Related papers: Corrections to reaction-diffusion dynamics above t…
The recently introduced method of excess collisions (MEC) is modified to estimate diffusion-controlled reaction times inside systems of arbitrary size. The resulting MEC-E equations contain a set of empirical parameters, which have to be…
We develop a statistical toolbox for a quantitative model evaluation of stochastic reaction-diffusion systems modeling space-time evolution of biophysical quantities on the intracellular level. Starting from space-time data $X_N(t,x)$, as,…
We study the diffusion-limited process $A+A\to A$ in one dimension, with finite reaction rates. We develop an approximation scheme based on the method of Inter-Particle Distribution Functions (IPDF), which was formerly used for the exact…
We investigate the late-time behavior of the thermal two-point function for a Bose gas in a curved space-time with a Killing horizon. We demonstrate that the late-time behavior undergoes a sharp transition at a critical temperature,…
Phase transitions are ubiquitous in our three-dimensional world. By contrast most conventional transitions do not occur in infinite uniform two-dimensional systems because of the increased role of thermal fluctuations. Here we explore the…
The large-scale expansion dynamics of quantum gases is a central tool for ultracold gas experiments and poses a significant challenge for theory. In this work we provide an exact reformulation of the Gross-Pitaevskii equation for the…
The change from the diffusion-limited to the reaction-limited cooperative behaviour in reaction-diffusion systems is analysed by comparing the universal long-time behaviour of the coagulation-diffusion process on a chain and on the Bethe…
Spatially resolved relative phase measurement of two adjacent 1D Bose gases is enabled by matter-wave interference upon free expansion. However, longitudinal dynamics is typically ignored in the analysis of experimental data. We provide an…
It has been established that there is an inherent limit to the accuracy of the reaction-diffusion master equation. Specifically, there exists a fundamental lower bound on the mesh size, below which the accuracy deteriorates as the mesh is…
We present an improved scheme for the precise evaluation of finite-temperature response functions of strongly correlated systems in the framework of the time-dependent density matrix renormalization group. The maximum times that we can…
Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or…
In reactions with $q \bar q$ production or $q\bar q$ annihilation, initial- and final-state interactions give rise to large corrections to the lowest-order cross sections. We evaluate the correction factor first for low relative kinetic…
We present a fully adaptive multiresolution scheme for spatially two-dimensional, possibly degenerate reaction-diffusion systems, focusing on combustion models and models of pattern formation and chemotaxis in mathematical biology.…
We study a homogeneous Bose gas with purely repulsive forces. Using the Kac scaling of the binary potential we derive analytically the form of the thermodynamic functions of the gas for small but finite values of the scaling parameter in…
Open biochemical systems of interacting molecules are ubiquitous in life-related processes. However, established computational methodologies, like molecular dynamics, are still mostly constrained to closed systems and timescales too small…
The number-conserving quantum phase space description of the Bose-Hubbard model is discussed for the illustrative case of two and three modes, as well as the generalization of the two-mode case to an open quantum system. The phase-space…
We study weakly interacting Bose gases using the functional renormalization group with a hydrodynamic effective action. We use a scale-dependent parametrization of the boson fields that interpolates between a Cartesian representation at…
We introduce a model of two coupled reaction-diffusion equations to describe the dynamics and propagation of flame fronts in random media. The model incorporates heat diffusion, its dissipation, and its production through coupling to the…
Using statistical physics methods, we study generative diffusion models in the regime where the dimension of space and the number of data are large, and the score function has been trained optimally. Our analysis reveals three distinct…
A class of $d$-dimensional reaction-diffusion models interpolating continuously between the diffusion-coagulation and the diffusion-annihilation models is introduced. Exact relations among the observables of different models are…