Related papers: Dynamics of one-dimensional tight-binding models w…
We derive an exact analytical solution to the time-dependent Schr\"odinger equation for transmission of a Gaussian wave packet through an arbitrary potential of finite range. We consider the situation where the initial Gaussian wave packet…
We introduce a new class of quantum models with time-dependent Hamiltonians of a special scaling form. By using a couple of time-dependent unitary transformations, the time evolution of these models is expressed in terms of related systems…
Comprehending the dynamical behaviour of quantum systems driven by time-varying Hamiltonians is particularly difficult. Systems with as little as two energy levels are not yet fully understood as the usual methods including diagonalisation…
The dynamics of time-dependent coupled oscillator model for the charged particle motion subjected to a time-dependent external magnetic field is investigated. We used canonical transformation approach for the classical treatment of the…
We simulate the time-dependent coherent dynamics of a spatially indirect exciton (an electron-hole pair with the two particles confined in different layers) in a GaAs coupled quantum well system. We use a unitary wave-packet propagation…
In the single band tight-binding approximation, we consider the transport properties of an electron in a homogeneous static electric field. We show that repeated interactions of the electron with two-level systems in thermal equilibrium…
We study the dynamics of electrons in crystalline solids in the presence of inhomogeneous external electric and magnetic fields. We present a manifestly gauge-invariant operator-based approach without relying on a semiclassical wavepacket…
An effective operational approach to quantum mechanics is to focus on the evolution of wave-packets, for which the wave-function can be seen in the semi-classical regime as representing a classical motion dressed with extra degrees of…
Representations of propagators by means of path integrals over velocities are discussed both in nonrelativistic and relativistic quantum mechanics. It is shown that all the propagators can only be expressed through bosonic path integrals…
In the present work, we have analyzed the motion of a structured matter wave in the presence of a constant magnetic field and under the influence of a time-dependent external force. We have introduced exact propagator kernels obtained from…
Transport and scattering phenomena in open quantum-systems with a continuous energy spectrum are conveniently solved using the time-dependent Schrodinger equation. In the time-dependent picture, the evolution of an initially localized…
Using adiabatic expansions formalism, upper bounds for interband transitions for Bloch electrons in slowly varying in time electric fields are obtained. These bounds imply the validity of one-band approximation on long time scales.
The evolution equations of Einstein's theory and of Maxwell's theory---the latter used as a simple model to illustrate the former--- are written in gauge covariant first order symmetric hyperbolic form with only physically natural…
Recently, we have shown theoretically [1] as well as experimentally [2] how the phase of an electromagnetic field can be determined by measuring the population of either of the two states of a two-level atomic system excited by this field,…
The time evolution of a closed quantum system is connected to its Hamiltonian through Schroedinger's equation. The ability to estimate the Hamiltonian is critical to our understanding of quantum systems, and allows optimization of control.…
The paper first discusses theoretically the off-resonance selective excitation method that is dependent on the atomic internal states and used to generate approximately a standard coherent state of harmonic oscillator. The coherent average…
The time evolution of wavepackets in crystals in the presence of a homogeneous electric field is formulated in k-space in a numerically tractable form. The dynamics is governed by separate equations for the motion of the waveform in k-space…
We consider solutions of a scalar reaction-diffusion equation of the ignition type with a random, stationary and ergodic reaction rate. We show that solutions of the Cauchy problem spread with a deterministic rate in the long time limit. We…
We consider a nonrelativistic quantum charged particle moving on a plane under the influence of a uniform magnetic field and driven by a periodically time-dependent Aharonov-Bohm flux. We observe an acceleration effect in the case when the…
A method of solving the time-dependent Schr\"odinger equation is presented, in which a finite region of space is treated explicitly, with the boundary conditions for matching the wave-functions on to the rest of the system replaced by an…