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Open Access
1D states of the beryllium atom: Quantum mechanical nonrelativistic calculations employing explicitly correlated Gaussian functions
(2011) Sharkey, Keeper L.; Bubin, Sergiy; Adamowicz, Ludwik
Very accurate finite-nuclear-mass variational nonrelativistic calculations are performed for the lowest five 1D states (1s2 2p2, 1s2 2s1 3d1, 1s2 2s1 4d1, 1s2 2s1 5d1, and 1s2 2s1 6d1) of the beryllium atom (9Be). The wave functions of the states are expanded in terms of all-electron explicitly correlated Gaussian functions. The exponential parameters of the Gaussians are optimized using the variational method with the aid of the analytical energy gradient determined with respect to those parameters. The calculations exemplify the level of accuracy that is now possible with Gaussians in describing bound states of a four-electron system where some of the electrons are excited into higher angular states
Open Access
A note on the definition of deformed exponential and logarithm functions
(2009) Oikonomou, Th.; Baris Bagci, G.
The recent generalizations of the Boltzmann–Gibbs statistics mathematically rely on the deformed logarithmic and exponential functions defined through some deformation parameters. In the present work, we investigate whether a deformed logarithmic/exponential map is a bijection from R+ /R set of positive real numbers/ all real numbers to R/R+, as their undeformed counterparts. We show that their inverse map exists only in some subsets of the aforementioned co domains. Furthermore, we present conditions which a generalized deformed function has to satisfy, so that the most important properties of the ordinary functions are preserved. The fulfillment of these conditions permits us to determine the validity interval of the deformation parameters. We finally apply our analysis to Tsallis q-deformed functions and discuss the interval of concavity of the Rényi entropy
Open Access
Accuracy limits on the description of the lowest S excitation in the Li atom using explicitly correlated Gaussian basis functions
(2008) Stanke, Monika; Komasa, Jacek; Kedziera, Dariusz; Bubin, Sergiy; Adamowicz, Ludwik
We have performed very accurate quantum-mechanical calculations for the two lowest S states of the lithium atom in order to determine the transition energy. In the nonrelativistic part of the calculations performed using the variational method, we explicitly included the nuclear motion. The nonrelativistic wave function was expanded in terms of explicitly correlated Gaussian functions. Next, this wave function was used to calculate the leading 2 relativistic correction is the fine-structure constant and the 3 QED correction. We also estimated the 4 QED correction by calculating its dominating component. The results obtained with Gaussians are compared with the most accurate results obtained recently with the Hylleraas-type basis functions
Open Access
Accurate non-Born-Oppenheimer calculations of the complete pure vibrational spectrum of D2 with including relativistic corrections
(2011) Bubin, Sergiy; Stanke, Monika; Adamowicz, Ludwik
In this work we report very accurate variational calculations of the complete pure vibrational spectrum of the D2 molecule performed within the framework where the Born-Oppenheimer (BO) approximation is not assumed. After the elimination of the center-of-mass motion, D2 becomes a threeparticle problem in this framework. As the considered states correspond to the zero total angular momentum, their wave functions are expanded in terms of all-particle, one-center, spherically symmetric explicitly correlated Gaussian functions multiplied by even non-negative powers of the internuclear distance. The nonrelativistic energies of the states obtained in the non-BO calculations are corrected for the relativistic effects of the order of α2 (where α = 1/c is the fine structure constant) calculated as expectation values of the operators representing these effects
Open Access
Accurate non-Born-Oppenheimer calculations of the complete pure vibrational spectrum of ditritium using all-particle explicitly correlated Gaussian functions
(2014) Bubin, Sergiy; Stanke, Monika; Adamowicz, Ludwik
Very accurate variational calculations of the complete pure vibrational spectrum of the ditritium (T2) molecule are performed within the framework where the Born-Oppenheimer approximation is not assumed. After separating out the center-of-mass motion from the total laboratory-frame Hamiltonian, T2 becomes a three-particle problem. States corresponding to the zero total angular momentum, which are pure vibrational states, are spherically symmetric in this framework. The wave functions of these states are expanded in terms of all-particle, one-center, spherically symmetric explicitly correlated Gaussian functions multiplied by even non-negative powers of the internuclear distance. In the calculations the total energies, the dissociation energies, and expectation values of some operators dependent on interparticle distances are determined.
