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We analyze the continuous time evolution of a $d$-dimensional system of $N$ self propelled particles with a kinematic constraint on the velocities inspired by the original Vicsek's one \cite{VCB-JCS}. Interactions among particles are…
We present the results of the quantum field theory approach to nuclear Yukawa model obtained by standard lattice techniques. We have considered the simplest case of two identical fermions interacting via a scalar meson exchange.…
The stability of the nuclear matter system with respect to density fluctuations is examined exploring in detail the pole structure of the electro-nuclear response functions. Making extensive use of the method of dispersion integrals we…
The Hubbard model of bosons on two dimensional lattices with a lowest flat band is discussed. In these systems there is a critical density, where the ground state is known exactly and can be represented as a charge density wave. Above this…
The theory of ultracold, dilute Bose gases is the subject of intensive studies, driven by new experimental applications, which also motivate the study of Bose-Einstein condensation (BEC) in low dimensions. From the theoretical point of view…
We investigate a system of Brownian particles weakly bound by attractive parity-symmetric potentials that grow at large distances as $V(x) \sim |x|^\alpha$, with $0 < \alpha < 1$. The probability density function $P(x,t)$ at long times…
We study the Dirac equation in confining potentials with pure vector coupling, proving the existence of metastable states with longer and longer lifetimes as the non-relativistic limit is approached and eventually merging with continuity…
A concentrated suspension of lamellar colloidal particles (e. g. clay) is modelled by considering a single, uniformly charged, finite platelet confined with co- and counterions to a Wigner-Seitz (WS) cell. The system is treated within…
In the first part of this paper, we apply a well known discrete-to-continuum approach to a Frenkel-Kontorova-type model of an infinitely long one-dimensional chain of atoms weakly interacting with a line of fixed atoms. The rescaled model…
By using coupling by change of conditional probability measure, the log-Harnack inequality for path dependent McKean-Vlasov SDEs with distribution dependent diffusion coefficients is established, which together with the exponential…
Ionic Bose polarons are quantum entities emerging from the interaction between an ion and a Bose-Einstein condensate (BEC), featuring long-ranged interactions that can compete with the gas healing length. This can result in strong…
We consider mathematical models of the weak decay of the vector bosons $W^{\pm}$ into leptons. The free quantum field hamiltonian is perturbed by an interaction term from the standard model of particle physics. After the introduction of…
We study the global existence and uniqueness of weak solutions to kinetic Kolmogorov-Vicsek models that can be considered a non-local non-linear Fokker-Planck type equation describing the dynamics of individuals with orientational…
Wheeler-DeWitt equation is applied to $k > 0$ Friedmann Robertson Walker metric with various types of matter. It is shown that if the Universe ends in the matter dominated era (e.g., radiation or pressureless gas) with zero cosmological…
We study evolution of various statistical quantities of smoothed cosmic density and velocity fields using N-body simulations. The parameter $C\equiv <V^2\delta>/(<V^2> <\delta^2>)$ characterizes nonlinear coupling of these two fields and…
We discuss the mean-field approximation for a trapped weakly-interacting Bose-Einstein condensate (BEC) and its connection with the exact many-body problem by deriving the Gross-Pitaevskii action of the condensate. The mechanics of the BEC…
The main quasi-particle characteristics of the one-dimensional polaron are estimated within and beyond the most general Gaussian approximation at arbitrary electron-phonon coupling. We have derived explicitly the ground-state energy and the…
Single component pseudo-potential lattice Boltzmann model has been widely applied in multiphase simulation due to its simplicity and stability. In many research, it has been claimed that this model can be stable for density ratios larger…
This study presents a systematic estimation of the relativistic correction to the binding energies of two-body hadronic molecular states by comparing the numerical solutions of the three-dimensional (3D) Schr{\"o}dinger, 3D Salpeter, and…
In processes involving small-x partons, like in deep inelastic scattering and in hadronic collisions at high energy, the final state can be expressed in terms of correlators of Wilson lines. We study such high-point correlators evolving…