Related papers: Determinantal structures in space inhomogeneous dy…
Understanding the dynamics of two inertial bodies coupled via a friction interface is essential for a wide range of systems and motion control applications. Coupling terms within the dynamics of an inertial pair connected via a passive…
A noncolliding diffusion process is a conditional process of $N$ independent one-dimensional diffusion processes such that the particles never collide with each other. This process realizes an interacting particle system with long-ranged…
Using the determinantal formula of Biane, Bougerol, and O'Connell, we give multitime joint probability densities to the noncolliding Brownian motion with drift, where the number of particles is finite. We study a special case such that the…
In this paper, we propose a new comparison tool for spatial homogeneity of point processes, based on the joint examination of void probabilities and factorial moment measures. We prove that determinantal and permanental processes, as well…
Expanding upon previous work, using the path-integral formalism we derive expressions for the one-particle reduced density matrix and the two-point correlation function for a quadratic system of bosons that interact through a general class…
This article focuses on a system of sticky Brownian motions, also known as Howitt-Warren martingale problem, and correlated Brownian motions and shows that infinite-dimensional orthogonal polynomials intertwine the dynamics of infinitely…
The Hamiltonian dynamics of chains of nonlinearly coupled particles is numerically investigated in two and three dimensions. Simple, off-lattice homopolymer models are used to represent the interparticle potentials. Time averages of…
We study a gas of point particles with hard-core repulsion in one dimension where the particles move freely in-between elastic collisions. We prepare the system with a uniform density on the infinite line. The velocities $\{v_i; i \in…
When two populations of "particles" move in opposite directions, like oppositely charged colloids under an electric field or intersecting flows of pedestrians, they can move collectively, forming lanes along their direction of motion. The…
Dirac structures are geometric objects that generalize both Poisson structures and presymplectic structures on manifolds. They naturally appear in the formulation of constrained mechanical systems. In this paper, we show that the evolution…
The extensive analysis of the dynamics of relativistic spinning particles is presented. Using the coadjoint orbits method the Hamiltonian dynamics is explicitly described. The main technical tool is the factorization of general Lorentz…
The Bessel process with parameter $D>1$ and the Dyson model of interacting Brownian motions with coupling constant $\beta >0$ are extended to the processes in which the drift term and the interaction terms are given by the logarithmic…
We define auto- and cross-correlation functions capable to capture dynamical characteristics induced by local phase space structures in a general dynamical system. These correlation functions are calculated in the Standard Map for a range…
This paper explores the relationship between Cartan symmetries, dynamical similarities, and dynamical symmetries in contact Hamiltonian mechanics. By introducing an alternative decomposition of vector fields, we characterize these…
The notion of a two-point susceptibility kernel used to describe linear electromagnetic responses of dispersive continuous media in non-relativistic phenomena is generalized to accommodate the constraints required of a causal formulation in…
Motivated by recent studies of colloidal particles in optical tweezer arrays, we study a two-dimensional model of a colloidal suspension in a periodic potential. The particles tend to stay near potential minima, approximating a lattice gas.…
We introduce a general method to construct classes of dynamical systems invariant under generalizations of the Carroll and of the Galilei groups. The method consists in starting from a space-time in $D+1$ dimensions and partitioning it in…
Turing patterns are a central paradigm for describing spatial patterns in nature. The corresponding theory of reaction-diffusion dynamics combines ideal diffusion with nonlinear reactions, resulting in patterns when species diffuse at…
Determinantal point processes are point processes whose correlation functions are given by determinants of matrices. The entries of these matrices are given by one fixed function of two variables, which is called the kernel of the point…
We study determinantal point processes on $\mathbb{C}$ induced by the reproducing kernels of generalized Fock spaces as well as those on the unit disc $\mathbb{D}$ induced by the reproducing kernels of generalized Bergman spaces. In the…