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This study investigates the potential for biological systems to be governed by a variational principle, suggesting that such systems may evolve to minimize or optimize specific quantities. To explore this idea, we focus on identifying…
We study bosonic atoms with two internal states in artificial gauge potentials whose strengths are different for the two components. A series of topological phases for such systems is proposed using the composite fermion theory and the…
Via molecular dynamics simulations we have studied kinetics of vapor-"solid" phase transition in an active matter model in which self-propulsion is introduced via the well-known Vicsek rule. The overall density of the particles is chosen in…
Lattice models are powerful tools for studying strongly correlated quantum many-body systems, but their general lack of exact solutions motivates efforts to simulate them in tunable platforms. Recently, a promising new candidate has emerged…
Taking advantage of the flexibility of the variational method with coordinate transformations, we derive a self-consistent set of equations of motion from a discretized Lagrangian to study kinetic plasmas using a Fourier decomposed…
In this work we investigate the collective behavior of self-propelled particles that deform due to local pairwise interactions. We demonstrate that this deformation alone can induce alignment of the velocity vectors. The onset of collective…
A 3D Cellular Automaton model developed by the authors to deal with the dynamics of N-body interactions has been adapted to investigate the head-on collision of two identical bound clusters of particles, and the ensuing process of…
Lagrangian and Hamiltonian formulations of a free spinning particle in 2+1-dimensions or {\it anyon} are established, following closely the analysis of Hanson and Regge. Two viable (and inequivalent) Lagrangians are derived. It is also…
We study the mathematical theory of second order systems with two species, arising in the dynamics of interacting particles subject to linear damping, to nonlocal forces and to external ones, and resulting into a nonlocal version of the…
We modify the standard Vicsek model to clearly distinguish between intrinsic noise due to imperfect alignment between organisms, and extrinsic noise due to fluid motion. We then consider the effect of a steady vortical flow, the Taylor…
We introduce a stochastic agent-based model for the flocking dynamics of self-propelled particles that exhibit velocity-alignment interactions with neighbours within their field of view. The stochasticity in the dynamics of the model arises…
A planar boundary introduced \`a la Symanzik in the 5D topological BF theory, with the only requirement of locality and power counting, allows to uniquely determine a gauge invariant, non topological 4D Lagrangian. The boundary condition on…
Considering the dynamics of non-interacting particles randomly moving on a lattice, the occurrence of a discontinuous transition in the values of the lattice parameters (lattice spacing and hopping times) determines the uprisal of two…
The variable-phase approach is applied to scattering and bound states in an attractive Coulomb potential, statically screened by a two-dimensional (2D) electron gas. A 2D formulation of Levinson's theorem is used for bound-state counting…
We investigate the dynamics of bound states of two interacting particles, either bosons or fermions, performing a continuous-time quantum walk on a one-dimensional lattice. We consider the situation where the distance between both particles…
Dixon's multipoles for a system of N relativistic positive-energy scalar particles are evaluated in the rest-frame instant form of dynamics. The Wigner hyper-planes (intrinsic rest frame of the isolated system) turn out to be the natural…
In the Hamiltonian formulation of chiral 2k-form electrodynamics, the 2k-form potential on the (4k+1)-space is defined up to the addition of either (i) a closed $2k$-form or (ii) an exact 2k-form, depending on the choice of chirality…
A number of successful theoretical models of hardness have been developed recently. A thermodynamic model of hardness, which supposes the intrinsic character of correlation between hardness and thermodynamic properties of solids, allows one…
We derive a general effective many-body theory for bosonic polar molecules in strong interaction regime, which cannot be correctly described by previous theories within the first Born approximation. The effective Hamiltonian has additional…
A Lagrangian based method is used to derive an analytical model for studying the dynamics of matter-wave bright soliton created in a harmonic potential which is attractive in the transverse direction and expulsive in the longitudinal…