Related papers: Generalised fractional Rabi problem
We show that the interaction between carriers confined in a quantum dot and the surrounding lattice under external driving of carrier dynamics has a dynamical, resonant character. The quality of Rabi oscillations in such a system depends on…
Rabi oscillations may be viewed as an interference phenomenon due to a coherent superposition of different quantum paths, like in the Young's two-slit experiment. The inclusion of the atomic external variables causes a non dissipative…
Standard dynamical systems approaches to economic modeling, such as those deriving the Cobb-Douglas and CES production functions from exponential growth trajectories, typically rely on integer-order differential equations. While effective,…
Fractional differential equations model processes with memory effects, providing a realistic perspective on complex systems. We examine time-delayed differential equations, discussing first-order and fractional Caputo time-delayed…
Rabi oscillations typify the inherent nonlinearity of optical excitations in quantum dots. Using an integral kernel formulation to solve the 3D Maxwell-Bloch equations in ensembles of up to $10^4$ quantum dots, we observe features in Rabi…
In this paper the author presents the results of the preliminary investigation of fractional dynamical systems based on the results of numerical simulations of fractional maps. Fractional maps are equivalent to fractional differential…
We propose a mechanism to explain the nature of the damping of Rabi oscillations with increasing driving-pulse area in localized semiconductor systems, and have suggested a general approach which describes a coherently driven two-level…
Recently, the research community has been exploring fractional calculus to address problems related to cosmology; in this approach, the gravitational action integral is altered, leading to a modified Friedmann equation, then the resulting…
A generalization of the economic model of natural growth, which takes into account the power-law memory effect, is suggested. The memory effect means the dependence of the process not only on the current state of the process, but also on…
In the paper we deal with linear fractional control problems with constant delays in the state. Single-order systems with fractional derivative in Caputo sense of orders between 0 and 1 are considered. The aim is to introduce a new…
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…
We investigate the dissipative phase transitions of the anisotropic quantum Rabi model with cavity decay and demonstrate that large spin fluctuations persist in the stationary state, having important consequences on the phase diagram and…
We examine the fractional derivative of composite functions and present a generalization of the product and chain rules for the Caputo fractional derivative. These results are especially important for physical and biological systems that…
Point-gap topology, characterized by spectral winding numbers, is crucial to non-Hermitian topological phases and dramatically alters real-time dynamics. In this paper, we study the evolution of quantum particles in dissipative systems with…
A vast collection of light-matter interactions are described by the single-frequency Rabi model. However, the physical world is polychromatic, and until now there is no general method to find analytic solutions to the multi-frequency Rabi…
We consider the evolution of correlation functions in a non-Markov version of the contact model in the continuum. The memory effects are introduced by assuming the fractional evolution equation for the statistical dynamics. This leads to a…
Electron Paramagnetic Resonance experiments show that the decay of Rabi oscillations of ensembles of spin qubits depends noticeably on the microwave power and more precisely on the Rabi frequency, an effect recently called "driven…
Dissipative structures are localized, stable patterns that arise due to the intricate balance among dissipation, dispersion, interaction, and external drive. Their creation and manipulation are of great interest in fields as diverse as…
We initiate an investigation into whether fractional calculus, with its intrinsic long-tailed memory and nonlocal features, can provide a viable model for gravitational-wave memory effects. We consider two toy constructions: ($i$) a…
This paper investigates Rabi transport and finite-size effects in one-dimensional discrete-time topological quantum walks. We demonstrate the emergence of localized states at boundaries between topologically distinct phases and analyze how…