Related papers: A regular version of Smilansky model
In this paper we suggest a new approach for the multichannel Coulomb scattering problem. The Schr\"{o}dinger equation for the problem is reformulated in the form of a set of inhomogeneous equations with a finite-range driving term. The…
Transmission through disordered samples can be controlled by illuminating a sample with waveforms corresponding to the eigenchannels of the transmission matrix. But can the TM be exploited to selectively excite quasi-normal modes and so…
While true phase transitions are forbidden in one-dimensional systems with short-range interactions, several models have recently been shown to exhibit sharp yet analytic thermodynamic anomalies that mimic thermal phase transitions. We show…
In order to overcome the limitations of small system sizes in spin-glass simulations, we investigate the one-dimensional Ising spin chain with power-law interactions. The model has the advantage over traditional higher-dimensional…
The relation between thermodynamic phase transitions in classical systems and topology changes in their configuration space is discussed for a one-dimensional, analytically tractable solid-on-solid model. The topology of a certain family of…
We prove sharp lower bounds on the spectral gap of 1-dimensional Schr\"odinger operators with Robin boundary conditions for each value of the Robin parameter. In particular, our lower bounds apply to single-well potentials with a centered…
A procedure is reported for numerical analysis of false vacuum transition in a model with multiple scalar fields. It is a refined version of the approach by Konstandin and Huber. The alteration makes it possible to tackle a class of…
In a system of noisy self-propelled particles with interactions that favor directional alignment, collective motion will appear if the density of particles is beyond a critical density. Starting with a reduced model for collective motion,…
We consider the problem of constraining a particle to a submanifold Sigma of configuration space using a sequence of increasing potentials. We compare the classical and quantum versions of this procedure. This leads to new results in both…
The desired shifts of the boundaries of spectral allowed zones of periodical systems are demonstrated. In particular, the phenomenon of merging neighbor allowed zones is exhibited and its simple explanation is given. It is also shown how to…
The rapid adoption of synthetic data for training Large Language Models (LLMs) has introduced the technical challenge of "model collapse"-a degenerative process where recursive training on model-generated content leads to a contraction of…
Band theory provides the foundation for understanding electronic structure in crystalline materials, but its reliance on exact translational symmetry limits its applicability to systems with defects, disorder, incommensurate modulations, or…
Percolation on a one-dimensional lattice and fractals such as the Sierpinski gasket is typically considered to be trivial because they percolate only at full bond density. By dressing up such lattices with small-world bonds, a novel…
We combine tools from effective field theory and generalized unitarity to construct a map between on-shell scattering amplitudes and the classical potential for interacting spinless particles. For general relativity, we obtain analytic…
We investigate the scattering phenomena produced by a general finite-range nonseparable potential in a multi-channel two-probe cylindrical nanowire heterostructure. The multi-channel current scattering matrix is efficiently computed using…
This work deals with the presence of localized static structures in the real line, described by relativistic real scalar fields in two spacetime dimensions. We consider models featuring both standard and modified kinematics, where we employ…
We have proposed an analytical approach for exact solution of multi-channel scattering problems, in presence of Dirac Delta function couplings. Our solution is quite general and is valid for any set of potentials, if the Green's functions…
In this note, we study the phase transitions arising in a modified Smoluchowski equation on the sphere with dipolar potential. This equation models the competition between alignment and diffusion, and the modification consists in taking the…
Alpha($^{4}$He)-cluster models have often been used to describe light nuclei. Towards the application to multi-cluster systems involving heavy clusters, we study the relative wave functions of the $\alpha+^{16}$O and $\alpha+^{40}$Ca…
Let (M, g) be a compact smooth Riemannian manifold. We obtain new off-diagonal estimates as {\lambda} tend to infinity for the remainder in the pointwise Weyl Law for the kernel of the spectral projector of the Laplacian onto functions with…