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System-environment interactions are intrinsically nonlinear and dependent on the interplay between many degrees of freedom. The complexity may be even more pronounced when one aims to describe biologically motivated systems. In that case,…
This study deals with continuous limits of interacting one-dimensional diffusive systems, arising from stochastic distortions of discrete curves with various kinds of coding representations. These systems are essentially of a…
In many instances, the dynamical richness and complexity observed in natural phenomena can be related to stochastic drives influencing their temporal evolution. For example, random noise allied to spatial asymmetries may induce…
First passage time experiments were used to explore the effects of low amplitude noise as a source of accelerated phase space diffusion in two-dimensional Hamiltonian systems, and these effects were then compared with the effects of…
Matter-wave interferometers with micro-particles will enable the next generation of quantum sensors to probe minute quantum phase information. Therefore, estimating the loss of coherence and the degree of entanglement degradation for such…
We investigate the stationary and dynamic properties of the celebrated Nos\'e-Hoover dynamics of many-body interacting Hamiltonian systems, with an emphasis on the effect of inter-particle interactions. To this end, we consider a model…
We review and complete the existing literature on the kinetic theory of spatially homogeneous systems with long-range interactions taking collective effects into account. The evolution of the system as a whole is described by the…
A spatially extended Lotka-Volterra system of two competing species in the presence of two correlated noise sources is analyzed: (i) an external multiplicative time correlated noise, which mimics the interaction between the system and the…
The property of quantum correlation has been studied in recent years, especially for the quantum and classical correlations affected by environment. The dynamics of quantum and classical correlations in two-qubit system under identical…
We explore the spontaneous generation and decay of quantum correlations between two identical atoms coupled to a common Markovian environment in the presence of electromagnetic field modes. For this purpose, we analyze the dynamics of…
Unlike closed systems, where the total energy and information are conserved within the system, open systems interact with the external environment which often leads to complex behaviors not seen in closed systems. The random fluctuations…
We present a series of results focused on the decay in time of solutions of classical and anomalous diffusive equations in a bounded domain. The size of the solution is measured in a Lebesgue space, and the setting comprises time-fractional…
In this article we numerically revisit the long-time solution behavior of the Camassa-Holm equation. The finite difference solution of this integrable equation is sought subject to the newly derived initial condition with Delta-function…
Noise-assisted transport phenomena highlight the nontrivial interplay between environmental effects and quantum coherence in achieving maximal efficiency. Due to the complexity of biochemical systems and their environments, effective open…
In this paper, we consider the $n$-dimensional ($n=2,3$) Camassa-Holm equations with fractional Laplacian viscosity in the whole space. In stark contrast to the Camassa-Holm equations without any nonlocal effect, to our best knowledge,…
We study the effects of hydrodynamic fluctuations in non-boost-invariant longitudinal expansion of matter formed in relativistic heavy ion collisions. We formulate the theory of thermal noise within second-order viscous hydrodynamics…
In this work, we investigate the dynamics of an inhomogeneous coupled nonlinear Schrodinger system with quadratic-type interactions. Such systems arise naturally in nonlinear dynamics and mathematical physics, particularly in nonlinear…
We address extended systems interacting with classical fluctuating environments and analyze the use of quantum probes to discriminate local noise, described by independent fluctuating fields, from common noise, corresponding to the…
We study a class of stochastic time-fractional equations on $\mathbb{R}^d$ driven by a centered Gaussian noise, involving a Caputo time derivative of order $\beta>0$, a fractional (power) Laplacian of order $\alpha>0$, and a…
This work addresses friction-induced modal interactions in jointed structures, and their effects on the passive mitigation of vibrations by means of friction damping. Under the condition of (nearly) commensurable natural frequencies, the…