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A convenient algebraic structure to describe some forms of dynamics of two hamiltonian systems with nonpotential (magnetic--type) interaction is considered. An algebraic mechanism of generation of such dynamics is explored on simple "toy"…
Interacting and open quantum systems can be formulated in terms of an effective non-Hermitian Hamiltonian (NHH), however, there are important constraints that must be satisfied by the effective action and the associated Green's functions.…
The thermodynamics and the dynamics of particle systems with infinite-range coupling display several unusual and new features with respect to systems with short-range interactions. The Hamiltonian Mean Field (HMF) model represents a…
This work concerns control-oriented and structure-preserving learning of low-dimensional approximations of high-dimensional physical systems, with a focus on mechanical systems. We investigate the integration of neural autoencoders in model…
This thesis investigates the interactions of different degrees of freedom of one joint system within the theory of stochastic thermodynamics. First, a comprehensive introduction to the subjects of stochastic processes, information theory…
A direct classical analog of the quantum dynamics of intrinsic decoherence in Hamiltonian systems, characterized by the time dependence of the linear entropy of the reduced density operator, is introduced. The similarities and differences…
We develop an efficient and robust approach to Hamiltonian identification for multipartite quantum systems based on the method of compressed sensing. This work demonstrates that with only O(s log(d)) experimental configurations, consisting…
Elastomeric mechanical metamaterials exhibit unconventional behaviour, emerging from their microstructures often deforming in a highly nonlinear and unstable manner. Such microstructural pattern transformations lead to non-local behaviour…
We investigate the emergence of rigid polycrystalline structures from atomistic particle systems. The atomic interaction is governed by a suitably normalized pair interaction energy, where the `sticky disk' interaction potential models the…
We consider nonequilibrium transport in a simple chain of identical mechanical cells in which particles move around. In each cell, there is a rotating disc, with which these particles interact, and this is the only interaction in the model.…
We combine experiments and numerical simulations to investigate the emergence of clogging in a system of interacting paramagnetic colloidal particles driven against a disordered landscape of larger obstacles. We consider a single aperture…
We give a mathematical framework to describe the evolution of an open quantum systems subjected to finitely many interactions with classical apparatuses. The systems in question may be composed of distinct, spatially separated subsystems…
In this study, Lagrangian and Hamiltonian systems, which are mathematical models of mechanical systems, were introduced on the horizontal and the vertical distributions of tangent and cotangent bundles. Finally, some geometrical and…
We introduce an alternative way to understand the decomposition of a quantum system into interacting parts and show that it is natural in several physical models. This enables us to define a reduced density operator for a working system…
Interaction of a two-level atom with a single mode of electromagnetic field including Kerr nonlinearity for the field and intensity-dependent atom-field coupling is discussed. The Hamiltonian for the atom-field system is written in terms of…
We describe a numerical algorithm for approximating the equilibrium-reduced density matrix and the effective (mean force) Hamiltonian for a set of system spins coupled strongly to a set of bath spins when the total system (system+bath) is…
We present a structure-preserving discretization of the hybrid magnetohydrodynamics (MHD)-driftkinetic system for simulations of low-frequency wave-particle interactions. The model equations are derived from a variational principle,…
With the development of low order scaling methods for performing Kohn-Sham Density Functional Theory, it is now possible to perform fully quantum mechanical calculations of systems containing tens of thousands of atoms. However, with an…
Interference dynamics is analyzed in the light of the complex quantum Hamilton-Jacobi formalism, using as a working model the collision of two Gaussian wave packets. Though simple, this model nicely shows that interference in quantum…
Alignment interactions in active matter are typically modeled as relaxational dynamics toward local consensus. In unbounded systems, this makes alignment effectively decoupled from local density and therefore unable to sustain self-confined…