables. Complex structures appear also, through Hodge duality, in…
We consider the linear and quadratic higher order terms associated to the response of the statistical properties of a dynamical system to suitable small perturbations. These terms are related to the first and second derivative of the…
We propose an optical lattice setup to investigate spin chains and ladders. Electric and magnetic fields allow us to vary at will the coupling constants, producing a variety of quantum phases including the Haldane phase, critical phases,…
In this paper we demonstrate the use of multivariate topological algorithms to analyse and interpret Lattice Quantum Chromodynamics (QCD) data. Lattice QCD is a long established field of theoretical physics research in the pursuit of…
In the study of chaotic behaviour of systems of many hard spheres, Lyapunov exponents of small absolute value exhibit interesting characteristics leading to speculations about connections to non-equilibrium statistical mechanics. Analytical…
The full spectrum of transfer matrices of the general eight-vertex model on a square lattice is obtained by numerical diagonalization. The eigenvalue spacing distribution and the spectral rigidity are analyzed. In non-integrable regimes we…
A one dimensional lattice model is formulated to study tapping dynamics and the long time steady distribution in granular media. The dynamics conserves the number of particles in the system, and density changes are associated to the…
Lattice structures have great potential for several application fields ranging from medical and tissue engineering to aeronautical one. Their development is further speeded up by the continuing advances in additive manufacturing…
We investigate the properties of Lindblad equations on $d$-dimensional lattices supporting a unique steady-state configuration. We consider the case of a time evolution weakly symmetric under the action of a finite group $G$, which is also…
Lattice field theory methods, usually associated with non-perturbative studies of quantum chromodynamics, are becoming increasingly common in the calculation of ground-state and thermal properties of strongly interacting non-relativistic…