相关论文: An explicit criterion for existence of the Magnus …
Approximate resolution of linear systems of differential equations with varying coefficients is a recurrent problem shared by a number of scientific and engineering areas, ranging from Quantum Mechanics to Control Theory. When formulated in…
We use a Magnus approximation at the level of the equations of motion for a harmonic system with a time-dependent frequency, to find an expansion for its in-out effective action, and a unitary expansion for the Bogoliubov transformation…
Magnus expansion (ME) provides a general way to expand the real-time propagator of a time-dependent Hamiltonian within the exponential such that the unitarity is satisfied at any order. We use this property and explicit integration of…
We develop a Magnus formalism for periodically driven systems which provides an expansion both in the driving term and the inverse driving frequency, applicable to isolated and dissipative systems. We derive explicit formulas for a driving…
A novel expansion -- which generalizes Magnus expansion -- of the evolution operator associated with a (in general, time-dependent) perturbed Hamiltonian is introduced. It is shown that it has a wide range of possible solutions that can be…
We develop perturbative methods to study and control dynamical phenomena related to exceptional points in Non-Hermitian systems. In particular, we show how to find perturbative solutions based on the Magnus expansion that accurately…
Using the Magnus expansion to the fourth order, we obtain analytic expressions for the atomic state of a two-level system driven by a laser pulse of arbitrary shape with small pulse area. We also determine the limitation of our obtained…
The computation of the Schr\"odinger equation featuring time-dependent potentials is of great importance in quantum control of atomic and molecular processes. These applications often involve highly oscillatory potentials and require…
We propose a unified approach for different exponential perturbation techniques used in the treatment of time-dependent quantum mechanical problems, namely the Magnus expansion, the Floquet--Magnus expansion for periodic systems, the…
We propose an alternative micromagnetic approach to determine the spin wave dispersion relations in magnonic structures. Characteristic of the method is that a limited area of the system is continuously excited with a spatially uniform…
The period and the period derivative of a pulsar are critical magnitudes for defining the properties of the magnetospheric size and plasma dynamics. The pulsar light cylinder, the magnetic field intensity nearby it, and the curvature radius…
Two different sufficient conditions are given for the convergence of the Magnus expansion arising in the study of the linear differential equation $Y' = A(t) Y$. The first one provides a bound on the convergence domain based on the norm of…
A new type of perturbative expansion is built in order to give a rigorous derivation and to clarify the range of validity of some commonly used model equations. This model describes the evolution of the modulation of two short and localized…
The global-in-time existence and uniqueness of bounded weak solutions to a spinorial matrix drift-diffusion model for semiconductors is proved. Developing the electron density matrix in the Pauli basis, the coefficients (charge density and…
We explain some phenomena existing generally in the timing residuals: amplitude and sign of the second derivative of a pulsar's spin-frequency ($\ddot\nu$), some sophisticated residual patterns, which also change with the time span of data…
Using pulsewidth data for 872 isolated radio pulsars we test the hypothesis that pulsars evolve through a progressive narrowing of the emission cone combined with progressive alignment of the spin and magnetic axes. The new data provide…
We investigate the validity of gaussian lower bounds for solutions to an electromagnetic Schr\"odinger equation with a bounded time-dependent complex electric potential and a time-independent vector magnetic potential. We prove that, if a…
We discuss the numerical solution of the Schr\"odinger equation with a time-dependent Hamilton operator using commutator-free time-propagators. These propagators are constructed as products of exponentials of simple weighted sums of the…
We extend the recently proposed Time-Dependent Multi-Determinant approach (ref.[1]) to the description of fermionic propagators. The method hinges on equations of motions obtained using variational principles of Dirac type. In particular we…
I derive a temporally propagated uni-directional optical pulse equation valid in the few cycle limit. Temporal propagation is advantageous because it naturally preserves causality, unlike the competing spatially propagated models. The exact…