Related papers: The super-critical contact process has a spectral …

We consider many-body systems with a global U(1) symmetry on a class of lattices with the (fractal) dimensions D<2 and their zero temperature correlations whose observables behave as a vector under the U(1) rotation. For a wide class of the…

We study the two-species symbiotic contact process (2SCP), recently proposed in [de Oliveira, Santos and Dickman, Phys. Rev. E {\bf 86}, 011121 (2012)] . In this model, each site of a lattice may be vacant or host single individuals of…

Point-contact measurements on the carbon-substituted Mg(B$_{1-x}$C$_x$)$_2$ filament/powder samples directly reveal a retention of the two superconducting energy gaps in the whole doping range from $x = 0$ to $x \approx 0.1$. The large gap…

The model of random interlacements on Z^d, d bigger or equal to 3, was recently introduced in arXiv:0704.2560. A non-negative parameter u parametrizes the density of random interlacements on Z^d. In the present note we investigate the…

We consider self-avoiding walk and percolation in $\Zd$, oriented percolation in $\Zd\times\Zp$, and the contact process in $\Zd$, with $p D(\cdot)$ being the coupling function whose range is denoted by $L<\infty$. For percolation, for…

We consider the contact process on scale-free percolation, a spatial random graph model where the degree distribution of the vertices follows a power law with exponent $\beta$. We study the extinction time $\tau_{G_n}$ of the contact…

This thesis investigates critical phenomena and equilibrium states in various stochastic models through three interconnected studies. In the first chapter, we analyze the Activated Random Walk model on a one-dimensional ring in the…

Lortz et al. [Phys. Rev. B 73, 024512 (2006)] have utilized specific heat and resistivity measurements as "thermal spectroscopies" to deconvolve the spectrum of the electron-phonon interaction in YB$_6$ assuming a major role of the low…

We study versions of the contact process with three states, and with infections occurring at a rate depending on the overall infection density. Motivated by a model described in [17] for vegetation patterns in arid landscapes, we focus on…

We consider the extinction time of the contact process on increasing sequences of finite graphs obtained from a variety of random graph models. Under the assumption that the infection rate is above the critical value for the process on the…

Electrical characteristics $(I(eV), dV/dI(eV), d^{2}V/dI^{2}(eV))$ are studied comprehensively for pressed submicron point contacts between fresh fractures of LaSrCuO ceramic pellets and a normal metal (Cu). Point contacts (PC) with the…

We present the experimental evidence for the existence of two exciting wavelengths, termed critical and cross-over wavelength in the transmission spectrum of fiber-optic directional coupler, whose properties are conjugate to each other. The…

The energy spectrum of the Hofstadter model has a fractal structure with infinitely many gaps. We prove the persistence of each gap in presence of Hubbard interaction in the case of small transversal hopping, even when the coupling is much…

We study the supercritical contact process on Galton-Watson trees and periodic trees. We prove that if the contact process survives weakly then it dominates a supercritical Crump-Mode-Jagers branching process. Hence the number of infected…

We consider a simple model of partially expanding map on the torus. We study the spectrum of the Ruelle transfer operator and show that in the limit of high frequencies in the neutral direction (this is a semiclassical limit), the spectrum…

We performed point-contact spectroscopy on the binary superconductor MgB$_2$. The differential conductance shows gap-related structures which vary in width and position from contact to contact. The distribution of energy gaps shows a…

We study the spectral gap for transfer operators of the skew product $F: \mathbb{T}^d\times \mathbb{T}^\ell\to \mathbb{T}^d\times \mathbb{T}^\ell$ given by $F(x,y)=(Tx, y+\tau(x) \pmod{ \mathbb{Z}^\ell})$, where $T: \mathbb{T}^d\to…

We study the stationary properties of the two-dimensional pair contact process, a nonequilibrium lattice model exhibiting a phase transition to an absorbing state with an infinite number of configurations. The critical probability and…

We identify universal properties of the low-energy subspace of a wide class of quantum optical models in the ultrastrong coupling limit, where the coupling strength dominates over all other energy scales in the system. We show that the…

We consider the contact process on a dynamic graph defined as a random $d$-regular graph with a stationary edge-switching dynamics. In this graph dynamics, independently of the contact process state, each pair $\{e_1,e_2\}$ of edges of the…