Exact two-body bound states with Coulomb repulsion in a periodic potential

2006 ◽  
Vol 39 (47) ◽  
pp. L667-L671 ◽  
Author(s):  
S M Mahajan ◽  
A Thyagaraja
Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 516
Author(s):  
Simone Taioli ◽  
Stefano Simonucci

In this work, we outline a general method for calculating Auger spectra in molecules, which accounts for the underlying symmetry of the system. This theory starts from Fano’s formulation of the interaction between discrete and continuum states, and it generalizes this formalism to deal with the simultaneous presence of several intermediate quasi-bound states and several non-interacting decay channels. Our theoretical description is specifically tailored to resonant autoionization and Auger processes, and it explicitly includes the incoming wave boundary conditions for the continuum states and an accurate treatment of the Coulomb repulsion. This approach is implemented and applied to the calculation of the K−LL Auger and autoionization spectra of ozone, which is a C2v symmetric molecule, whose importance in our atmosphere to filter out radiation has been widely confirmed. We also show the effect that the molecular point group and, in particular, the localization of the core-hole in the oxygen atoms related by symmetry operations, has on the electronic structure of the Auger states and on the spectral lineshape by comparing our results with the experimental data.


2012 ◽  
Vol 319 (2) ◽  
pp. 557-573 ◽  
Author(s):  
Rupert L. Frank ◽  
Elliott H. Lieb ◽  
Robert Seiringer

2019 ◽  
Vol 150 (1) ◽  
pp. 171-204
Author(s):  
Tomáš Dohnal ◽  
Dmitry Pelinovsky

AbstractThe stationary Gross–Pitaevskii equation in one dimension is considered with a complex periodic potential satisfying the conditions of the 𝒫𝒯 (parity-time reversal) symmetry. Under rather general assumptions on the potentials, we prove bifurcations of 𝒫𝒯-symmetric nonlinear bound states from the end points of a real interval in the spectrum of the non-selfadjoint linear Schrödinger operator with a complex 𝒫𝒯-symmetric periodic potential. The nonlinear bound states are approximated by the effective amplitude equation, which bears the form of the cubic nonlinear Schrödinger equation. In addition, we provide sufficient conditions for the appearance of complex spectral bands when the complex 𝒫𝒯-symmetric potential has an asymptotically small imaginary part.


2019 ◽  
Vol 7 (3) ◽  
Author(s):  
André Melo ◽  
Sebastian Rubbert ◽  
Anton Akhmerov

We propose a new setup for creating Majorana bound states in a two-dimensional electron gas Josephson junction. Our proposal relies exclusively on a supercurrent parallel to the junction as a mechanism of breaking time-reversal symmetry. We show that combined with spin-orbit coupling, supercurrents induce a Zeeman-like spin splitting. Further, we identify a new conserved quantity—charge-momentum parity—that prevents the opening of the topological gap by the supercurrent in a straight Josephson junction. We propose breaking this conservation law by adding a third superconductor, introducing a periodic potential, or making the junction zigzag-shaped. By comparing the topological phase diagrams and practical limitations of these systems we identify the zigzag-shaped junction as the most promising option.


2000 ◽  
Vol 68 (8) ◽  
pp. 715-722 ◽  
Author(s):  
D. W. L. Sprung ◽  
J. D. Sigetich ◽  
Hua Wu ◽  
J. Martorell

Author(s):  
Simone Taioli ◽  
Stefano Simonucci

In this work we outline a general method for calculating Auger spectra in molecules, which accounts for the underlying symmetry of the system. This theory starts from Fano’s formulation of the interaction between discrete and continuum states and generalizes this formalism to deal with the simultaneous presence of several intermediate quasi-bound states and several non-interacting decay channels. Our theoretical description is specifically tailored to resonant autoionization and Auger processes, and includes explicitly the incoming wave boundary conditions for the continuum states and an accurate treatment of the Coulomb repulsion. This approach is implemented and applied to the calculation of the K−LL Auger and autoionization spectra of ozone, which is a C2v symmetric molecule, whose importance in our atmosphere to filter out radiation has been widely confirmed. We also show the effect that the molecular point group, and in particular the localization of the core-hole in the oxygen atoms related by symmetry operations, has on the electronic structure of the Auger states and on the spectral lineshape by comparing our results with experimental data.


1988 ◽  
Vol 102 ◽  
pp. 129-132
Author(s):  
K.L. Baluja ◽  
K. Butler ◽  
J. Le Bourlot ◽  
C.J. Zeippen

SummaryUsing sophisticated computer programs and elaborate physical models, accurate radiative and collisional atomic data of astrophysical interest have been or are being calculated. The cases treated include radiative transitions between bound states in the 2p4and 2s2p5configurations of many ions in the oxygen isoelectronic sequence, the photoionisation of the ground state of neutral iron, the electron impact excitation of the fine-structure forbidden transitions within the 3p3ground configuration of CℓIII, Ar IV and K V, and the mass-production of radiative data for ions in the oxygen and fluorine isoelectronic sequences, as part of the international Opacity Project.


Author(s):  
P. Fraundorf ◽  
J. Tentschert

Since the discovery of their etchability in the early 1960‘s, nuclear particle tracks in insulators have had a diverse and exciting history of application to problems ranging from the selective filtration of cancer cells from blood to the detection of 244Pu in the early solar system. Their usefulness stems from the fact that they are comprised of a very thin (e.g. 20-40Å) damage core which etches more rapidly than does the bulk material. In fact, because in many insulators tracks are subject to radiolysis damage (beam annealing) in the transmission electron microscope, the body of knowledge concerning etched tracks far outweighs that associated with latent (unetched) tracks in the transmission electron microscope.With the development of scanned probe microscopies with lateral resolutions on the near atomic scale, a closer look at the structure of unetched nuclear particle tracks, particularly at their point of interface with solid surfaces, is now warranted and we think possible. The ion explosion spike model of track formation, described loosely, suggests that a burst of ionization along the path of a charged particle in an insulator creates an electrostatically unstable array of adjacent ions which eject one another by Coulomb repulsion from substitutional into interstitial sites. Regardless of the mechanism, the ejection process which acts to displace atoms along the track core seems likely to operate at track entry and exit surfaces, with the added feature of mass loss at those surfaces as well. In other words, we predict pits whose size is comparable to the track core width.


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