Related papers: Physics in non-fixed spatial dimensions via random…
Eigenspectra of a spinless quantum particle trapped inside a rigid, rectangular, two-dimensional (2D) box subject to diverse inner potential distributions are investigated under hermitian, as well as non-hermitian antiunitary $\mathcal{PT}$…
In this article we investigate consistency and asymptotic normality of the maximum likelihood and the posterior distribution of the parameters in the context of state space stochastic differential equations (SDEs). We then extend our…
In wireless networks, the knowledge of nodal distances is essential for several areas such as system configuration, performance analysis and protocol design. In order to evaluate distance distributions in random networks, the underlying…
In spatial networks vertices are arranged in some space and edges may cross. When arranging vertices in a 1-dimensional lattice edges may cross when drawn above the vertex sequence as it happens in linguistic and biological networks. Here…
We consider a quantum system that is initially localized at $x_{in}$ and that is repeatedly projectively probed with a fixed period $\tau$ at position $x_d$. We ask for the probability that the system is detected in $x_d$ for the very first…
The spectral dimension has been widely used to understand transport properties on regular and fractal lattices. Nevertheless, it has been little studied for complex networks such as scale-free and small world networks. Here we study the…
We survey recent results on spectral properties of random Schr\"odinger operators. The focus is set on the integrated density of states (IDS). First we present a proof of the existence of a self-averaging IDS which is general enough to be…
We consider a one-dimensional network in which the nodes at Euclidean distance $l$ can have long range connections with a probabilty $P(l) \sim l^{-\delta}$ in addition to nearest neighbour connections. This system has been shown to exhibit…
The classical and quantum dynamics of a particle trapped in a one-dimensional infinite square well with a time periodic pulsed field is investigated. This is a two-parameter non-KAM generalization of the kicked rotor, which can be seen as…
We develop a statistical mechanics approach for random networks with uncorrelated vertices. We construct equilibrium statistical ensembles of such networks and obtain their partition functions and main characteristics. We find simple…
In this work we discuss the symmetric construction of bosonic and fermionic networks and we present a case of a network showing a mixed quantum statistics. This model takes into account the different nature of nodes, described by a random…
We set up and analyse a model for the non-equilibrium evolution of a network of cosmic strings initially containing only loops and no infinite strings. Due to this particular initial condition, our analytical approach differs significantly…
Several aspects of classical and quantum mechanics applied to a class of strongly chaotic systems are studied. These consist of single particles moving without external forces on surfaces of constant negative Gaussian curvature whose…
We find the laws for the spreading of the spatial widths (parallel and transverse to the direction of average motion) of the relativistic position probability density for a massive, spinless particle. We find that when the momentum width of…
Recently, it became possible to experimentally generate and characterize a very thin silica system on a substrate which can be basically described as a 2D random network. The key structural properties, in particular related to the ring…
We consider two-dimensional (2D) "artificial atoms" confined by an axially symmetric potential $V(\rho)$. Such configurations arise in circular quantum dots and other systems effectively restricted to a 2D layer. Using the semiclassical…
Physics-informed neural networks have shown promise in solving partial differential equations (PDEs) by integrating physical constraints into neural network training, but their performance is sensitive to the sampling of points. Based on…
Inelastic electron scattering by the adsorbate covered Pt(100) single crystal surface is studied by Disappearance Potential Spectroscopy and density of states (DOS) calculations. Two peculiar channels of elastic electron consumption are…
The spectral properties of the Laplacian on a class of quantum graphs with random metric structure are studied. Namely, we consider quantum graphs spanned by the simple $\ZZ^d$-lattice with $\delta$-type boundary conditions at the vertices,…
We study the dynamics of density fluctuations in the steady state of a non-equilibrium system, the Zero-Range Process on a ring lattice. Measuring the time series of the total number of particles in a \emph{segment} of the lattice, we find…