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Using molecular dynamics simulations we investigate the thermodynamic of particles interacting with a continuous and a discrete versions of a core-softened (CS) intermolecular potential composed by a repulsive shoulder. Dynamic and…
For quantum meta-stable problems with three particles, the $^{6}$Be and $^{16}$Ne nuclei as two-proton ($2p$) emitters provide a testing field. Considering the complexity of many-body meta-stable systems, a tractable solver has been on…
We present a new time-dependent Density Functional approach to study the relaxational dynamics of an assembly of interacting particles subject to thermal noise. Starting from the Langevin stochastic equations of motion for the velocities of…
The physics of active systems of self-propelled particles, in the regime of a dense liquid state, is an open puzzle of great current interest, both for statistical physics and because such systems appear in many biological contexts. We…
In this paper, we develop a large-$N$ field theory for a system of $N$ classical particles in one dimension at thermal equilibrium. The particles are confined by an arbitrary external potential, $V_\text{ex} (x)$, and repel each other via a…
Precision measurements at low energy search for physics beyond the Standard Model in a way complementary to searches for new particles at colliders. In the weak sector the most general $\beta$ decay Hamiltonian contains, besides vector and…
In this work, we analytically examine the validity of molecular dynamics for a soft potential system by considering a simple one-dimensional system with a piecewise continuous linear repulsive potential wall having a constant slope $a$. We…
For finite interacting particle systems with strong repulsing-attracting or general interactions, we prove global weak well-posedness almost up to the critical threshold of the strengths of attracting interactions (independent of the number…
In this work, we investigate the dynamics of interacting particle systems subjected to repulsive forces, such as lattices of magnetized particles. To this end, we first develop a general model capable of capturing the complete dynamical…
Two families of stochastic interacting particle systems, the interacting Brownian motions and Bessel processes, are defined as extensions of Dyson's Brownian motion models and the eigenvalue processes of the Wishart and Laguerre processes…
We derive expressions for determination of the stress and the elastic constants in systems composed of particles interacting via non-central two-body potentials as thermal averages of products of first and second partial derivatives of the…
Unlike equilibrium systems, active matter is not governed by the conventional laws of thermodynamics. Through a series of analytic calculations and Langevin dynamics simulations, we explore how systems cross over from equilibrium to active…
We construct the traveling wave solutions of an FKPP growth process of two densities of particles, and prove that the critical traveling waves are locally stable in a space where the perturbations can grow exponentially at the back of the…
We study the stability of unitary quantum dynamics of composite systems (for example: central system + environment) with respect to weak interaction between the two parts. Unified theoretical formalism is applied to study different physical…
We examine the problem of a repulsive, weakly-interacting and harmonically trapped Bose-Einstein condensate under rotation. We derive a simple analytic expression for the energy incorporating the interactions when the angular momentum per…
We consider the long time behavior of the solutions to the Burgers-FKPP equation with advection of a strength $\beta\in\mathbb{R}$. This equation exhibits a transition from pulled to pushed front behavior at $\beta_c=2$. We prove…
We show that heterogeneity in self-propulsion speed can lead to the emergence of a robust effective short-range repulsion among active particles interacting via long-range attractive potentials. Using the example of harmonically coupled…
A recently developed nonlinear analytical model for axially loaded thin-walled stringer-stiffened plates based on variational principles is extended to include local buckling of the main plate. Interaction between the weakly stable global…
We use the Fokker-Planck equation and its moment equations to study the collective behavior of interacting particles in unsteady one-dimensional flows. Particles interact according to a long-range attractive and a short-range repulsive…
We consider quantum chains whose Hamiltonians are perturbations by interactions of short range of a Hamiltonian that does not couple the degrees of freedom located at different sites of the chain and has a strictly positive energy gap above…