相关论文: Interacting Particle Systems and Jacobi Style Iden…
Accurate interaction potentials between microscopic components such as colloidal particles or cells are crucial to understanding a range of processes, including colloidal crystallization, bacterial colony formation, and cancer metastasis.…
The Gibbs Mixing Paradox is a conceptual touchstone for understanding mixtures in statistical mechanics. While debates over the theoretical subtleties of particle distinguishability continue to this day, we seek to extend the discussion in…
We present a study of three families of Kronecker coefficients, which we describe in terms of reduced Kronecker coefficients. This study is grounded on the generating function of the coefficients, proved by a bijection between two…
We study three classes of continuous time Markov processes (inclusion process, exclusion process, independent walkers) and a family of interacting diffusions (Brownian energy process). For each model we define a boundary driven process…
In this paper we derive intertwining relations for a broad class of conservative particle systems both in discrete and continuous setting. Using the language of point process theory, we are able to derive a natural framework in which…
For the random eigenvalues with density corresponding to the Jacobi ensemble $$c \cdot \prod_{i < j} | \lambda_i - \lambda_j |^\beta \prod^n_{i=1} (2 - \lambda_i)^a (2 + \lambda_i)^b I_{(-2,2)} (\lambda_i) $$ $(a, b > -1, \beta > 0) $ a…
We consider interacting particle systems and their mean-field limits, which are frequently used to model collective aggregation and are known to demonstrate a rich variety of pattern formations. The interaction is based on a pairwise…
Local perturbations in conservative particle systems can have a non-local influence on the stationary measure. To capture this phenomenon, we analyze in this paper two toy models. We study the symmetric exclusion process on a countable set…
In these two companion papers, we give infinite families of partition identities which generalise Primc's and Capparelli's identities, and study their consequences on the theory of crystal bases of the affine Lie algebra $A_{n-1}^{(1)}.$ In…
Born's rule, one of the cornerstones of quantum mechanics, relates detection probabilities to the modulus square of the wave function. Single-particle interference is accordingly limited to pairs of quantum paths and higher-order…
Even though the evolution of an isolated quantum system is unitary, the complexity of interacting many-body systems prevents the observation of recurrences of quantum states for all but the smallest systems. For large systems one can not…
This work is an enquiry into the circumstances under which entropy methods can give an answer to the questions of both quantum separability and classical correlations of a composite state. Several entropy functionals are employed to examine…
Even though strongly correlated systems are abundant, only a few exceptional cases admit analytical solutions. In this paper we present a large class of solvable systems with strong correlations.. We consider a set of $N$ independent and…
We consider a class of Dean-Kawasaki type equations on $\mathbb{T}$ with logarithmic repulsive interactions depending on the inverse temperature $\beta$ and a new spectral approximation to the noise part, which approximately features Otto's…
Motivated by a general principle governing regulation mechanisms in biological cells, we investigate a general interaction scheme between different populations of particles and specific particles, referred to as agents. Assuming that each…
We use molecular dynamics simulations in 2d to study multi-component fluid in the limiting case where {\it all the particles are different} (APD). The particles are assumed to interact via Lennard-Jones (LJ) potentials, with identical size…
We present a method for solving trapped few-body problems and apply it to three equal-mass particles in a one-dimensional harmonic trap, interacting via a contact potential. By expressing the relative Hamiltonian in Jacobi cylindrical…
It is shown that the irreversible behavior of classical systems of interacting particles is a common property for both few-body and many-body systems. It is due to the delay in the interactions between the particles. PACS: 45.50.Jf Few- and…
We study the limiting behavior of interacting particle systems indexed by large sparse graphs, which evolve either according to a discrete time Markov chain or a diffusion, in which particles interact directly only with their nearest…
We prove that on the spectrum the integrated density of states (IDS for short) of periodic Jacobi matrices is related to the discriminant. The method is to count the number of generalized zeros of Bloch wave solutions.