The Resonance Phenomena Associated with the Time Asymmetry in Non-Hermitian Quantum Mechanics

Resonances are defined as the poles of the scattering matrix. The poles are associated with the complex eigenvalues of the Hamiltonian which are embedded in the lower half of the complex plane. The asymptotes of the corresponding eigenfunctions are exponentially diverged. Therefore, the resonance eigenfunctions are not embedded in the Hermitian domain of the Hamiltonian. The time asymmetric problem is discussed for these types of non-Hermitian Hamiltonians and several solutions of this problem are proposed.     

Fermi and Coulomb correlations in the 21 S state of the helium isoelectronic sequence

The Fermi and Coulomb holes of the 2¹ S state of the helium isoelectronic sequence are investigated. Several interesting differences between the results obtained and those which might be expected on the basis of the corresponding 2³ S state are pointed out and discussed.     

Dynamical tunneling through a chaotic region

It is shown that a non-vibrating diatomic molecule (i.e. a rigid rotor) in the presence of a strong laser field changes its hindered rotational motion (which on the average is in resonance with the oscillating time dependent field) from anti-clockwise to clockwise (hindered) rotational motion. This transition is classically forbidden and is another example of a quantum mechanical tunneling phenomenon occurring due to the time-reversal symmetry of the Hamiltonian. Classically, the two stable rotational modes are separated by an extended chaotic region in phase space. The Husimi representation of the quasienergy states of the time-periodic quantum system enables us to localize wave packets inside the classical stability islands. The effect of the field and the molecular parameters on the perioid of this oscillation is obtained from the quasienergy splittings without the need to carry out long time dependent computations. An analytical analysis of the dynamical tunneling using an extended version of the (t,t) formalism recently developed (J. Chem. Phys.99, 4590 (1993)) is in remarkable agreement with the numerical results.Member of the Minerva center of non-linear physics of complex systems at the Technion     

Fused Fluorinated Bis-β-diketones and Luminescent-Spectral Properties of Their Complexes with Europium

Russian Journal of General Chemistry - Claisen condensation of diacetylated fused aromatic and heteroaromatic compounds (fluorene, dibenzofuran, dibenzothiophene, or carbazole) with...     

Perturbation approach to the complex-rotation method

Non-degenerate and almost degenerate perturbation theory is applied to the problem of calculating autoionizing resonances of the helium atom using the complex-rotation method. The radii of convergence of the series are often found to be too small to allow the perturbation method to have general utility.     

Electromagnetic realization of orders-of-magnitude tunneling enhancement in a double well system

We report on tunneling enhancement in a periodically perturbed double well system. The double well system was realized by a structure of two optical waveguides. The transfer of light power from one waveguide to the another as induced by the periodic variations of the waveguide geometry was investigated. Our experimental measurements show that, in the presence of periodic perturbation, this transfer of light power can be enhanced by more than 500 times. We use an analogy between electromagnetic wave optics and the quantum wave phenomena to provide an experimental support to the theoretical model of tunneling enhancement of a quantum particle, facilitated by its interaction with auxiliary quantum states.     

Interatomic coulombic decay in van der waals clusters and impact of nuclear motion

It is demonstrated that excited van der Waals systems can relax by electron emission via a novel interatomic mechanism. The process is analyzed by means of extensive ab initio calculations of potential energy surfaces and electronic decay rates. The electronic emission, taking place on the same time scale as the motion of the atomic nuclei, is accompanied by interesting dynamical effects amenable to experimental observations. These effects arise as a consequence of the weak chemical bond in van der Waals clusters and the Coulomb repulsion pattern originating from electron emission.     

Study of predissociation resonances by the complex coordinate method

The complex coordinate method is applied to the predissociation resonances of two-state model system. The stability of the resonance positions and their widths, as well as the affect of using real and complex basis sets are studied.     

Visualization of branch points in PT-symmetric waveguides

The visualization of an exceptional point in a PT-symmetric directional coupler (DC) is demonstrated. In such a system the exceptional point can be probed by varying only a single parameter. Using the Rayleigh-Schr?dinger perturbation theory we prove that the spectrum of a PT-symmetric Hamiltonian is real as long as the radius of convergence has not been reached. We also show how one can use a PT-symmetric directional coupler to measure the radius of convergence for non-PT-symmetric structures. For such systems the physical meaning of the rather mathematical term radius of convergence is exemplified.     

Reflection-free complex absorbing potential for electronic structure calculations: Feshbach-type autoionization resonances of molecules

The reflection-free complex absorbing potential (RF-CAP) method has been already applied to the study of the autoionization resonance of helium [Sajeev et al., Chem. Phys. 329, 307 (2006)]. The present work introduces a systematic way for implementing RF-CAP for the electronic structure calculations using Gaussian basis sets for molecules. As a test case study we applied the RF-CAP method to the lowest (1)Sigma(g) (+) and (1)Sigma(u) (+) Feshbach-type autoionization resonances of hydrogen molecule. Since thin RF-CAP absorbs fast electrons much better than the slow ones, a weak dc field has been added to the RF-CAP in the peripheral region of the molecule.