Related papers: Finite size scaling in crossover among different r…
We study the probability distribution of the ratio of consecutive level spacings for embedded one plus two-body random matrix ensembles with and without spin degree of freedom and for both fermion and boson systems. The agreement between…
We perform a dynamical finite-size scaling analysis of a nonequilibrium Bose gas which is confined in the transverse plane. Varying the transverse size, we establish a dimensional crossover for universal scaling properties far from…
Accurate numerical results are presented for the three-dimensional equivalent-neighbor model on a cubic lattice, for twelve different interaction ranges (coordination number between 18 and 250). These results allow the determination of the…
For theoretical analyses there are two specifics distinguishing GP from many other areas of evolutionary computation. First, the variable size representations, in particular yielding a possible bloat (i.e. the growth of individuals with…
A Gaussian quantum theory of bosonic modes has been widely used to describe quantum optical systems, including coherent Ising machines (CIMs) that consist of $\chi^{(2)}$ degenerate optical parametric oscillators (DOPOs) as nonlinear…
Suppose some random resource (energy, mass or space) $\chi \geq 0$ is to be shared at random between (possibly infinitely many) species (atoms or fragments). Assume ${\Bbb E}\chi =\theta <\infty $ and suppose the amount of the individual…
We present a finite-size scaling analysis of the droplet condensation-evaporation transition of a lattice gas (in two and three dimensions) and a Lennard-Jones gas (in three dimensions) at fixed density. Parallel multicanonical simulations…
Interacting many-particle systems with a mean-field one body part plus a chaos generating random two-body interaction having strength $\lambda$, exhibit Poisson to GOE and Breit-Wigner (BW) to Gaussian transitions in level fluctuations and…
We theoretically study the scale-invariant relaxation dynamics in segregating two-component Bose-Einstein condensates with large particle-number imbalance, and uncover that random walk of droplet for the minor component plays a fundamental…
Random matrix theory has proven very successful in the understanding of the spectra of chaotic systems. Depending on symmetry with respect to time reversal and the presence or absence of a spin 1/2 there are three ensembles, the Gaussian…
We prove that the distribution function of the largest eigenvalue in the Gaussian Unitary Ensemble (GUE) in the edge scaling limit is expressible in terms of Painlev\'e II. Our goal is to concentrate on this important example of the…
We study crossover phenomena in a model of self-avoiding walks with medium-range jumps, that corresponds to the limit $N\to 0$ of an $N$-vector spin system with medium-range interactions. In particular, we consider the critical crossover…
The focus of this survey paper is on the distribution function for the largest eigenvalue in the finite N Gaussian ensembles (GOE,GUE,GSE) in the edge scaling limit of N->infinity. These limiting distribution functions are expressible in…
We present a new unified theory of critical finite-size scaling for lattice statistical mechanical models with periodic boundary conditions above the upper critical dimension. Our theory is based on recent mathematically rigorous results…
The physical mass scales that determine the behaviour of general (simply-laced) Homogeneous Sine-Gordon models are investigated by means of a study of their finite-size effects, using the thermodynamic Bethe ansatz. These models describe…
From the random matrix theory all the energy levels should be strongly correlated due to the presence of all off-diagonal entries.In this work we introduce two new statistics to more accurately characterize these long-distance interactions…
Irregular distribution in latent space causes posterior collapse, misalignment between posterior and prior, and ill-sampling problem in Variational Autoencoders (VAEs). In this paper, we introduce a novel adaptable three-stage Uniform…
Laser-driven Bose-Einstein condensate of ultracold atoms loaded into a lossy high-finesse optical resonator exhibits critical behavior and, in the thermodynamic limit, a phase transition between stationary states of different symmetries.…
We study a class of interacting particle systems on $\mathbb{R}$ which was recently investigated by F. G\"otze and the second author [GV14]. These ensembles generalize eigenvalue ensembles of Hermitian random matrices by allowing different…
The spontaneous breaking of a global discrete translational symmetry in the finite, lattice quantum sine-Gordon model is demonstrated by a density matrix renormalization group. A phase diagram in the coupling constant - inverse system size…