相关论文: Shape phase transitions and random interactions
Based on numerical simulation and local stability analysis we describe the structure of the phase space of the edge/triangle model of random graphs. We support simulation evidence with mathematical proof of continuity and discontinuity for…
Modelling randomness in shape data, for example, the evolution of shapes of organisms in biology, requires stochastic models of shapes. This paper presents a new stochastic shape model based on a description of shapes as functions in a…
We argue that the phase transition in the mean-field XY model is related to a particular change in the topology of its configuration space. The nature of this topological transition can be discussed on the basis of elementary Morse theory…
Motivated by the role that spectral properties play for the dynamical evolution of a quantum many-body system, we investigate the level spacing statistic of the extended Bose-Hubbard model. In particular, we focus on the distribution of the…
A model of holographic dark energy with an interaction with matter fields has been investigated. Choosing the future event horizon as an IR cutoff, we have shown that the ratio of energy densities can vary with time. With the interaction…
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…
A rotationally invariant random interaction ensemble was realized in a single-j fermion model. The dominance of ground states with zero and maximum spin was confirmed and explained with a statistical approach based on the random coupling of…
The confluence of unitary dynamics and non-unitary measurements gives rise to intriguing and relevant phenomena, generally referred to as measurement-induced phase transitions. These transitions have been observed in quantum systems…
Topological phases of matter are often understood and predicted with the help of crystal symmetries, although they don't rely on them to exist. In this chapter we review how topological phases have been recently shown to emerge in amorphous…
We consider a generalized model of repeated quantum interactions, where a system $\mathcal{H}$ is interacting in a random way with a sequence of independent quantum systems $\mathcal{K}_n, n \geq 1$. Two types of randomness are studied in…
We derive sufficient conditions for the mixing of all orders of interacting transformations of a spatial Poisson point process, under a zero-type condition in probability and a generalized adaptedness condition. This extends a classical…
A class of solid-on-solid growth models with short range interactions and sequential updates is studied. The models exhibit both smooth and rough phases in dimension d=1. Some of the features of the roughening transition which takes place…
Simulations show that sliding bilayers of colloidal particles can exhibit a new phase, the ``melt-freeze'' phase, where the layers stochastically alternate between solidlike and liquidlike states. We introduce a mean field phenomenological…
Directly interacting particles are considered in the multitime formalism of predictive relativistic mechanics. When the equations of motion leave a phase-space volume invariant, it turns out that the phase average of any first integral,…
Higher-order interactions have recently emerged as a promising framework for describing new dynamical phenomena in heterogeneous contagion processes. However, a fundamental open question is how to understand their contribution from the…
As phenomena that necessarily emerge from the collective behavior of interacting particles, phase transitions continue to be difficult to predict using statistical thermodynamics. A recent proposal called the topological hypothesis suggests…
Shape/phase transitions in atomic nuclei have first been discovered in the framework of the Interacting Boson Approximation (IBA) model. Critical point symmetries appropriate for nuclei at the transition points have been introduced as…
The advent of high resolution imaging has made data on surface shape widespread. Methods for the analysis of shape based on landmarks are well established but high resolution data require a functional approach. The starting point is a…
We consider a homogeneous Bose gas of particles with an attractive interaction. Mean field theory predicts for this system a spontaneous symmetry breaking at a certain value of the interaction strength. We show that at this point a…
We study the phase diagram of the one-dimensional boson gas trapped inside an optical lattice with contact and dipolar interaction taking into account next-nearest terms for both tunneling and interaction. Using the density matrix…