Related papers: Collective Coordinate Methods and Their Applicabil…
In this paper, we develop the dressing method to study the exact solutions for the vector sine-Gordon equation. The explicit formulas for one kink and one breather are derived. The method can be used to construct multi-soliton solutions.…
We show, using covariant Lyapunov vectors in addition to standard Lyapunov analysis, that there exists a set of collective Lyapunov modes in large chaotic systems exhibiting collective dynamics. Associated with delocalized Lyapunov vectors,…
We investigate and provide optimal sets of reaction coordinates for mixed pairs of molecules displaying polar, uniaxial, or spherical symmetry in two and three dimensions. These coordinates are non-redundant, i.e., they implicitly involve…
The transition from integrable to non-integrable highly-dispersive nonlinear models is investigated. The sine-Gordon and $\phi^4$-equations with the additional fourth-order spatial and spatio-temporal derivatives, describing the higher…
We present a comprehensive examination of learning methodologies employed for the structural identification of dynamical systems. These techniques are designed to elucidate emergent phenomena within intricate systems of interacting agents.…
In this paper, we review state-of-the-art results on the collective behaviors for Lohe type first-order aggregation models. Collective behaviors of classical and quantum many-body systems have received lots of attention from diverse…
We review a recent approach for the simulation of many-body interacting systems based on an efficient generalization of the Lanczos method for Quantum Monte Carlo simulations. This technique allows to perform systematic corrections to a…
This article reviews recent research on the collective dynamical behavior of colloids with dipolar or multipolar interactions. Indeed, whereas equilibrium structures and static self-assembly of such systems are now rather well understood,…
Motivated by recent experiments, we model the dynamics of bright solitons formed by cold gases in quasi-1D traps. A dynamical variational ansatz captures the far-from equilibrium excitations of these solitons. Due to a separation of scales,…
We study a coupled system that describes the interacting dynamics between a bulk field, confined to a finite region with timelike boundary, and a boundary observable. In our system the dynamics of the boundary observable prescribes…
The emergence of violations of conformal invariance in the form of non-local operators in the two-dimensional action describing solitons inevitably leads to the introduction of collective coordinates as two dimensional ``wormhole…
We examine various recently proposed discretizations of the well-known $\phi^4$ field theory. We compare and contrast the properties of their fundamental solutions including the nature of their kink-type solitary waves and the spectral…
We study the emergence of collective dynamics in the integrable Hamiltonian system of two finite ensembles of coupled harmonic oscillators. After identification of a collective degree of freedom, the Hamiltonian is mapped onto a model of…
In this letter, we show how to build bridges between field-theoretic models that have kink solutions with different asymptotic behavior. We study transformational properties of kinks in models with a real scalar field in two-dimensional…
Living systems exhibit complex yet organized behavior on multiple spatiotemporal scales. To investigate the nature of multiscale coordination in living systems, one needs a meaningful and systematic way to quantify the complex dynamics, a…
We have studied the problem of the dissipative motion of Bloch walls considering a totally anisotropic one dimensional spin chain in the presence of a magnetic field. Using the so-called "collective coordinate method" we construct an…
In strong perpendicular magnetic fields double-quantum-well systems can sometimes occur in unusual broken symmetry states which have interwell phase coherence in the absence of interwell hopping. When hopping is present in such systems and…
We undertake a detailed comparison of the results of direct numerical simulations of the integrable soliton gas dynamics with the analytical predictions inferred from the exact solutions of the relevant kinetic equation for solitons. We use…
Using the collective variables (CV) method the basic relations of statistical field theory of a multicomponent non-homogeneous fluids are reconsidered. The corresponding CV action depends on two sets of scalar fields - fields…
Many processes of scientific and technological interest are characterized by time scales that render their simulation impossible if one uses present day simulation capabilities. To overcome this challenge a variety of enhanced simulation…