Related papers: Front motion for phase transitions in systems with…
The motion of particles, where the particles: electrons, ions in microtubules or migrated peoples can be described as the superposition of diffusion and ordered waves. In this paper it is shown that the master equation for transport…
We discuss adiabatic spectra and dynamics of the quantum, i.e. transverse field, Hopfield model with dilute memories (the number of stored patterns $p < log_2 N$, where $N$ is the number of qubits). At some critical transverse field the…
Field equations with time and coordinates derivatives of noninteger order are derived from stationary action principle for the cases of power-law memory function and long-range interaction in systems. The method is applied to obtain a…
Reduced Order Models (ROMs) of complex, nonlinear dynamical systems often require closure, which is the process of representing the contribution of the unresolved physics on the resolved physics. The Mori-Zwanzig (M-Z) procedure allows one…
This article is devoted to the study of certain models for phase transitions involving nonlocal energies. A first part is concerned with to the asymptotic analysis of a system of fractional elliptic equations of Allen-Cahn type as a…
In this paper, we derive the time-fractional Cahn-Hilliard equation from continuum mixture theory with a modification of Fick's law of diffusion. This model describes the process of phase separation with nonlocal memory effects. We analyze…
Based on a recent work on traveling waves in spatially nonlocal reaction-diffusion equations, we investigate the existence of traveling fronts in reaction-diffusion equations with a memory term. We will explain how such memory terms can…
Approximate asymptotic conditions on the motion of compact, electrically charged particles are derived within the framework of general relativity using the Einstein- Infeld-Hoffmann (EIH) surface integral method. While superficially similar…
We study the systematic numerical approximation of a class of Allen-Cahn type problems modeling the motion of phase interfaces. The common feature of these models is an underlying gradient flow structure which gives rise to a decay of an…
We describe a class of evolution systems of linear partial differential equations with the Caputo-Dzhrbashyan fractional derivative of order $\alpha \in (0,1)$ in the time variable $t$ and the first order derivatives in spatial variables…
Time-fractional partial differential equations are nonlocal in time and show an innate memory effect. In this work, we propose an augmented energy functional which includes the history of the solution. Further, we prove the equivalence of a…
Just like decent classical difference-difference systems define symplectic maps on suitable phase spaces, their counterparts with properly ordered noncommutative entries come as Heisenberg equations of motion for corresponding quantum…
A large class of linear memory differential equations in one dimension, where the evolution depends on the whole history, can be equivalently described as a projection of a Markov process living in a higher dimensional space. Starting with…
We explore the concept of memory in scalar active matter, focusing on the collective dynamics of particles whose interactions depend on their evolutionary history rather than solely on their current configuration. We introduce the idea of…
We examine the emergence of dynamical memory effects in quantum processes having indefinite time direction and causal order. In particular, we focus on the class of phase-covariant qubit channels, which encompasses some of the most…
We study in this note the Fisher-KPP equation where the Laplacian is replaced by the generator of a Feller semigroup with slowly decaying kernel, an important example being the fractional Laplacian. Contrary to what happens in the standard…
The classical Maxwell--Born--Infeld field equations coupled with a Hamilton--Jacobi law of point charge motion are partially quantized by coupling the Hamilton-Jacobi phase function with an amplitude function, which combines with the phase…
The path integral Lindblad dynamics (PILD) method [A. Bose, J. Phys. Chem. Lett. 15(12), 3363-3368 (2024)] had been introduced as a way of incorporating the impact of certain empirical processes like pumps and drains on the dynamics of…
The quantum theory of Brownian motion is discussed in the Schwinger version wherein the notion of a coordinate moving forward in time $x(t)$ is replaced by two coordinates, $x_+(t)$ moving forward in time and $x_-(t)$ moving backward in…
Memory effects in a quantum system coupled to an environment are one of the central features in the theory of open quantum systems. The dynamics of such quantum systems are typically governed by an equation of motion with a time-convolution…