Related papers: Exact non-Markovian evolution with multiple reserv…
A sufficient condition for non-Markovian master equation which ensures the complete positivity of the resulting time evolution is presented.
A Markov evolution of a system of point particles in $\mathbb{R}^d$ is described at micro-and mesoscopic levels. The particles reproduce themselves at distant points (dispersal) and die, independently and under the influence of each other…
We extend the non-Markovian quantum state diffusion (QSD) equation to open quantum systems which exhibit multi-channel coupling to a harmonic oscillator reservoir. Open quantum systems which have multi-channel reservoir coupling are those…
There are various measures to compute correlation in various conditions, but none of them can be used publicly, because each of them has abnormality in their calculations or behaviors. These abnormalities do not depend on genus of…
We derive the evolution equation for the density matrix of a UV- and IR- limited band of comoving momentum modes of the canonically normalized scalar degree of freedom in two examples of nearly de Sitter universes. Including the effects of…
We consider the hydrodynamic behavior of some conservative particle systems with degenerate jump rates without exclusive constraints. More precisely, we study the particle systems without restrictions on the total number of particles per…
We consider Vlasov-type scaling for Markov evolution of birth-and-death type in continuum, which is based on a proper scaling of corresponding Markov generators and has an algorithmic realization in terms of related hierarchical chains of…
We propose a class of evolutionary models that involves an arbitrary exchangeable process as the breeding process and different selection schemes. In those models, a new genome is born according to the breeding process, and then a genome is…
We present a detailed microscopic derivation for a non-Markovian master equation for a driven two-state system interacting with a general structured reservoir. The master equation is derived using the time-convolutionless projection…
Two coupled spatial birth-and-death Markov evolutions on $\mathbb{R}^d$ are obtained as unique weak solutions to the associated Fokker-Planck equations. Such solutions are constructed by its associated sequence of correlation functions…
In this paper mathematical models for the evolutionary conserved Notch-Delta pathway are developed and analyzed in order to better understand how two neighboring biological cells can become different. We pursue a structure-based…
We show that any non-relativistic quantum N-body dynamics problem with pairwise interactions can be exactly reformulated in terms of N well behaved 1-body stochastic density equations. Specifically, the time evolving N-body density matrix…
We consider the evolution of a population of fixed size with no selection. The number of generations $G$ to reach the first common ancestor evolves in time. This evolution can be described by a simple Markov process which allows one to…
We investigate the time evolution process of one selected (initially prepared by optical pumping) vibrational molecular state, coupled to all other intra-molecular vibrational states of the same molecule, and also to its environment.…
We study Markovian symmetry and non-symmetry random evolutions in $\mathbf{R}^n$. Weak convergence of Markovian symmetry random evolution to Wiener process and of Markovian non-symmetry random evolution to a diffusion process with drift is…
By modeling the interaction of a system with an environment through a renewal approach, we demonstrate that completely positive non-Markovian dynamics may develop some unexplored non-standard statistical properties. The renewal approach is…
We study the effects of inhomogeneities on the evolution of the Universe, by considering a range of cosmological models with discretized matter content. This is done using exact and fully relativistic methods that exploit the symmetries in…
We define non-Markovian quantum dynamics as evolution in which the current state depends on all past states, and completely characterize its structure under the assumptions of complete positivity and non-signalling. The resulting…
Non-Markovian effects are often significant when the system-environment coupling is not weak. Indeed, we find that the non-Markovianity is negligible for a single two-level system undergoing pure dephasing via a weak interaction with a…
By using the effective non-Markovian measure [H.P. Breuer, E.M. Laine, J. Piilo, Phys. Rev. Lett. 103, 210401 (2009)], we investigate non-Markovian dynamics of a pair of two-level atoms (TLAs) system, each of which interacting with a local…