Related papers: Fractional contact model in the continuum
With the discovery of new superconductors there was a running to find the justifications for the new properties found in these materials. In order to describe these new effects some theories were adapted and some others have been tried. In…
This paper is concerned with correlation functions of stochastic systems with memory, a prominent example being a molecule or colloid moving through a complex (e.g., viscoelastic) fluid environment. Analytical investigations of such systems…
One successful model of interacting biological systems is the Boolean network. The dynamics of a Boolean network, controlled with Boolean functions, is usually considered to be a Markovian (memory-less) process. However, both self…
We consider additive functionals of Markov processes in continuous time with general (metric) state spaces. We derive concentration bounds for their exponential moments and moments of finite order. Applications include diffusions,…
The importance of fractional time-derivative to take care of memory effects has been brought out by considering the example of a simple oscillator.
We investigate non-Markovianity measure using two-time correlation functions for open quantum systems. We define non-Markovianity measure as the difference between the exact two-time correlation function and the one obtained in the Markov…
The contact process is a non-equilibrium Hamiltonian model that, even in one dimension, lacks an exact solution and has been extensively studied via Monte Carlo simulations, both in steady-state and time-dependent scenarios. Although the…
One of the most popular methods of controlling dynamical systems is feedback. It can be used without acquiring detailed knowledge of the underlying system. In this work, we study the stability of fractional-order linear difference equations…
The visible dynamics of small-scale systems are strongly affected by unobservable degrees of freedom, which can belong either to external environments or internal subsystems and almost inevitably induce memory effects. Formally, such…
Fractional, anomalous diffusion in space-periodic potentials is investigated. The analytical solution for the effective, fractional diffusion coefficient in an arbitrary periodic potential is obtained in closed form in terms of two…
We consider, within the algebraic formalism, the time dependence of fidelity for qubits encoded into an open physical system. We relate the decay of fidelity to the evolution of correlation functions and, in the particular case of a…
A fractional derivative is a temporally nonlocal operation which is computationally intensive due to inclusion of the accumulated contribution of function values at past times. In order to lessen the computational load while maintaining the…
Discrete dynamics arise naturally in systems with broken temporal translation symmetry and are typically described by first-order recurrence relations representing classical or quantum Markov chains. When memory effects induced by hidden…
We show a relation between fractional calculus and fractals, based only on physical and geometrical considerations. The link has been found in the physical origins of the power-laws, ruling the evolution of many natural phenomena, whose…
Subdiffusion on graphs is often modeled by time-fractional diffusion equations, yet its structural and dynamical consequences remain unclear. We show that subdiffusive transport on graphs is a memory-driven process generated by a random…
In this study, we explore the field of physics through the lens of fractional dimensionality. We propose that space is not confined to integer dimensions alone, but can also be understood as a superposition of spaces that exist between…
We address memory effects in the dynamics of a two-level open quantum system interacting with a classical fluctuating field via dipole interaction. In particular, we study the backflow of information for a field with a Lorentzian spectrum,…
In the paper the memory effect in the system consisting from a trajectory of process and an environment is considered. The environment is presented by scalar potential and noise. The evolution of system is interpreted as process of the…
We propose a generalization of the widely used fractional Brownian motion (FBM), memory-multi-FBM (MMFBM), to describe viscoelastic or persistent anomalous diffusion with time-dependent memory exponent $\alpha(t)$ in a changing environment.…
We study the time evolution of a chain of nonlinear oscillators. We focus on the fractal features of the spectral entropy and analyze its characteristic intermediate timescales as a function of the nonlinear coupling. A Brownian motion is…