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When quantum back-reaction by fluctuations, correlations and higher moments of a state becomes strong, semiclassical quantum mechanics resembles a dynamical system with a high-dimensional phase space. Here, systematic computational methods…
Network science has evolved into an indispensable platform for studying complex systems. But recent research has identified limits of classical networks, where links connect pairs of nodes, to comprehensively describe group interactions.…
We define bipartite and monopartite relational networks of chemical elements and compounds using two different datasets of inorganic chemical and material compounds, as well as study their topology. We discover that the connectivity between…
When particles interact via two-body short-range central potential wells, binding can occur for some critical values of the coupling constants. Using the envelope theory, upper bounds for critical coupling constants are computed for quantum…
When a massive quantum body is put into a spatial superposition, it is of interest to consider the quantum aspects of the gravitational field sourced by the body. We argue that in order to understand how the body may become entangled with…
The topological framework of circuit topology has recently been introduced to complement knot theory and to help in understanding the physics of molecular folding. Naturally evolved linear molecular chains, such as proteins and nucleic…
In this study, firstly, the k-th order extension of complex product manifold is consid- ered. Then the higher order vertical, complete lifts of geometric structures on product manifold to its extended spaces are given. Also higher order…
Gauge theories with compact symmetry groups possess topologically non-trivial configurations of gauge field. This has dramatic implications for the vacuum structure of Quantum Chromo-Dynamics (QCD) and for the behavior of QCD plasma, as…
In this review, we discuss the electronic structure of finite quantal systems on the nanoscale. After a few general remarks on the many-particle physics of the harmonic oscillator -- likely being the most studied example for the many-body…
With any state of a multipartite quantum system its separability polytope is associated. This is an algebro-topological object (non-trivial only for mixed states) which captures the localisation of entanglement of the state. Particular…
A general inequality between entanglement entropy and a number of topologically ordered states is derived, even without using the properties of the parent Hamiltonian or the formalism of topological quantum field theory. Given a quantum…
Higher-order interactions that nonlinearly couple more than two nodes are important in many networked systems, and their effects on collective dynamics are increasingly being studied. Here we provide an overview of this rapidly growing…
Quantum link models are extensions of Wilson-type lattice gauge theories which realize exact gauge invariance with finite-dimensional Hilbert spaces. Quantum link models not only reproduce the standard features of Wilson's lattice gauge…
It has long been thought that strongly correlated systems are adiabatically connected to their noninteracting counterpart. Recent developments have highlighted the fallacy of this traditional notion in a variety of settings. Here we use a…
Motivated by a geometric decomposition of the vector field associated with the Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) equation for finite-level open quantum systems, we propose a generalization of the recently introduced contact…
We outline the basic ideas of the topological mechanisms of superconductivity. A gauged model of correlated electronic system where a topological fluid is formed as a result of a strong interaction is discussed.
The statistical mechanics of a long knotted collapsed polymer is determined by a free-energy with a knot-dependent subleading term, which is linked to the length of the shortest polymer that can hold such knot. The only other parameter…
Geometric quantum mechanics aims to express the physical properties of quantum systems in terms of geometrical features preferentially selected in the space of pure states. Geometric characterisations are given here for systems of one, two,…
The dynamical model on 3+1 dimensional spacetime admitting soliton solutions is discussed. The proposal soliton is localized in the vicinity of a closed contour, which could be linked and/or knotted. The topological charge is Hopf…
Topological physics opens a door towards flexible routing and resilient localization of waves of various nature. Recently proposed higher-order topological insulators provide advanced control over wave localization in the structures of…