Related papers: Topological defects, fractals and the structure of…
The concept of discrepancy plays an important role in the study of uniformity properties of point sets. For sets of random points, the discrepancy is a random variable. We apply techniques from quantum field theory to translate the problem…
Topological defects (TDs) are crucial for understanding important physical properties of crystalline materials including mechanical failure, ion transport, and two-dimensional melting. This concept has not translated to disordered materials…
The study of topology in solids is undergoing a renaissance following renewed interest in the properties of ferroic domain walls as well as recent discoveries regarding topological insulators and skyrmionic lattices. Each of these systems…
We extend effective field theory to the case of spontaneous symmetry breaking in genuinely finite quantum systems such as small superfluid systems, molecules or atomic nuclei, and focus on deformed nuclei. In finite superfluids, symmetry…
We study the nonequilibrium dynamics leading to the formation of topological defects in a symmetry-breaking phase transition of a quantum scalar field with \lambda\Phi^4 self-interaction in a spatially flat, radiation-dominated…
We review some aspects of the relation between ordinary coherent states and q-deformed generalized coherent states with some of the simplest cases of quantum Lie algebras. In particular, new properties of (q-)coherent states are utilized to…
The topic of the review is the application of new ideas of unconventional quantum states to the physics of condensed matter, in particular of solid state, in the context of modern field theory. A comparison is made with classical papers on…
The q-deformed coherent states for a quantum particle on a circle are introduced and their properties investigated.
We study quantum chaos in open dynamical systems and show that it is characterized by quantum fractal eigenstates located on the underlying classical strange repeller. The states with longest life times typically reveal a scars structure on…
This report provides a brief review of recently developed extended framework for fundamental physics, designated as Quantum Field Mechanics and including causally complete and intrinsically unified theory of explicitly emerging elementary…
We investigate the global structure of topological defects which wrap a submanifold $F\subset M$ in a quantum field theory defined on a closed manifold $M$. The Pontryagin-Thom construction oversees the interplay between the global…
In the first one of these two lectures, I give an introductory review of phase transitions in finite temperature field theories. I highlight the differences between theories with global and local symmetries, and the similarities between…
We show how conformal field theory topological defects can relate solutions of open string field theory for different boundary conditions. To this end we generalize the results of Graham and Watts to include the action of defects on…
Topological defects and smooth excitations determine the properties of systems showing collective order. We introduce a generic non-singular field theory that comprehensively describes defects and excitations in systems with $O(n)$ broken…
We propose a unifying mathematical framework describing the higher categorical structures formed by topological defects in quantum field theory equipped with tangential structures, such as orientations, framings, or…
The convenience of coherent state representation is discussed from the viewpoint of what is in a broad sense called the measurement problem in quantum mechanics. Standard quantum theory in coherent state representation is intrinsically…
Current theories of particle physics lead to the unavoidable conclusion that there must have been several phase transitions in the early universe. Further, in the context of these theories, it is possible that cosmological phase transitions…
These notes offer an introduction to the functorial and algebraic description of 2-dimensional topological quantum field theories `with defects', assuming only superficial familiarity with closed TQFTs in terms of commutative Frobenius…
Conformal defects -- extended objects in conformal field theories -- carry localised excitations inherited from symmetry currents, known as the displacements and tilts. They capture the linear response of the defect to deformations of its…
We study the behaviour of a nonrelativistic quantum particle interacting with different potentials in the spacetimes of topological defects. We find the energy spectra and show how they differ from their free-space values.