Related papers: Fractional dynamics of systems with long-range int…
In this paper, a multi-dimensional fractional wave equation that describes propagation of the damped waves is introduced and analyzed. In contrast to the fractional diffusion-wave equation, the fractional wave equation contains fractional…
We try to go beyond the geometrical optics approximation, by showing that a massless polarized particle allows a wide class of non minimal interactions with an arbitrary gravitational field. One specific example of a curvature-dependent…
The propagation of stable coherent entities of an electromagnetic field in nonlinear media with parameters varying in space can be described in the framework of iterations of nonlinear integral transformations. It is shown that for a set of…
The 1D discrete fractional Laplacian operator on a cyclically closed (periodic) linear chain with finitenumber $N$ of identical particles is introduced. We suggest a "fractional elastic harmonic potential", and obtain the $N$-periodic…
By applying complementary analytic and numerical methods, we investigate the dynamics of spin-$1/2$ XXZ models with variable-range interactions in arbitrary dimensions. The dynamics we consider is initiated from uncorrelated states that are…
A wide range of quasi-one-dimensional materials, consisting of weakly coupled chains, undergo three-dimensional phase transitions that can be described by a complex order parameter. A Ginzburg-Landau theory is derived for such a transition.…
Partially-projected Gutzwiller variational wavefunctions are used to describe the ground state of disordered interacting systems of fermions. We compare several different variational ground states with the exact ground state for disordered…
Inspired by recent studies on deterministic oscillator models, we introduce a stochastic one-dimensional model for a chain of interacting particles. The model consists of $N$ oscillators performing continuous-time random walks on the…
This paper investigates the approximate controllability of linear fractional impulsive evolution equations in Hilbert spaces. The system under consideration involves the Caputo fractional derivative of order $0<\alpha\leq 1$, a closed…
In this paper we are concerned with the asymptotic behavior of nonautonomous fractional approximations of oscillon equation $$ u_{tt}-\mu(t)\Delta u+\omega(t)u_t=f(u),\ x\in\Omega,\ t\in\mathbb{R}, $$ subject to Dirichlet boundary condition…
We consider the usual Langevin equation depending on an internal time. This parameter is substituted by a first passage time of a self-similar Markov process. Then the Gaussian process is parent, and the hitting time process is directing.…
We relate the convergence of time-changed processes driven by fractional equations to the convergence of corresponding Dirichlet forms. The fractional equations we dealt with are obtained by considering a general fractional operator in…
We consider quantum systems described by the fractional powers of the negative Laplacian and the interaction potentials. When a slowly decaying potential function is given, we prove the nonexistence of the wave operators, under the…
We report the clean experimental realization of cubic-quintic complex Ginzburg-Landau physics in a single driven, damped system. Four numerically predicted categories of complex dynamical behavior and pattern formation are identified for…
The coupled Stuart-Landau equation serves as a fundamental model for exploring synchronization and emergent behavior in complex dynamical systems. However, understanding its dynamics from a comprehensive nonlinear perspective remains…
This paper proposes and analyzes an efficient difference scheme for the nonlinear complex Ginzburg-Landau equation involving fractional Laplacian. The scheme is based on the implicit midpoint rule for the temporal discretization and a…
Multi-frequency forcing of systems undergoing a Hopf bifurcation to spatially homogeneous oscillations is investigated using a complex Ginzburg-Landau equation that systematically captures weak forcing functions that simultaneously hit the…
We investigate the generic transport in a one-dimensional strongly correlated fermionic chain beyond linear response. Starting from a Gaussian wave packet with positive momentum on top of the ground state, we find that the numerical time…
By fractional relativity we mean a theoretical framework to study physics with the dispersion relation $E^{\alpha}=m^{\alpha}c^{2\alpha}+p^{\alpha}c^{\alpha}$, which recovers special relativity at $\alpha=2$. One such framework is…
In this paper we consider a generalized classical mechanics with fractional derivatives. The generalization is based on the time-clock randomization of momenta and coordinates taken from the conventional phase space. The fractional…