Related papers: Algebraic Approach to Interacting Quantum Systems
We describe quantum and classical Hamiltonian dynamics in a common Hilbert space framework, that allows the treatment of mixed quantum-classical systems. The analysis of some examples illustrates the possibility of entanglement between…
We construct some new Integrable Systems (IS) both classical and quantum associated with elliptic algebras. Our constructions are partly based on the algebraic integrability mechanism given by the existence of commuting families in skew…
As the field of quantum physics evolves, researchers naturally form subgroups focusing on specialized problems. While this encourages in-depth exploration, it can limit the exchange of ideas across structurally similar problems in different…
Interactions in complex systems are widely observed across various fields, drawing increased attention from researchers. In mathematics, efforts are made to develop various theories and methods for studying the interactions between spaces.…
Interacting systems are ubiquitous in nature and engineering, ranging from particle dynamics in physics to functionally connected brain regions. These interacting systems can be modeled by graphs where edges correspond to the interactions…
Theoretical and computational frameworks of modern science are dominated by binary structures. This binary bias, seen in the ubiquity of pair-wise networks and formal operations of two arguments in mathematical models, limits our capacity…
The quantum mechanics formalism introduced new revolutionary concepts challenging our everyday perceptions. Arguably, quantum entanglement, which explains correlations that cannot be reproduced classically, is the most notable of them.…
In this Thesis we examine the interplay between the encoding of information in quantum systems and their geometrical and topological properties. We first study photonic qubit probes of space-time curvature, showing how gauge-independent…
In the previous article, we presented a quantum-inspired framework for modeling semantic representation and processing in Large Language Models (LLMs), drawing upon mathematical tools and conceptual analogies from quantum mechanics to offer…
Full formal descriptions of algorithms making use of quantum principles must take into account both quantum and classical computing components and assemble them so that they communicate and cooperate. Moreover, to model concurrent and…
We systematise and develop a graphical approach to the investigations of quantum integrable vertex statistical models and the corresponding quantum spin chains. The graphical forms of the unitarity and various crossing relations are…
We present an algebraic study of a kind of quantum systems belonging to a family of superintegrable Hamiltonian systems in terms of shape-invariant intertwinig operators, that span pairs of Lie algebras like $(su(n),so(2n))$ or…
We propose a semiclassical framework for solving open quantum dynamics in driven-dissipative spin systems. Our method consists of generalized spin-wave approximations tailored to describing quantum trajectories unravelled from the master…
We give complete presentations for the dagger-compact props of affine Lagrangian and coisotropic relations over an arbitrary field. This provides a unified family of graphical languages for both affinely constrained classical mechanical…
This paper is a physicist's review of the major conceptual issues concerning the problem of spectral universality in quantum systems. Here we present a unified, graph-based view of all archetypical models of such universality (billiards,…
This work exploits a framework whereby a graph (in the mathematical sense) serves to connect a classical system to a state space that we call `quantum-like' (QL). The QL states comprise arbitrary superpositions of states in a tensor product…
In this paper we present an alternative approach to formalize the theory of logic programming. In this formalization we allow existential quantified variables and equations in queries. In opposite to standard approaches the role of answer…
The regular structures obtained by optical lattice technology and their behaviour are analysed from the quantum information perspective. Initially, we demonstrate that a triangular optical lattice of two atomic species, bosonic or…
We present the elements of a new approach to the foundations of quantum theory and probability theory which is based on the algebraic approach to integration, information geometry, and maximum relative entropy methods. It enables us to deal…
A hallmark of the computational campaign in nuclear and particle physics is the lattice-gauge-theory program. It continues to enable theoretical predictions for a range of phenomena in nature from the underlying Standard Model. The…