Related papers: Classical and Quantized Affine Models of Structure…
Localized patterns are coherent structures embedded in a quiescent state and occur in both discrete and continuous media across a wide range of applications. While it is well-understood how domain covering patterns (for example stripes and…
Models which allow an explicit application to structurally modulated substances are reviewed within the frame of a symmetry-based approach starting from discrete lattice theory. Focus is set on models formulated in terms of local variables…
This is a short introduction to affine and convex spaces, written especially for physics students. It summarizes different elementary presentations available in the mathematical literature, and blends analytic- and geometric-flavoured…
Canonical quantization covers a broad class of classical systems, but that does not include all the problems of interest. Affine quantization has the benefit of providing a successful quantization of many important problems including the…
This paper is devoted to constructing and studying exactly solvable dynamical systems in discrete time obtained from some algebraic operations on matrices, to reductions of such systems leading to classical field theory models in…
We consider the application of deep generative models in propagating uncertainty through complex physical systems. Specifically, we put forth an implicit variational inference formulation that constrains the generative model output to…
This paper aims at presenting a few models of quantum dynamics whose description involves the analysis of random unitary matrices for which dynamical localization has been proven to hold. Some models come from physical approximations…
Neuromorphic control is receiving growing attention due to the multifaceted advantages it brings over more classical control approaches, including: sparse and on-demand sensing, information transmission, and actuation; energy-efficient…
Dynamics of the structured particles consisting of potentially interacting material points is considered in the framework of classical mechanics. Equations of interaction and motion of structured particles have been derived. The expression…
We describe a $q$-deformed dynamical system corresponding to the quantum free particle moving along the circle. The algebra of observables is constructed and discussed. We construct and classify irreducible representations of the system.
Till now, the foundation of quantum physics is still mysterious. To explore the mysteries in the foundation of quantum physics, people always take it for granted that quantum processes must be some types of fields/objects on a rigid space.…
Bimetric variational formalism was recently employed to construct novel bimetric gravity models. In these models an affine connection is generated by an additional tensor field which is independent of the physical metric. In this work we…
Classical dynamical density functional theory (DDFT) has become one of the central modeling approaches in nonequilibrium soft matter physics. Recent years have seen the emergence of novel and interesting fields of application for DDFT. In…
We discuss a new approach to the problem of quantum gravity in which the quantum mechanical structures that are traditionally fixed, such as the Fubini-Study metric in the Hilbert space of states, become dynamical and so implement the idea…
We introduce a quantum generalization of classical kinetic Ising models, described by a certain class of quantum many body master equations. Similarly to kinetic Ising models with detailed balance that are equivalent to certain Hamiltonian…
Gauge invariance in discrete dynamical systems and its connection with quantization are considered. For a complete description of gauge symmetries of a system we construct explicitly a class of groups unifying in a natural way the space and…
We introduce closed-form transition density expansions for multivariate affine jump-diffusion processes. The expansions rely on a general approximation theory which we develop in weighted Hilbert spaces for random variables which possess…
We study the dynamics of classical and quantum particles with spin and dipole moments in external fields within the framework of the general approach by making use of the projection technique. Applications include the neutrino physics in…
Basic issues of the general model-building framework of the mechanics of complex bodies are discussed. Attention is focused on the representation of the material elements, the conditions for the existence of ground states in conservative…
Dynamics of systems of structured particles consisting of potentially interacting material points is considered in the framework of classical mechanics. Equations of interaction and motion of structured particles have been derived. The…