相关论文: Interacting and noninteracting integrable systems

Observability is a modelling property that describes the possibility of inferring the internal state of a system from observations of its output. A related property, structural identifiability, refers to the theoretical possibility of…

Hallmarks of quantum mechanics include superposition and entanglement. In the context of large complex systems, these features should lead to situations like Schrodinger's cat, which exists in a superposition of alive and dead states…

We study the effect of inter-component interactions on the dynamical properties of quantum walkers. We consider the simplest situation of two indistinguishable non-interacting walkers on a tilted optical lattice interacting with a walker…

We provide a description of interacting quantum fields in terms of density matrices for any occupation numbers in Fock space in a momentum basis. As a simple example, we focus on a real scalar field interacting with another real scalar…

We investigate the finite and large $N$ behaviors of independent-value O(N)-invariant matrix models. These are models defined with matrix-type fields and with no gradient term in their action. They are generically nonrenormalizable but can…

Quantum dynamics of integrable systems is discussed. Localized wave packets generalizing the conventional coherent states of minimal uncertainty are constructed. The wave packet moves along a certain trajectory and does not change its shape…

We study a family of integrable systems of nonlinearly coupled harmonic oscillators on the classical and quantum levels. We show that the integrability of these systems follows from their symmetry characterized by algebras called here…

A method allowing to distinguish interacting from non-interacting systems based on available time series is proposed and investigated. Some facts concerning generalized Renyi dimensions that form the basis of our method are proved. We show…

The incoherent dynamical properties of open quantum systems are generically attributed to an ongoing correlation between the system and its environment. Here, we propose a novel way to assess the nature of these system-environment…

The integrability has been playing an essential role in the field of differential equations. This property may better help us obtain the topological structure and even the global dynamics for the considered system. A system is called…

We propose a topological order parameter for interacting topological insulators, expressed in terms of the full Green's functions of the interacting system. We show that it is exactly quantized for a time reversal invariant topological…

We consider parameterized concurrent systems consisting of a finite but unknown number of components, obtained by replicating a given set of finite state automata. Components communicate by executing atomic interactions whose participants…

In this PhD thesis we investigate some properties of one-dimensional quantum systems, focusing on two important aspects of integrable models: Their entanglement properties at equilibrium and their dynamical correlators after a quantum…

A combinatorial characterization of measurable filters on a countable set is found. We apply it to the problem of measurability of the intersection of nonmeasurable filters.

Constrained Hamiltonian dynamics of a quantum system of nonlinear oscillators is used to provide the mathematical formulation of a coarse-grained description of the quantum system. It is seen that the evolution of the coarse-grained system…

In this paper we study the general concept of integrability in the broad sense within the frame of differential Galois theory. We concentrate on the gradient systems which are not integrable. In spite of it, if we consider them as the real…

In this article we present a full description of the quantum Kerr Ising model---a linear optical network of parametrically pumped Kerr non-linearities. We consider the non-dissapative Kerr Ising model and, using variational techniques, show…

We consider interacting particle systems with unbounded interaction range on general countably infinite graphs $S$ and prove explicit non-asymptotic error bounds for approximations of the infinite-volume dynamics by systems of finitely many…

The electromagnetic interaction is characterised by discrete states for bound systems in contrast to continuous states for unbound systems. The difference merely arises because the characteristic equations do not exhibit the same behaviour…

We provide an explicit construction of entangled states in a noncommutative space with nonclassical states, particularly with the squeezed states. Noncommutative systems are found to be more entangled than the usual quantum mechanical…