Integrable three‐particle systems, hidden symmetries and deformations of the Calogero–Moser system

1995 ◽  
Vol 36 (7) ◽  
pp. 3541-3558 ◽  
Author(s):  
Manuel F. Rañada
Keyword(s):  
Particle Systems ◽  
Hidden Symmetries ◽  
Moser System

scholarly journals Duality and Hidden Symmetries in Interacting Particle Systems

2009 ◽  
Vol 135 (1) ◽  
pp. 25-55 ◽  
Author(s):  
Cristian Giardinà ◽  
Jorge Kurchan ◽  
Frank Redig ◽  
Kiamars Vafayi
Keyword(s):  
Interacting Particle Systems ◽  
Particle Systems ◽  
Hidden Symmetries ◽  
Interacting Particle

scholarly journals Joint Eigenfunctions for the Relativistic Calogero–Moser Hamiltonians of Hyperbolic Type. III. Factorized Asymptotics

2020 ◽  
Author(s):  
Martin Hallnäs ◽  
Simon Ruijsenaars
Keyword(s):  
Hyperbolic Type ◽  
Particle Systems ◽  
Type Iii ◽  
Recursion Scheme ◽  
Joint Eigenfunctions ◽  
Moser System

Abstract In the two preceding parts of this series of papers, we introduced and studied a recursion scheme for constructing joint eigenfunctions $J_N(a_+, a_-,b;x,y)$ of the Hamiltonians arising in the integrable $N$-particle systems of hyperbolic relativistic Calogero–Moser type. We focused on the 1st steps of the scheme in Part I and on the cases $N=2$ and $N=3$ in Part II. In this paper, we determine the dominant asymptotics of a similarity-transformed function $\textrm{E}_N(b;x,y)$ for $y_j-y_{j+1}\to \infty $, $j=1,\ldots , N-1$ and thereby confirm the long-standing conjecture that the particles in the hyperbolic relativistic Calogero–Moser system exhibit soliton scattering. This result generalizes a main result in Part II to all particle numbers $N>3$.

Statistical 3D Analysis and Modeling of Complex Particle Systems based on Tomographic Image Data

2019 ◽  
Vol 56 (12) ◽  
pp. 787-796
Author(s):  
O. Furat ◽  
B. Prifling ◽  
D. Westhoff ◽  
M. Weber ◽  
V. Schmidt
Keyword(s):  
Image Data ◽  
Particle Systems ◽  
3D Analysis ◽  
Tomographic Image ◽  
Complex Particle

scholarly journals Condensation of SIP Particles and Sticky Brownian Motion

2021 ◽  
Vol 183 (3) ◽  
Author(s):  
Mario Ayala ◽  
Gioia Carinci ◽  
Frank Redig
Keyword(s):  
Brownian Motion ◽  
Interacting Particle Systems ◽  
Particle Systems ◽  
Self Duality ◽  
Inclusion Process ◽  
Interacting Particle ◽  
New Information ◽  
Homogeneous Product ◽  
Coarsening Dynamics ◽  
The Difference

AbstractWe study the symmetric inclusion process (SIP) in the condensation regime. We obtain an explicit scaling for the variance of the density field in this regime, when initially started from a homogeneous product measure. This provides relevant new information on the coarsening dynamics of condensing interacting particle systems on the infinite lattice. We obtain our result by proving convergence to sticky Brownian motion for the difference of positions of two SIP particles in the sense of Mosco convergence of Dirichlet forms. Our approach implies the convergence of the probabilities of two SIP particles to be together at time t. This, combined with self-duality, allows us to obtain the explicit scaling for the variance of the fluctuation field.

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