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General formulas are derived for the quasiparticle effective mass and the equation of state of the Fermi system with account of the interparticle attraction at long distances and repulsion at short distances. Calculations are carried out of…
A number of experimental platforms for quantum simulations of disordered quantum matter, from dipolar systems to trapped ions, involve degrees of freedom which are coupled by power-law decaying hoppings or interactions, yet the interplay of…
We examine the problem of two particles confined in an isotropic harmonic trap, which interact via a finite-ranged Gaussian-shaped potential in two spatial dimensions. We derive an approximative transcendental equation for the energy and…
Realistic physical systems are characterised by emergent interactions across multiple length and time scales, posing a significant challenge for predictive machine learning (ML) models. Most scientific ML models focus on a narrow range of…
We study a two-species bidirectional exclusion process, and a single species variant, which is motivated by the motion of organelles and vesicles along microtubules. Specifically, we are interested in the clustering of the particles and…
Quasiperiodic potentials can be used to interpolate between localization and delocalization in one dimension. With the rise of optical platforms engineering dipolar interactions, a key question is the stability of quasicrystalline phases…
We consider N fermions in a two-dimensional harmonic oscillator potential interacting with a very short-range repulsive pair-wise potential. The ground-state energy of this system is obtained by performing a Thomas-Fermi as well as a…
We examine a one-dimensional two-component fermionic system in a trap, assuming that all particles have the same mass and interact through a strong repulsive zero-range force. First we show how a simple system of three strongly interacting…
The composite system, formed by two $S=1$ particles, is considered. The field operators of constituents are transformed on the $(1,0)\oplus (0,1)$ representation of the Lorentz group. The problem of interaction of $S=1$ particle with the…
We employ \textit{ab initio} methods of quantum chemistry to investigate spin-1/2 fermions interacting via a two-body contact potential in a one-dimensional harmonic trap. The convergence of the total energy with the size of the…
Motivated by recent findings, we discuss the existence of a direct and robust mechanism providing discontinuous absorbing transitions in short range systems with single species, with no extra symmetries or conservation laws. We consider…
Because of the potentially large number of important applications of nonlinear optics, researchers have expended a great deal of effort to optimize the second-order molecular nonlinear-optical response, called the hyperpolarizability. The…
The exactly solvable model of two indistinguishable quantum particles (bosons or fermions) confined in a one-dimensional harmonic trap and interacting via finite-range soft-core interaction is presented and many properties of the system are…
A continuous infinite system of point particles with strong superstable interaction is considered in the framework of classical statistical mechanics. The family of approximated correlation functions is determined in such a way, that they…
Spatial scale separation often leads to sharp interfaces that can be fully localized pulses or transition layer fronts connecting different states. This paper concerns the asymptotic interaction laws of pulses and fronts in the so-called…
Quantum systems composed of $N$ distinct particles in $\R^2$ with two-body contact interactions of TMS type are shown to arise as limits - in the norm resolvent sense - of Schr\"odinger operators with suitably rescaled pair potentials.
We provide a description of interacting quantum fields in terms of density matrices for any occupation numbers in Fock space in a momentum basis. As a simple example, we focus on a real scalar field interacting with another real scalar…
We investigate a class of continuum models for the motion of a two-dimensional biological group under the influence of nonlocal social interactions. The dynamics may be uniquely decomposed into incompressible motion and potential motion.…
This paper is devoted to the study of the asymptotic behavior of solutions to multi-order fractional cooperative systems. First, we demonstrate the boundedness of solutions to fractional-order systems under certain conditions imposed on the…
We study non-topological solitons, so called Q-balls, which carry a non-vanishing Noether charge and arise as lump solutions of self-interacting complex scalar field models. Explicit examples of new axially symmetric non-spinning Q-ball…