Related papers: Conditions for realizing one-point interactions fr…
The so-called $\delta'$-interaction as a particular example in Kurasov's distribution theory developed on the space of discontinuous (at the point of singularity) test functions, is identified with the diagonal transmission matrix, {\em…
We derive an effective equation for the dynamics of many identical bosons in dimension one in the presence of a tiny impurity. The interaction between every pair of bosons is mediated by the impurity through a positive three-body potential.…
The states of an open quantum system interact ("talk") with one another via the extended environment into which the localized system is embedded. This interaction is mediated by the source term of the Schr\"odinger equation which describes…
In the semiclassical limit h to 0, we analyze a class of self-adjoint Schr\"odinger operators H_h = h^2 L + h W + V id_E acting on sections of a vector bundle E over an oriented Riemannian manifold M where L is a Laplace type operator, W is…
We provide a thorough characterisation of the zero-temperature one-particle density matrix of trapped interacting anyonic gases in one dimension, exploiting recent advances in the field theory description of spatially inhomogeneous quantum…
Multi-time wave functions are wave functions that have a time variable for every particle, such as $\phi(t_1,x_1,\ldots,t_N,x_N)$. They arise as a relativistic analog of the wave functions of quantum mechanics but can be applied also in…
We investigate the dependence of the structural phase transitions in an infinite quasi-one-dimensional system of repulsively interacting particles on the profile of the confining channel. Three different functional expressions for the…
Quantum coherence plays an important role in quantum information protocols that provide an advantage over classical information processing. The amount of coherence that can exist between two orthogonal subspaces is limited by the positivity…
Let $G$ be a connected Lie group acting locally simply transitively on a manifold $M$. By connecting curves in $M$ we mean the orbits of one-parameter subgroups of $G$. To block a pair of points $m_1,m_2\in M$ is to find a finite set…
A simple Lennard-Jones fluid confined in a slit nanopore with hard walls is studied on the basis of a multilayer structured model. Each layer is homogeneous and parallel to the walls of the pore. The Helmholtz energy of this system is…
We consider two-dimensional systems of point particles located on rectangular lattices and interacting via pairwise potentials. The goal of this paper is to investigate the phase transitions (and their nature) at fixed density for the…
Linear square-well Schr\"{o}dinger equation endowed with a singular logarithmic spike in the origin is studied. The study is methodical, motivated by the problem of non-gausson states $\psi_n(x)$, $n \neq 0$ generated by nonlinear…
The pressure-temperature phase diagram of a one-component system, with particles interacting through a spherically symmetric pair potential in two dimensions is studied. The interaction consists of a hard core plus an additional repulsion…
For one-dimensional many-body systems interacting via the \textit{Coulomb force} and with \textit{arbitrary} external potential energy, we derive (\textit{i}) the \textit{node coalescence condition} for the wave function. This condition…
We consider an aggregation-diffusion equation modelling particle interaction with non-linear diffusion and non-local attractive interaction using a homogeneous kernel (singular and non-singular) leading to variants of the Keller-Segel model…
The problems of the intermediate-range atomic structure of glasses and of the mechanism for the glass transition are approached from the low-temperature end in terms of a scenario for the atomic organization that justifies the use of an…
The pressure-temperature phase diagram of a one-component system, with particles interacting through a spherically symmetric pair potential is studied. It is shown that if the pair potential allows for a discontinuous reduction of the…
This paper investigates the long time dynamics of interacting particle systems subject to singular interactions. We consider a microscopic system of $N$ interacting point particles, where the time evolution of the joint distribution…
Limited bonding valence, usually accompanied by well-defined directional interactions and selective bonding mechanisms, is nowadays considered among the key ingredients to create complex structures with tailored properties: even though…
We study a system of particles in two dimensions interacting via a dipolar long-range potential $D/r^3$ and subject to a square-lattice substrate potential $V({\bf r})$ with amplitude $V$ and lattice constant $b$. The isotropic interaction…