Related papers: Particle Systems with Repulsion Exponent $\beta$ a…
We propose a general coarse-graining method to derive a continuity equation that describes any dissipative system of repulsive particles interacting through short-ranged potentials. In our approach, the effect of particle-particle…
Distance control in many-particle systems is a fundamental problem in nature. This becomes particularly relevant in systems of active agents, which can sense their environment and react by adjusting their direction of motion. We employ…
In the classical $\beta$-ensembles of random matrix theory, setting $\beta = 2 \alpha/N$ and taking the $N \to \infty$ limit gives a statistical state depending on $\alpha$. Using the loop equations for the classical $\beta$-ensembles, we…
Because of the potentially large number of important applications of nonlinear optics, researchers have expended a great deal of effort to optimize the second-order molecular nonlinear-optical response, called the hyperpolarizability. The…
We consider consistent particle systems, which include independent random walkers, the symmetric exclusion and inclusion processes, as well as the dual of the KMP model. Consistent systems are such that the distribution obtained by first…
In this paper a general theorem of constructing infinite particle systems of jump types with long range interactions is presented. It can be applied to the system that each particle undergoes an $\alpha$-stable process and interaction…
This work shows that dynamical features typical of full random matrices can be observed also in the simple finite one-dimensional (1D) noninteracting Anderson model with nearest neighbor couplings. In the thermodynamic limit, all…
We study a one-dimensional particles system, in the overdamped limit, where nearest particles attract with a force inversely proportional to a power of their distance and coalesce upon encounter. The detailed shape of the distribution…
We reinvestigate the validity of mapping the problem of two onsite interacting particles in a random potential onto an effective random matrix model. To this end we first study numerically how the non-interacting basis is coupled by the…
A unified treatment for the existence of free energy in several random energy models is presented. If the sequence of distributions associated with the particle systems obeys a large deviation principle, then the free energy exists almost…
We investigate the entanglement properties of multiparticle systems, concentrating on the case where the entanglement is robust against disposal of particles. Two qubits -belonging to a multipartite system- are entangled in this sense iff…
We consider a self-propelled particle system which has been used to describe certain types of collective motion of animals, such as fish schools and bird flocks. Interactions between particles are specified by means of a pairwise potential,…
For itinerant fermionic and bosonic systems, we study `particle entanglement', defined as the entanglement between two subsets of particles making up the system. We formulate the general structure of particle entanglement in many-fermion…
We study the local relaxation of closed quantum systems through the relative entropy between the reduced density matrix and its long time limit. We show, using analytic arguments combined with numerical checks, that this relative entropy…
We investigate the behaviour of a system of particles with the different character of interaction. The approach makes it possible to describe systems of interacting particles by statistical methods taking into account a spatial…
We study the spectral properties of a class of random matrices where the matrix elements depend exponentially on the distance between uniformly and randomly distributed points. This model arises naturally in various physical contexts, such…
A system of a particle and a harmonic oscillator, which have pure point spectrum if uncoupled, is known to acquire absolutely continuous spectrum when the particle and the oscillator are coupled by a sufficiently strong point interaction.…
A two-dimensional statistical model of N charged particles interacting via logarithmic repulsion in the presence of an oppositely charged regular closed region K whose charge density is determined by its equilibrium potential at an inverse…
We introduce and study a class of discrete particle ensembles that naturally arise in connection with classical random matrix ensembles, log-gases and Jack polynomials. Under technical assumptions on a general analytic potential we prove…
Introducing sets of constraints, we define new classes of random-matrix ensembles, the constrained Gaussian unitary (CGUE) and the deformed Gaussian unitary (DGUE) ensembles. The latter interpolate between the GUE and the CGUE. We derive a…