Related papers: Point interactions in a strip
We discuss of a ring-shaped soft quantum wire modeled by $\delta$ interaction supported by the ring of a generally nonconstant coupling strength. We derive condition which determines the discrete spectrum of such systems, and analyze the…
A variational approach for constructing an effective particle description of the low-energy physics of one-dimensional quantum spin chains is presented. Based on the matrix product state formalism, we compute the one- and two-particle…
In this paper, we consider the one-dimensional semirelativistic Schr\"{o}dinger equation for a particle interacting with $N$ Dirac delta potentials. Using the heat kernel techniques, we establish a resolvent formula in terms of an $N \times…
The unusual electronic properties of single-layer graphene make it a promising material system for fundamental advances in physics, and an attractive platform for new device technologies. Graphene's spin transport properties are expected to…
Inhomogeneities and junctions in wires are natural sources of scattering, and hence resistance. A conducting fixed point usually requires an adiabatically smooth system. One notable exception is "healing", which has been predicted in…
We construct models of many-particle quantum graphs with singular two-particle contact interactions, which can be either hardcore- or delta-interactions. Self-adjoint realisations of the two-particle Laplacian including such interactions…
We consider a 2D Schroedinger operator H0 with constant magnetic field, on a strip of finite width. The spectrum of H0 is absolutely continuous, and contains a discrete set of thresholds. We perturb H0 by an electric potential V which…
We study interaction-induced backscattering in clean quantum wires with adiabatic contacts exposed to a voltage bias. Particle backscattering relaxes such systems to a fully equilibrated steady state only on length scales exponentially…
In this thesis we deal with the specific collective phenomena in condensed matter - striped-structures formation. Such structures are observed in different branches of condensed matter physics, like surface physics or physics of…
Spectroscopic labels for a few particles with spin that are harmonically trapped in one-dimension with effectively zero-range interactions are provided by quantum numbers that characterize the symmetries of the Hamiltonian: permutations of…
Low-energy scattering is well described by the effective-range expansion. In quantum mechanics, a tower of contact interactions can generate terms in this expansion after renormalization. Scattering parameters are also encoded in the…
A non-relativistic scalar particle moving on a curved surface undergoes a geometric scattering whose behavior is sensitive to the theoretically ambiguous values of the intrinsic and extrinsic curvature coefficients entering the expression…
We address the occurrence of narrow planetary rings and some of their structural properties, in particular when the rings are shepherded. We consider the problem as Hamiltonian {\it scattering} of a large number of non-interacting massless…
We analyze the spectrum of the "local" Iwatsuka model, i.e. a two-dimensional charged particle interacting with a magnetic field which is homogeneous outside a finite strip and translationally invariant along it. We derive two new…
The prospect of controlling entanglement in interacting quantum systems offers a myriad of technological and scientific promises, given the progress in experimental studies in systems such as ultracold trapped gases. This control is often…
Owing to the Klein tunneling phenomenon, the permanent confinement or localization of electrons within a graphene quantum dot is unattainable. Nonetheless, a constant magnetic field can transiently ensnare an electron within the quantum…
We study various temporal correlation functions of a tagged particle in one-dimensional systems of interacting point particles evolving with Hamiltonian dynamics. Initial conditions of the particles are chosen from the canonical thermal…
The physics of interacting integer-spin chains has been a topic of intense theoretical interest, particularly in the context of symmetry-protected topological phases. However, there has not been a controllable model system to study this…
Non-relativistic charged particles and strings coupled with abelian gauge fields are quantized in a geometric representation that generalizes the Loop Representation. We consider three models: the string in self-interaction through a…
We connect quantum compact graphs with infinite leads, and turn them into scattering systems. We derive an exact expression for the scattering matrix, and explain how it is related to the spectrum of the corresponding closed graph. The…