Related papers: Spectral filtering in quantum Y-junction
A simple formalism for exploring quantum scattering and possible bound states in an arbitrary symmetric and localized potential in a unified way is presented. The symmetric square barrier and well potentials are used for illustrating the…
We have previously studied properties of a one-dimensional potential with $N$ equally spaced identical barriers in a (fixed) finite interval for both finite and infinite $N$. It was observed that scattering and spectral properties depend…
We consider a quasi one-dimensional chain of N chaotic scattering elements with periodic boundary conditions. The classical dynamics of this system is dominated by diffusion. The quantum theory, on the other hand, depends crucially on…
We discuss the properties of interacting electrons on a finite chain with open boundary conditions. We extend the Haldane Luttinger liquid description to these systems and study how the presence of the boundaries modifies various…
The paper discusses quantum graphs with a vertex coupling which interpolates between the common one of the $\delta$ type and a coupling introduced recently by two of the authors which exhibits a preferred orientation. Describing the…
The multichannel generalization of the theory of spectral, scattering and decay control is presented. New universal algorithms of construction of complex quantum systems with given properties are suggested. Particularly, transformations of…
We investigate the SU(N) Principal Chiral Model on a half-line with a particular set of boundary conditions (BCs). In previous work these BCs have been shown to correspond to boundary scattering matrices (K-matrices) which are…
We generalized the 't Hooft-Veltman method of unitary regulators to put forward a path-integral framework for finite, alternative theories to a given quantum field theory. And we demonstrated that the proposed framework is feasible by…
The pattern of quantum numbers in the leptons and quarks indicate that precisely two fixed hypercharge splittings are observed in nature. The $|\Delta Y|=1$ splitting corresponds to the $SU(2)_L$ scalar and doublet spacing, indicative of…
The scattering of a fermion in the background of a smooth step potential is considered with a general mixing of vector and scalar Lorentz structures with the scalar coupling stronger than or equal to the vector coupling. Charge-conjugation…
We study the properties of singular values of mixing matrices embedded within an experimentally determined interval matrix. We argue that any physically admissible mixing matrix needs to have the property of being a contraction. This…
Using a representation of multichannel quantum defect theory in terms of a quantum Poincar\'e map for bound Rydberg molecules, we apply Jung's scattering map to derive a generalized quantum map, that includes the continuum. We show, that…
We discuss a general parametrization for vertices of quantum graphs and show, in particular, how the $\delta'_s$ and $\delta'$ coupling at an $n$ edge vertex can be approximated by means of $n+1$ couplings of the $\delta$ type provided the…
Let $\Delta_{\alpha,Y}$ be the bounded from above self-adjoint realization in $L^{2}({\mathbb R}^{3})$ of the Laplacian with $n$ point scatterers placed at $Y=\{y_{1},\dots,y_{n}\}\subset{\mathbb R}^{3}$, the parameters…
We analyze spectral properties of a leaky wire model with a potential bias. It describes a two-dimensional quantum particle exposed to a potential consisting of two parts. One is an attractive $\delta$-interaction supported by a…
Elastic scattering in a quantum wire has several novel features not seen in 1D, 2D or 3D. In this work we consider a single channel quantum wire as its application is inevitable in making devices based on quantum interference effects. We…
We address the electronic properties of quantum dots in the two-dimensional $\alpha-\mathcal{T}_3$ lattice when subjected to a perpendicular magnetic field. Implementing an infinite mass boundary condition, we first solve the eigenvalue…
The theory of scattering of atom pairs in a periodic potential is presented for the case of different atoms. When the scattering dynamics is restricted to the lowest Bloch band of the periodic potential, a separation in relative and average…
We consider optical media which feature antilinear symmetries. We show that: (i) spectral singularities of such media (if any) are always self-dual, i.e., correspond to CPA-lasers; (ii) under the change of a system's parameter the self-dual…
We study the spectral properties of a system of electrons interacting through long-range Coulomb potential on a one-dimensional chain. When the interactions dominate over the electronic bandwidth, the charges arrange in an ordered…