Related papers: Correlation functions of integrable models: a desc…
We construct integrable generalised models in a systematic way exploring different representations of the gl(N) algebra. The models are then interpreted in the context of atomic and molecular physics, most of them related to different types…
Models defined by stochastic differential equations (SDEs) allow for the representation of random variability in dynamical systems. The relevance of this class of models is growing in many applied research areas and is already a standard…
We derive a new representation for spin-spin correlation functions of the finite XXZ spin-1/2 Heisenberg chain in terms of a single multiple integral, that we call the master equation. Evaluation of this master equation gives rise on the…
Finite temperature correlation functions in integrable quantum field theories are formulated only in terms of the usual, temperature-independent form factors, and certain thermodynamic filling fractions which are determined from the…
Cluster Perturbation Theory (CPT) is a computationally economic method commonly used to estimate the momentum and energy resolved single-particle Green's function. It has been used extensively in direct comparisons with experiments that…
A new one-dimensional fermion model depending on two independent interaction parameters is formulated and solved exactly by the Bethe ansatz method. The Hamiltonian of the model contains the Hubbard interaction and correlated hopping as…
The model describing interaction between two-level atoms and a single mode field in an optical cavity enclosed by a medium with Kerr nonlinearity is considered in our paper. We study the model within the framework of the analytical solution…
Correlation functions, such as static and dynamic structure factors, offer a versatile approach to analyzing atomic-scale structure and dynamics. By having access to the full dynamics from atomistic simulations, they serve as valuable tools…
We consider topological dynamical systems over $\ZZ$ and, more generally, locally compact, $\sigma$-compact abelian groups. We relate spectral theory and diffraction theory. We first use a a recently developed general framework of…
Analytical results on the correlation functions of strongly correlated many-body systems are rare in the literature and their importance cannot be overstated. We present determinant representations for the space-, time-, and…
Capsule networks (see e.g. Hinton et al., 2018) aim to encode knowledge and reason about the relationship between an object and its parts. In this paper we specify a \emph{generative} model for such data, and derive a variational algorithm…
To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…
We give a pedagogical introduction to the thermodynamic Bethe ansatz, a method that allows us to describe the thermodynamics of integrable models whose spectrum is found via the (asymptotic) Bethe ansatz. We set the stage by deriving the…
Theoretical models of spins coupled to bosons provide a simple setting for studying a broad range of important phenomena in many-body physics, from virtually mediated interactions to decoherence and thermalization. In many atomic,…
We study the dynamics of a single spin-1/2 coupled to a bath of spins-1/2 by inhomogeneous Heisenberg couplings including a central magnetic field. This central-spin model describes decoherence in quantum bit systems. An exact formula for…
We develop a transfer matrix method to compute exactly the spin-spin correlation functions of Bethe lattice spin models in the external magnetic field h and for any temperature T. We first compute the correlation function for the most…
We review recent progress in the lattice investigations of near-conformal non-abelian gauge theories relevant for dynamical symmetry breaking and model building of composite Higgs models. The emphasis is placed on the mass spectrum and the…
By putting together an abstract view on quantum mechanics and a quantum-optics picture of the interactions of an atom with light, we develop a corresponding set of C++ classes that set up the numerical analysis of an atom with an arbitrary…
A new symplectic time-reversible algorithm for numerical integration of the equations of motion in magnetic liquids is proposed. It is tested and applied to molecular dynamics simulations of a Heisenberg spin fluid. We show that the…
We give exact formulae for a wide family of complexity measures that capture the organization of hidden nonlinear processes. The spectral decomposition of operator-valued functions leads to closed-form expressions involving the full…