Related papers: On the duality between particles and polymers
Polynomial dynamical systems describing interacting particles in the plane are studied. A method replacing integration of a polynomial multi--particle dynamical system by finding polynomial solutions of a partial differential equations is…
We study structure formation in systems of classical particles in two dimensions with long-range attractive short-range repulsive two-body interactions and repulsive three-body interactions. Stripe, gossamer, and glass phases are found as a…
We study the directed last-passage percolation model on the planar integer lattice with nearest-neighbor steps and general i.i.d. weights on the vertices, outside the class of exactly solvable models. Stationary cocycles are constructed for…
Failure of amorphous materials is characterized by the emergence of dissipation. The connection between particle dynamics, dissipation, and overall material rheology, however, has still not been elucidated. Here, we take a new approach…
An elastic rod model for semi-flexible polymers is presented. Theory for a continuum rod is reviewed, and it is shown that a popular discretised model used in numerical simulations gives the correct continuum limit. Correlation functions…
We construct a two-class asymmetric interacting particle system with $U_q(so_6)$ or $U_q(so_8)$ symmetry, in which up to two particles may occupy a site if the two particles have different class. The particles exhibit a drift, but there is…
We study a stochastic model of a copolymerization process that has been extensively investigated in the physics literature. The main questions of interest include: (i) what are the criteria for transience, null recurrence, and positive…
The entanglement between two bosons or fermions can be accessed if there exists an auxiliary degree of freedom which can be used to label and effectively distinguish the two particles. For some types of entanglement between two…
When a polymer solution undergoes viscoelastic phase separation, the polymer-rich phase forms a network-like structure even if it is a minor phase. This unique feature is induced by polymer dynamics, which are constrained by the temporal…
We introduce the $q$-Hahn PushTASEP --- an integrable stochastic interacting particle system which is a 3-parameter generalization of the PushTASEP, a well-known close relative of the TASEP (Totally Asymmetric Simple Exclusion Process). The…
We find all factorized duality functions for a class of interacting particle systems. The functions we recover are self-duality functions for interacting particle systems such as zero-range processes, symmetric inclusion and exclusion…
Many integrable stochastic particle systems in one space dimension (such as TASEP - totally asymmetric simple exclusion process - and its various deformations, with a notable exception of ASEP) remain integrable when we equip each particle…
We address how the interplay between the finite availability and carrying capacity of particles at different parts of a spatially extended system can control the steady state currents and density profiles in the one-dimensional…
The interaction of flexible polymers with fluid flows leads to a number of intriguing phenomena observed in laboratory experiments, namely drag reduction, elastic turbulence and heat transport modification in natural convection, and is one…
The processes of Coulomb gas ordering in 3D layered system are studied by means of Brownian dynamics approach. It is found that at different densities of the carriers the 3D lattice of charges as well as new specific structures are possible…
Last passage percolation (LPP) is a model of a directed metric and a zero-temperature polymer where the main observable is a directed path evolving in a random environment accruing as energy the sum of the random weights along itself. When…
Granular flows through pipes show interesting phenomena, e.g. clogging and density waves, 1/f-noise. These things are fairly good studied by computer-experiments, but there is a lack in theoretical and analytical consideration. We introduce…
Recent progress in cooling and trapping of polarized clouds of chromium $^{52}Cr$, dysprosium $^{164}Dy$ and erbium $^{168}Er$ opens a road-map to quantum systems where shapes of inter-particle interactions can be customized. The main…
We introduce a new method, which we call stochastic fusion, which takes an exclusion process and constructs an interacting particle systems in which more than one particle may occupy a lattice site. The construction only requires the…
Motivated by experiments on cell segregation, we present a two-species model of interacting particles, aiming at a quantitative description of this phenomenon. Under precise scaling hypothesis, we derive from the microscopic model a…