Related papers: Two populations mean-field monomer-dimer model
Quenched thermodynamic states of an amorphous ferromagnet are studied. The magnet is a countable collection of point particles chaotically distributed over $\mathbb{R}^d$, $d\geq 2$. Each particle bears a real-valued spin with symmetric a…
In this paper we derive a two dimensional spray model with gyroscopic effects as the mean-field limit of a system modeling the interaction between an incompressible fluid and a finite number of solid particles. This spray model has been…
We analyse the thermodynamic properties of a generalised Dicke model, i.e. a collection of three-level systems interacting with two bosonic modes. We show that at finite temperatures the system undergoes first-order phase transitions only,…
The mean-field limit for the dynamics of bosons with random interactions is rigorously studied. It is shown that, for interactions that are almost-surely bounded, the many-body quantum evolution can be replaced in the mean-field limit by a…
Exact and approximate expressions for thermodynamic characteristics of heated matter, which consists of particles with finite mass-widths, are constructed. They are expressed in terms of Fermi/Bose distributions and spectral functions,…
We study the thermodynamics of the one-dimensional extended Hubbard model at half-filling using a density-matrix renormalization group method applied to transfer matrices. We show that the various phase transitions in this system can be…
We consider a model of fermions interacting via point interactions, defined via a certain weighted Dirichlet form. While for two particles the interaction corresponds to infinite scattering length, the presence of further particles…
Mean-field Ring Polymer Molecular Dynamics (MF-RPMD) offers a computationally efficient method for the simulation of reaction rates in multi-level systems. Previous work has established that, to model a nonadiabatic state-to-state reaction…
A one-dimensional reaction-diffusion model consisting of two species of particles and vacancies on a ring is introduced. The number of particles in one species is conserved while in the other species it can fluctuate because of creation and…
The existence and search for thermodynamic phase transitions is of unfading interest. In this paper, we present numerical evidence of dynamical phase transitions occurring in boundary driven systems with a constrained integrated current. It…
The transition from a few-body system to a many-body system can result in new length scales, novel collective phenomena or even in a phase transition. Such a threshold behavior was shown for example in 4He droplets, where 4He turns into a…
We develop a statistical model for a confined chain molecule based on a monomer grand canonical ensemble. The molecule is subject to an external chemical potential, a backbone interaction, and an attractive interaction between all monomers.…
We propose a class of mean-field models for the isostatic transition of systems of soft spheres, in which the contact network is modeled as a random graph and each contact is associated to $d$ degrees of freedom. We study such models in the…
A finite-volume scheme for a cross-diffusion model arising from the mean-field limit of an interacting particle system for multiple population species is studied. The existence of discrete solutions and a discrete entropy production…
We study the collective dynamics of a population of particles/organisms subject to self-consistent attraction-repulsion interactions and an external velocity field. The starting point of our analysis is a mean-field kinetic model and we…
We study the average density of states in a small metallic grain coupled to two superconductors with the phase difference $\pi$, in a magnetic field. The spectrum of the low-energy excitations in the grain is described by the random matrix…
Understanding quantum many-body systems with long-range or infinite-range interactions is of relevance across a broad set of physical disciplines, including quantum optics, nuclear magnetic resonance and nuclear physics. From a theoretical…
The dynamics of a mean-field model of three coupled condensates is studied for initial states characterized by twin condensates. Condensates occupy an open three-well chain, where the central potential-well depth is an independent…
The properties of statistical ensembles with abelian charges close to the thermodynamic limit are discussed. The finite volume corrections to the probability distributions and particle density moments are calculated. Results are obtained…
Magnetic phenomena of the superantiferromagnetic Ising model in both uniform longitudinal ($H$) and transverse ($\Omega $) magnetic fields are studied by employing a mean-field variational approach based on Peierls-Bogoliubov inequality for…