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Motivated by recent results concerning the asymptotic behaviour of differential operators with highly contrasting coefficients, which have involved effective descriptions involving generalised resolvents, we construct the functional model…
For a bi-partite quantum system defined in a finite dimensional Hilbert space we investigate in what sense entanglement change and interactions imply each other. For this purpose we introduce an entanglement operator, which is then shown to…
We propose a dynamical toy model of agents which possess a quantity and have an interaction radius depending on the amount of the quantity. They exchange the quantity with agents existing within their interaction radii. It is shown in the…
The intermediate scattering function is interpreted as a correlation function of thermal wave packets of the scattering centers perturbed by the scattering particles at different times. A proof of concept is given at the example of…
This book presents a detailed study of a system of interacting Brownian motions in one dimension. The interaction is point-like such that the $n$-th Brownian motion is reflected from the Brownian motion with label $n-1$. This model belongs…
In this paper, we introduce a new method for the task of interaction transfer. Given an example interaction between a source object and an agent, our method can automatically infer both surface and spatial relationships for the agent and…
The isotropic XY model $(s=1/2)$ in a transverse field, with uniform long-range interactions among the transverse components of the spins, on the inhomogeneous periodic chain, is studied. The model, composed of $N$ segments with $n$…
This paper proposes a step toward obtaining general models of knowledge for facial analysis, by addressing the question of multi-source transfer learning. More precisely, the proposed approach consists in two successive training steps: the…
Models in which causation arises from higher level structures as well as from microdynamics may be relevant to unifying quantum theory with classical physics or general relativity. They also give a way of defining a form of panprotopsychist…
We analyze work done on a quantum system driven by a control field. The average work depends on the whole dynamics of the system, and is obtained as the integral of the average power operator. As a specific example we focus on a…
I describe a toy model of quantum measurement in which wave function collapse is described as a stochastic entropically-driven event guided by interactions between a measured two-state particle and an Ising-like measurement device. The…
Systems switching between different dynamical phases is an ubiquitous phenomenon. The general understanding of such a process is limited. To this end, we present a general expression that captures fluctuations of a system exhibiting a…
Spatio-temporal extensions of familiar compartment models for disease transmission incorporating diffusive behavior, or interactions between individuals at separate locations, are explored. The models considered have the character of…
We study quantum intergrable systems of interacting particles from the point of view, proposed in our previous paper. We obtain Calogero-Moser and Sutherland systems as well their Ruijsenaars relativistic generalization by a Hamiltonian…
Real-world systems are characterized by complex interactions of their internal degrees of freedom, while living in ever-changing environments whose net effect is to act as additional couplings. Here, we introduce a paradigmatic interacting…
We consider a generalization of the weighted random ball model. The model is driven by a random Poisson measure with a product heavy tailed intensity measure. Such a model typically represents the transmission of a network of stations with…
New functional representation for the strongly interacting systems is proposed which contains a new type of the quantum coherent state. As a result the new algebraic structure- so called "tower of algebras" appears which gives the tower (or…
We study a system of functional relations among a commuting family of row-to-row transfer matrices in solvable lattice models. The role of exact sequences of the finite dimensional quantum group modules is clarified. We find a curious…
We study causal self-attention dynamics -- a toy model for decoder Transformers -- which we interpret as a non-exchangeable interacting particle system. Adapting cumulant expansions to the triangular causal dependency structure of the…
Scattering processes in high-energy physics are inherently quantum mechanical, yet are typically analyzed at the level of final states, where entanglement appears as a property of the outcome rather than a consequence of the underlying…