Related papers: Multi-frequency averaging and uniform accuracy tow…
Waves scattering from unbounded structures are always complicated problems for numerical simulations. For the case that the non-periodic incident field scattered by (locally perturbed) periodic surfaces, with the help of the Bloch…
The asymptotic behavior of a one-dimensional spectral problem with periodic coefficient is addressed for high frequency modes by a method of Bloch wave homogenization. The analysis leads to a spectral problem including both microscopic and…
We study a realistic model for driven qubits using the numerical solution of the Bloch-Redfield equation as well as analytical approximations using a high-frequency scheme. Unlike in idealized rotating-wave models suitable for NMR or…
We present simulation results on the structure and dynamics of micromagnetic point singularities with atomistic resolution. This is achieved by embedding an atomistic computational region into a standard micromagnetic algorithm. Several…
Magnetic resonance fingerprinting (MRF) is one novel fast quantitative imaging framework for simultaneous quantification of multiple parameters with pseudo-randomized acquisition patterns. The accuracy of the resulting multi-parameters is…
The standard Bloch oscillation normally refers to the oscillatory tunneling dynamics of quantum particles in a periodic lattice plus a linear gradient. In this work we theoretically investigate the generalized form of the Bloch oscillation…
We investigate the quantum dynamics of a two-level system driven by a bichromatic field, using a non-perturbative analysis. We make special emphasis in the case of two large frequencies, where the Magnus expansion can fail, and in the case…
We present an efficient theoretical method for calculating the time evolution of the density matrix of a multilevel quantum system weakly interacting with incoherent light. The method combines the Bloch-Redfield theory with a partial…
A systematic, rigorous, and complete investigation of the Bloch equations in time-harmonic driving classical field is performed. Our treatment is unique in that it takes full advantage of the partial fraction decomposition over real number…
We study the local dynamics of $L^{2}\left(\mathbb{R}\right)$-perturbations to the zero solution of spatially $2\pi$-periodic coefficient reaction-diffusion systems. In this case the spectrum of the linearization about the zero solution is…
We study numerically the dynamics of a one-electron wave packet in a two-dimensional random lattice with long-range correlated diagonal disorder in the presence of a uniform electric field. The time-dependent Schr\"{o}dinger equation is…
Rough surface scattering problems are always very challenging both theoretically and numerically. In this paper, we adopt the Bloch transform and the perturbation theory to investigate a special case, i.e., when the rough surface is a…
We obtain equilibration rates for a one-dimensional nonlocal Fokker-Planck equation with time-dependent diffusion coefficient and drift, modeling the relaxation of a large swarm of robots, feeling each other in terms of their distance,…
Welch's method provides an estimator of the power spectral density that is statistically consistent. This is achieved by averaging over periodograms calculated from overlapping segments of a time series. For a finite length time series,…
This study looks at the finite-dimensional adiabatic evolution influenced by weak perturbations, extending the analysis to the asymptotic time limit. Beginning with the fundamentals of adiabatic transformations and time-dependent effective…
Using nonequilibrium dynamical mean-field theory, we study the isolated Hubbard model in a static electric field in the limit of weak interactions. Linear response behavior is established at long times, but only if the interaction exceeds a…
Stochastic averaging allows for the reduction of the dimension and complexity of stochastic dynamical systems with multiple time scales, replacing fast variables with statistically equivalent stochastic processes in order to analyze…
Bloch-type equations for description of coherent transport in mesoscopic systems are applied for a study of the continuous measurement process. Both the detector and the measured system are described quantum mechanically. It is shown that…
Bloch-Redfield equation is a common tool for studying evolution of qubit systems weakly coupled to environment. We investigate the accuracy of the Born approximation underlying this equation. We find that the high order terms in the…
In the present contribution we investigate some features of dynamical lattice systems near periodic traveling waves. First, following the formal averaging method of Whitham, we derive modulation systems expected to drive at main order the…