Related papers: Resonant state expansion applied to one-dimensiona…
The resonant state expansion (RSE), a rigorous perturbative method in electrodynamics, is applied to two-dimensional open optical systems. The analytically solvable homogeneous dielectric cylinder is used as unperturbed system, and its…
The full set of resonant states in double and triple quantum well/barrier structures is investigated. This includes bound, anti-bound and normal resonant states which are all eigensolutions of Schrodinger's equation with generalized…
The resonant state expansion, a recently developed method in electrodynamics, is generalized here to planar open optical systems with non-normal incidence of light. The method is illustrated and verified on exactly solvable examples, such…
The resonant state of the open quantum system is studied from the viewpoint of the outgoing momentum flux. We show that the number of particles is conserved for a resonant state, if we use an expanding volume of integration in order to take…
The dispersive resonant-state expansion, developed for an accurate calculation of the resonant states in open optical systems with frequency dispersion, is applied here to realistic materials, such as metallic nanoparticles and…
The resonant-state expansion (RSE), a rigorous perturbative method developed in electrodynamics for non-dispersive optical systems is applied to media with an Ohm's law dispersion, in which the frequency dependent part of the permittivity…
We present two alternative complete sets of static modes of a homogeneous dielectric sphere, for their use in the resonant-state expansion (RSE), a rigorous perturbative method in electrodynamics. Physically, these modes are needed to…
We present a general analytic expansion in powers of $1/n$ of the resonant states of quantum-mechanical systems, where $n=1,2,3,\cdots$ is the excitation number. Explicit formulas are obtained for some potential barrier models.
The resonant-state expansion, a recently developed powerful method in electrodynamics, is generalized here for open optical systems containing magnetic, chiral, or bi-anisotropic materials. It is shown that the key matrix eigenvalue…
Resonance states of a two-electron quantum dot are studied using a variational expansion with both real basis-set functions and complex scaling methods. We present numerical evidence about the critical behavior of the density of states in…
We first show that quantum resonant states observe particle number conservation and hence are consistent with the probabilistic interpretation of quantum mechanics. We then present for a class of quantum open systems, a resonant-state…
The resonant state expansion (RSE), a novel perturbation theory of Brillouin-Wigner type developed in electrodynamics [Muljarov, Langbein, and Zimmermann, Europhys. Lett., 92, 50010(2010)], is applied to planar, effectively one-dimensional…
We present a new paradigm in the field of photonic crystals and metamaterials, applying the resonant-state expansion (RSE) to planar photonic-crystal structures. The RSE allows us to understand and quantify optical resonances in…
The numerical extraction of resonant states of open quantum systems is usually a difficult problem. Regularization techniques, such as the mapping to complex coordinates or the addition of Complex Absorbing Potentials are typically…
We prove a robust extension of the quantum adiabatic theorem. The theorem applies to systems that have resonances instead of bound states, and to systems for which just an approximation to a bound state is known. To demonstrate the…
Resonant tunnelling is studied numerically and analytically with the help of a three-well quantum one-dimensional time-independent model. The simplest cases are considered where the three-well potential is polynomial or piecewise constant.
Rotating-wave approximation and its validity in multi-state quantum systems are studied through analytic approach. Their applicability is also verified from the viewpoint of generic states by the use of direct numerical integrations of the…
We review and extend, in a self-contained way, the mathematical foundations of numerical simulation methods that are based on the use of random states. The power and versatility of this simulation technology is illustrated by calculations…
The Random Phase Approximation (RPA) and its variations and extensions are, without any doubt, the most widely used tools to describe Giant Resonances within a microscopic theory. In this chapter, we will start by discussing how RPA comes…
Quantum resonances, i.e., metastable states with a finite lifetime, play an important role in nuclear physics and other domains. Describing this phenomenon theoretically is generally a challenging task. In this work, we combine two…