Related papers: The geometrically broken object
We sketch a new framework for the analysis of disordered systems, in particular mean field spin glasses, which is variational in nature and within the formalism of classical thermodynamics. For concreteness, only the Sherrington-Kirkpatrick…
The effect of quantum collapse and revival is a fascinating interference phenomenon. In this paper the phenomenon is demonstrated analytically and numerically for a simple system, a slightly anharmonic Hamiltonian. The initial wave-function…
Complex fission phenomena are studied in a unified way. Very general reflection asymmetrical equilibrium (saddle point) nuclear shapes are obtained by solving an integro-differential equation without being necessary to specify a certain…
We consider the dynamics of an arbitrary quantum system coupled to a large arbitrary and fully quantum mechanical environment through a random interaction. We establish analytically and check numerically the typicality of this dynamics, in…
A simple geometrical model is presented for the gravity-driven motion of a single particle on a rough inclined surface. Adopting a simple restitution law for the collisions between the particle and the surface, we arrive at a model in which…
We present a variationally separable splitting technique for the generalized-$\alpha$ method for solving parabolic partial differential equations. We develop a technique for a tensor-product mesh which results in a solver with a linear cost…
We show that the size distributions of fragments created by high energy nuclear collisions are remarkably well reproduced within the framework of a parameter free percolation model. We discuss two possible scenarios to explain this…
We present a new route to ergodicity breaking via Hilbert space fragmentation that displays an unprecedented level of robustness. Our construction relies on a single emergent (prethermal) conservation law. In the limit when the conservation…
The paper presents a versatile framework for solids which undergo nonisothermal processes with irreversibly changing microstructure at large strains. It outlines rate-type and incremental variational principles for the full thermomechanical…
Perhaps the most important aspect of symmetry in physics is the idea that a state does not need to have the same symmetries as the theory that describes it. This phenomenon is known as spontaneous symmetry breaking. In these lecture notes,…
We design three dimensional electromagnetic cloaks, starting from a small region of complex shape instead of a point. We derive the expression of a transformation matrix describing an objet with a surface of revolution and its associated…
We prove the existence of spontaneous symmetry breaking in suitably low-energy eigenstates of certain gapless and frustrated many-body quantum systems, namely symmetric quantum perturbations to classical models which exhibit spontaneous…
The modeling of damage processes in materials constitutes an ill-posed mathematical problem which manifests in mesh-dependent finite element results. The loss of ellipticity of the discrete system of equations is counteracted by…
A model of the thin shell expanding into a uniform ambient medium is developed. Density perturbations are described using equations with linear and quadratic terms, and the linear and the nonlinear solutions are compared. We follow the time…
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…
The nature of polyamorphism and amorphous-to-amorphous transition is investigated by means of an exactly solvable model with quenched disorder, the spherical s+p multi-spin interaction model. The analysis is carried out in the framework of…
We consider numerical solution of elliptic problems with heterogeneous diffusion coefficients containing thin highly conductive structures. Such problems arise e.g. in fractured porous media, reinforced materials, and electric circuits. The…
Random shapes arise naturally in many contexts. The topological and geometric structure of such objects is interesting for its own sake, and also for applications. In physics, for example, such objects arise naturally in quantum gravity, in…
Dissipative phenomena manifest in multiple mechanical systems. In this dissertation, different geometric frameworks for modelling non-conservative dynamics are considered. The objective is to generalize several results from conservative…
We investigate the overdamped stochastic dynamics of a particle in an asymptotically flat external potential field, in contact with a thermal bath. For an infinite system size, the particles may escape the force field and diffuse freely at…