Related papers: Attractive nearest-neighbor spin systems on the in…
This thesis presents studies performed on open quantum systems, that is, quantum systems interacting with their surrounding environment. Such systems are important not only in understanding the quantum-to-classical transition but also for…
We use a random pinning procedure to study amorphous order in two glassy spin models. On increasing the concentration of pinned spins at constant temperature, we find a sharp crossover (but no thermodynamic phase transition) from bulk…
Markov chains in random environments (MCREs) have recently attracted renewed interest, as these processes naturally arise in many applications, such as econometrics and machine learning. Although specific asymptotic results, such as the law…
We prove the existence of a solution to an equation governing the number density within a compact domain of a discrete particle system for a prescribed class of particle interactions taking into account the effects of the diffusion and…
We describe theoretically the process of multi-beam reflection in a two-dimensional electron system with a lateral potential barrier. Due to spin-orbital interaction, the reflection process leads to the formation of three beams with…
An expansion in inverse spin anisotropy, which enables us to study the behaviour of discrete spin models as the spins soften, is developed. In particular we focus on models, such as the chiral clock model and the $p$-state clock model with…
The trace distance between two states of an open quantum system quantifies their distinguishability, and for a fixed environmental state can increase above its initial value only in the presence of initial system-environment correlations.…
Data-based inference of directed interactions in complex dynamical systems is a problem common to many disciplines of science. In this work, we study networks of spatially separate dynamical entities, which could represent physical systems…
Biological information processing networks consist of many components, which are coupled by an even larger number of complex multivariate interactions. However, analyses of data sets from fields as diverse as neuroscience, molecular…
A computer code is written that simulates the relaxation back to thermal equilibrium of an ensemble of particles after a pi/2 pulse. Beginning with Bloch's equations the exponential relaxation behavior is discussed and the transition into a…
Understanding the dynamics of open quantum systems is a highly important task for the implementation of emerging quantum technologies. To make the problem tractable theoretically, it is common to neglect initial system-environment…
We analyze the dynamics of N interacting spins (quantum register) collectively coupled to a thermal environment. Each spin experiences the same environment interaction, consisting of an energy conserving and an energy exchange part. We find…
We address the dynamics of interacting particles on a disordered lattice formed by a random comb. The dynamics comprises that of the asymmetric simple exclusion process, whereby motion to nearest-neighour sites that are empty is more likely…
We study the limiting behavior of an interacting particle system evolving on the lattice $Z^{d}$ for $d\ge 3$. The model is known as the contact process with rapid stirring. The process starts with a single particle at the origin. Each…
We study the formation of spontaneous spin polarization in inhomogeneous electron systems with pair interaction localized in a small region that is not separated by a barrier from surrounding gas of non-interacting electrons. Such a system…
Motivated by a model of an area-wide integrated pest management, we develop an interacting particle system evolving in a random environment. It is a generalised contact process in which the birth rate takes two possible values, determined…
We exhibit a class of integer spin systems whose free energy can be written in term of an absolutely convergent series at any temperature. This class includes spin systems on $\Z^d$ interacting through infinite range pair potential…
Recent developments in attosecond spectroscopy yield access to the correlated motion of electrons on their intrinsic time scales. Spin-flip dynamics is usually considered in the context of valence electronic states, where spin-orbit…
A subcritical branching process in random environment (BPRE) is considered whose associated random walk does not satisfy the Cramer condition. The asymptotics for the survival probability of the process is investigated, and a Yaglom type…
Rate processes are simple and analytically tractable models for many dynamical systems which switch stochastically between a discrete set of quasi stationary states but they may also approximate continuous processes by coarse grained,…