Related papers: Algebraic Approach to Interacting Quantum Systems
Various aspects of the theory of quantum integrable systems are reviewed. Basic ideas behind the construction of integrable ultralocal and nonultralocal quantum models are explored by exploiting the underlying algebraic structures related…
The mathematical formalism of quantum mechanics has been successfully employed in the last years to model situations in which the use of classical structures gives rise to problematical situations, and where typically quantum effects, such…
Ising models, and the physical systems described by them, play a central role in generating entangled states for use in quantum metrology and quantum information. In particular, ultracold atomic gases, trapped ion systems, and Rydberg atoms…
This chapter provides an introduction to the use of diagrammatic language, or perhaps more accurately, diagrammatic calculus, in quantum information and quantum foundations. We illustrate the use of diagrammatic calculus in one particular…
In this work, we have studied classical and quantum systems in interaction by means of geometric reduction procedure. The main target is the description in these terms of fundamental interactions. We have shown that, to describe in a…
We develop a model describing long-range atom-atom interactions in a two-dimensional periodic or a-periodic lattice of optical centers considering spectral and spatial broadening effects. Using both analytical and numerical Green's function…
We introduce and investigate the concept of Stratified Algebra, a new algebraic framework equipped with a layer-based structure on a vector space. We formalize a set of axioms governing intra-layer and inter-layer interactions, study their…
In quantum mechanical many-body systems, long-range and anisotropic interactions promote rich spatial structure and can lead to quantum frustration, giving rise to a wealth of complex, strongly correlated quantum phases. Long-range…
We introduce an elementary quantum system consisting of a set of spins on a graph and a particle hopping between its nodes. The quantum state is build sequentially, applying a unitary transformation that couples neighboring spins and, at a…
According to the stochastic-quantum correspondence, a quantum system can be understood as a stochastic process unfolding in an old-fashioned configuration space based on ordinary notions of probability and `indivisible' stochastic laws,…
Atomic planar arrays offer a novel emerging quantum-optical many-body system in which light mediates strong interactions between the atoms. The regular lattice structure provides a cooperatively enhanced light-matter coupling and allows for…
A system of quantum reasoning for a closed system is developed by treating non-relativistic quantum mechanics as a stochastic theory. The sample space corresponds to a decomposition, as a sum of orthogonal projectors, of the identity…
Physical systems, characterized by an ensemble of interacting elementary constituents, can be represented and studied by different algebras of observables or operators. For example, a fully polarized electronic system can be investigated by…
We show that the stochastic dynamics of a large class of one-dimensional interacting particle systems may be presented by integrable quantum spin Hamiltonians. Using the Bethe ansatz and similarity transformations this yields new exact…
Precise rules are developed in order to formalize the reasoning processes involved in standard non-relativistic quantum mechanics, with the help of analogies from classical physics. A classical or quantum description of a mechanical system…
Any particular classical system and its quantum version are normally viewed as separate formulations that are strictly distinct. Our goal is to overcome the two separate languages and create a smooth and common procedure that provides a…
When two or more subsystems of a quantum system interact with each other they can become entangled. In this case the individual subsystems can no longer be described as pure quantum states. For systems with only 2 subsystems this…
The rigorous approach aimed at providing exact analytical results for hybrid classical-quantum models is elaborated on the grounds of generalized algebraic mapping transformations. This conceptually simple method allows one to obtain novel…
A new (in)finite dimensional algebra which is a fundamental dynamical symmetry of a large class of (continuum or lattice) quantum integrable models is introduced and studied in details. Finite dimensional representations are constructed and…
Quantum systems inside high-Q cavities offer an excellent testbed for the control of emergent symmetries induced by light and their interplay with quantum matter. Recently several developments in cavity experiments with neutral atoms and…