Related papers: Statistical Characterization of a 1D Random Potent…
The run-and-tumble particle (RTP) is one of the simplest examples of an active particle in which the direction of constant motion randomly switches. In the one-dimensional (1D) case this means switching between rightward and leftward…
A density matrix describes the statistical state of a quantum system. It is a powerful formalism to represent both the quantum and classical uncertainty of quantum systems and to express different statistical operations such as measurement,…
In this article we study a fully relativistic model of a two dimensional hard-disk gas. This model avoids the general problems associated with relativistic particle collisions and is therefore an ideal system to study relativistic effects…
In this thesis, we study three physically relevant models of strongly correlated random variables: trapped fermions, random matrices and random walks. In the first part, we show several exact mappings between the ground state of a trapped…
Optical microscopy provides rich spatio-temporal information characterizing in vivo molecular motion. However, effective forces and other parameters used to summarize molecular motion change over time in live cells due to latent state…
We introduce a path sampling method for obtaining statistical properties of an arbitrary stochastic dynamics. The method works by decomposing a trajectory in time, estimating the probability of satisfying a progress constraint, modifying…
There has been a recent surge of interest in understanding charge transport at atomic scales. The motivations are myriad, including understanding the conductance properties of peptides measured experimentally. In this study, we propose a…
Calculations and mechanistic explanations for the probabilistic movement of objects at the highly relevant cm length scales has been lacking and overlooked due to the complexity of current techniques. Predicting the final-configuration…
We study the 1D Hamilton systems and their statistical behaviour, assuming the initial microcanonical distribution and describing its change under a parametric kick, which by definition means a discontinuous jump of a control parameter of…
We examine the localization properties of the three-dimensional (3D) Anderson Hamiltonian with off-diagonal disorder using the transfer-matrix method (TMM) and finite-size scaling (FSS). The nearest-neighbor hopping elements are chosen…
A well-known approach to describe the dynamics of an open quantum system is to compute the master equation evolving the reduced density matrix of the system. This approach plays an important role in describing excitation transfer through…
We examine the fundamental aspects of statistical mechanics, dividing the problem into a discussion purely about probability, which we analyse from a Bayesian standpoint. We argue that the existence of a unique maximising probability…
We study numerical methods for dissipative particle dynamics (DPD), which is a system of stochastic differential equations and a popular stochastic momentum-conserving thermostat for simulating complex hydrodynamic behavior at mesoscales.…
We study the entanglement spectrum of a translationally-invariant lattice system under a random partition, implemented by choosing each site to be in one subsystem with probability $p\in[0, 1]$. We apply this random partitioning to a…
Accurate descriptions of reference systems are a central task in liquid-state theories for the study of more complex systems. Using scaled particle theory (SPT), we derive a fully analytical description of the thermodynamic properties of a…
The densities of states are evaluated for very short chain molecules made up of overlapping monomers, using a model which has previously been shown to produce helical structure. The results of numerical calculations are presented for…
Computer simulations generate trajectories at a single, well-defined thermodynamic state point. Statistical reweighting offers the means to reweight static and dynamical properties to different equilibrium state points by means of analytic…
We derive a powerful yet simple method for analyzing the local density of states in gapless one dimensional fermionic systems, including extensions such as momentum dependent interaction parameters and hard-wall boundaries. We study the…
Equilibrium statistical mechanics is intended to link the microscopic dynamics of particles to the thermodynamic laws for macroscopic quantities. However, the modern statistical theory is faced with significant difficulties, as applied to…
We propose a new statistical mechanics model for the melting transition of DNA. Base pairing and stacking are treated as separate degrees of freedom, and the interplay between pairing and stacking is described by a set of local rules which…