Reply to "Comment on 'Thomson rings in a disk' ".

We demonstrate that our model [Phys. Rev. E 91, 032312 (2015)PLEEE81539-375510.1103/PhysRevE.91.032312] serves as a useful tool to trace the evolution of equilibrium configurations of one-component charged particles confined in a disk. Our approach reduces significantly the computational effort in minimizing the energy of equilibrium configurations, and it demonstrates a remarkable agreement with the values provided by molecular-dynamics calculations. We show that the Comment misrepresents our paper and fails to provide plausible arguments against the formation hexagonal structure for n≥200 in molecular-dynamics calculations.

All-optical light storage in bound states in the continuum and release by demand.

In the framework of the temporal coupled mode theory we consider bound states embedded in the continuum (BSC) of photonic crystal waveguide as a capacity for light storage. A symmetry protected BSC occurs in two off-channel microresonators positioned symmetrically relative to the waveguide. We demonstrate that the symmetry protected BSC captures a fraction of a light pulse due to the Kerr effect as the pulse passes by the microresonators. However the amount of captured light is found to be strongly sensitive to the parameters of the gaussian light pulse such as basic frequency, duration and intensity. In contrast to the above case the BSC resulted from a full destructive interference of two eigenmodes of a single microresonator accumulates a fixed amount of light dependent on the material parameters of the microresonator but independent of the light pulse. The BSCs in the Fabry-Perot resonator show similar effects. We also show that the accumulated light can be released by a secondary pulse. These phenomena pave a way for all-optical storage and release of light.

Quantum nonequilibrium approach for fast electron transport in open systems: photosynthetic reaction centers.

Creation of electrons or excitons by external fields in a system with initially statistically independent unrelaxed vibrational modes leads to an initial condition term. The contribution of this term in the time convolution generalized master-equation approach is studied in the second order of the perturbation theory in path-integral formalism. The developed approach, applied for the analysis of dynamics in the photosynthetic reaction center, exhibits the key role of the initial condition terms at the primary stage of electron transfer.

Understanding quantum scattering properties in terms of purely classical dynamics: two-dimensional open chaotic billiards.

We study classical and quantum scattering properties of particles in the ballistic regime in two-dimensional chaotic billiards that are models of electron- or micro-waveguides. To this end we construct the purely classical counterparts of the scattering probability (SP) matrix |S(n,m)|(2) and Husimi distributions specializing to the case of mixed chaotic motion (incomplete horseshoe). Comparison between classical and quantum quantities allows us to discover the purely classical dynamical origin of certain general as well as particular features that appear in the quantum description of the system. On the other hand, at certain values of energy the tunneling of the wave function into classically forbidden regions produces striking differences between the classical and quantum quantities. A potential application of this phenomenon in the field of microlasers is discussed briefly. We also see the manifestation of whispering gallery orbits as a self-similar structure in the transmission part of the classical SP matrix.

Classical versus quantum structure of the scattering probability matrix: chaotic waveguides.

The purely classical counterpart of the scattering probability matrix (SPM)/S(n,m)/(2) of the quantum scattering matrix S is defined for two-dimensional quantum waveguides for an arbitrary number of propagating modes M. We compare the quantum and classical structures of /S(n,m)/(2) for a waveguide with generic Hamiltonian chaos. It is shown that even for a moderate number of channels, knowledge of the classical structure of the SPM allows us to predict the global structure of the quantum one and, hence, understand important quantum transport properties of waveguides in terms of purely classical dynamics. It is also shown that the SPM, being an intensity measure, can give additional dynamical information to that obtained by the Poincaré maps.

Whispering gallery modes in open quantum billiards.

The poles of the S matrix and the wave functions of open two-dimensional quantum billiards with convex boundary of different shape are calculated by using the method of complex scaling. Two leads are attached to the cavities. The conductance of the cavities is calculated at energies with one, two, and three open channels in each lead. Bands of overlapping resonance states appear that are localized along the convex boundary of the cavities and contribute coherently to the conductance. These bands correspond to the whispering gallery modes known from classical calculations.

Two-component interference effect: model of a spin-polarized transport.

The effect of spin-involved interaction on the transport properties of disordered two-dimensional electron systems with ferromagnetic contacts is described using a two-component model. Components representing spin-up and spin-down states are supposed to be coupled at a discrete set of points. We have found that due to the additional interference arising in two-component systems the difference between conductances for the parallel and antiparallel orientations of the contact magnetization changes its sign as a function of the length of the conducting channel.