Related papers: Boundary effects on localized structures in spatia…
The scope of this Ph.D thesis is to study the effects of the presence of a boundary from a Quantum Field Theoretical perspective, searching for new physics and explanations of observed phenomena. In particular, thanks to the formal QFT…
Topological phases of matter have been widely studied for their robustness against impurities and disorder. The broad applicability of topological materials relies on the reliable transition from idealized, mathematically perfect models to…
We consider an instationary macroscopic system of self-interacting particles with an additional potential, the so called Bohm's potential. We study the existence of non-negative global solutions to the (4-th order) system of equations and…
Mobility edge transitions from localized to extended states have been observed in two and three dimensional systems, for which sound theoretical explanations have also been derived. One-dimensional lattice models have failed to predict…
The energy method can be used to identify well-posed initial boundary value problems for quasi-linear, symmetric hyperbolic partial differential equations with maximally dissipative boundary conditions. A similar analysis of the discrete…
We present a theory of viscoelasticity of amorphous media, which takes into account the effects of confinement along one of three spatial dimensions. The framework is based on the nonaffine extension of lattice dynamics to amorphous…
We study smoothness of generalized solutions of nonlocal elliptic problems in plane bounded domains with piecewise smooth boundary. The case where the support of nonlocal terms can intersect the boundary is considered. We find conditions…
A modification of General Relativity that is based on the gravitational Standard-Model Extension and incorporates nondynamical background fields has recently been studied via the ADM formalism. Our objective in this paper is to develop a…
The ensemble-switch method for computing wall excess free energies of condensed matter is extended to estimate the interface free energies between coexisting phases very accurately. By this method, system geometries with linear dimensions…
We analyze the quantum dynamics of a non-relativistic particle moving in a bounded domain of physical space, when the boundary conditions are rapidly changed. In general, this yields new boundary conditions, via a dynamical composition law…
Pattern formation often occurs in confined systems, yet how boundaries shape patterning dynamics is unclear. We develop techniques to analyze confinement effects in nonlocal advection-diffusion equations, which generically capture the…
We study $s$-wave superconductivity in hyperbolic spaces using the Bogoliubov-de Gennes theory for discrete hyperbolic lattices and the Ginzburg-Landau theory for the continuous hyperbolic plane. Hyperbolic lattices maintain a finite…
Critical fluctuations of some order parameter describing a fluid generates long-range forces between boundaries. Here, we discuss fluctuation-induced forces associated to a disordered Landau-Ginzburg model defined in a $d$-dimensional slab…
We develop a rigorous theory of external influences on finite discrete dynamical systems, going beyond the perturbation paradigm, in that the external influence need not be a small contribution. Indeed, the covariance condition can be…
These lecture notes focus on the application of ideas of locality, in particular Lieb-Robinson bounds, to quantum many-body systems. We consider applications including correlation decay, topological order, a higher dimensional…
In this chapter we review recent results concerning localized and extended dissipative solutions of the discrete complex Ginzburg-Landau equation. In particular, we discuss discrete diffraction effects arising both from linear and nonlinear…
In this paper we study the time-dependent Ginzburg-Landau equations on a smooth, bounded domain $\Omega \subset \Rn{2}$, subject to an electrical current applied on the boundary. The dynamics with an applied current are non-dissipative, but…
Equations built on fractional derivatives prove to be a powerful tool in the description of complex systems when the effects of singularity, fractal supports, and long-range dependence play a role. In this paper, we advocate an application…
We consider the spectral and dynamical properties of quantum systems of $n$ particles on the lattice $\Z^d$, of arbitrary dimension, with a Hamiltonian which in addition to the kinetic term includes a random potential with iid values at the…
The interest in the topological properties of materials brings into question the problem of topological phase transitions. As a control parameter is varied, one may drive a system through phases with different topological properties. What…