Open Access
Accurate variational calculations of the ground 2Po(1s22s22p) and excited 2S(1s22s2p2) and 2Po(1s22s23p) states of singly ionized carbon atom
(2011) Bubin, Sergiy; Adamowicz, Ludwik
In this article we report accurate nonrelativistic variational calculations of the ground and two excited states of C+ ion. We employ extended and well optimized basis sets of all-electron explicitly correlated Gaussians to represent the wave functions of the states. The optimization of the basis functions is performed with a procedure employing the analytic gradient of the energy with respect to the nonlinear parameters of the Gaussians. The calculations explicitly include the effects due to the finite nuclear mass. The calculated transition energies between the three states are compared to the experimentally derived values. Finally, we present expectation values of some small positive and negative powers of the interparticle distances and contact densities
Open Access
Achieving Anomalous Refraction with Metasurfaces Composed by Two Ordinary Dielectric Materials
(Metamaterials, 2018) Tsitsas, N. L.; Valagiannopoulos, Constantinos
The optimal parameters of a dielectric metasurface, composed of two alternating rectangular rods, are investigated so that it exhibits significant enhancement in the −1- diffracted order in the transmission region. An efficient integral-equation methodology is used for the numerical computations. Representative results of initial optimizations are presented
Open Access
Aharonov-Bohm detection of two-dimensional magnetostatic cloaks
(2015) Valagiannopoulos, Constantinos; Askarpour, Amir Nader; Al`, Andrea
Two-dimensionalmagnetostatic cloaks, evenwhen perfectly designed tomitigate the magnetic field disturbance of a scatterer, may be still detectable with Aharonov-Bohm (AB) measurements, and therefore may affect quantum interactions and experiments with elongated objects. We explore a multilayered cylindrical cloak whose permeability profile is tailored to nullify the magnetic-flux perturbation of the system, neutralizing its effect on AB measurements, and simultaneously optimally suppress the overall scattering. In this way, our improved magnetostatic cloak combines substantial mitigation of the magnetostatic scattering response with zero detectability by AB experiments
Open Access
Algorithm for quantum-mechanical finite-nuclear-mass variational calculations of atoms with two p electrons using all-electron explicitly correlated Gaussian basis functions
(2009) Sharkey, Keeper L.; Pavanello, Michele; Bubin, Sergiy; Adamowicz, Ludwik
A new algorithm for calculating the Hamiltonian matrix elements with all-electron explicitly correlated Gaussian functions for quantum-mechanical calculations of atoms with two p electrons or a single d electron have been derived and implemented. The Hamiltonian used in the approach was obtained by rigorously separating the center-of-mass motion and it explicitly depends on the finite mass of the nucleus. The approach was employed to perform test calculations on the isotopes of the carbon atom in their ground electronic states and to determine the finite-nuclear-mass corrections for these states
Open Access
All black holes in Lemaˆıtre-Tolman-Bondi inhomogeneous dust collapse
(2015-09-08) Joshi, Pankaj S.; Malafarina, D.
Within the Lemaˆıtre-Tolman-Bondi formalism for gravitational collapse of inhomogeneous dust we analyze the parameter space that leads to the formation of a globally covered singularity (i.e. a black hole) when some physically reasonable requirements are imposed (namely positive radially decreasing and quadratic profile for the energy density and avoidance of shell crossing singularities). It turns out that a black hole can occur as the endstate of collapse only if the singularity is simultaneous as in the standard Oppenheimer-Snyder scenario. Given a fixed density profile then there is one velocity profile for the infalling particles that will produce a black hole. All other allowed velocity profiles will terminate the collapse in a locally naked singularity.
Open Access
An accurate non-Born–Oppenheimer calculation of the first purely vibrational transition in LiH molecule
(2005) Bubin, Sergiy; Adamowicz, Ludwik; Molski, Marcin
In this work we study the ground and the first vibrationally excited states of LiH molecule. We performed an extensive nonrelativistic variational calculations of the two states without using the Born–Oppenheimer approximation. The results are analyzed and compared with the data extracted from recent experiments. The 0←1 transition energy obtained in the calculations converged to a value which is less than a wave number above the transition energy estimated from the available experimental data concerning the LiH rovibrational transitions. We discuss the remaining discrepancy and the procedure used to determine the “experimental” transition frequencies
Open Access
An algorithm for calculating atomic D states with explicitly correlated Gaussian functions
(2011) Sharkey, Keeper L.; Bubin, Sergiy; Adamowicz, Ludwik
An algorithm for the variational calculation of atomic D states employing n-electron explicitly correlated Gaussians is developed and implemented. The algorithm includes formulas for the first derivatives of the Hamiltonian and overlap matrix elements determined with respect to the Gaussian nonlinear exponential parameters. The derivatives are used to form the energy gradient which is employed in the variational energy minimization. The algorithm is tested in the calculations of the two lowest D states of the lithium and beryllium atoms. For the lowest D state of Li the present result is lower than the best previously reported result
Open Access
ANALOG PARTICLE PRODUCTION MODEL FOR GENERAL CLASSES OF TAUB-NUT BLACK HOLES
(Universe, 2021-09-20) Foo, Joshua; Good, Michael R. R.; Mann, Robert B.
We derive a correspondence between the Hawking radiation spectra emitted from general classes of Taub-NUT black holes with that induced by the relativistic motion of an accelerated Dirichlet boundary condition (i.e., a perfectly reflecting mirror) in (1+1)-dimensional flat spacetime. We demonstrate that the particle and energy spectra is thermal at late times and that particle production is suppressed by the NUT parameter. We also compute the radiation spectrum in the rotating, electrically charged (Kerr–Newman) Taub-NUT scenario, and the extremal case, showing, explicitly, how these parameters affect the outgoing particle and energy fluxes
Open Access
Analytical energy gradient in variational calculations of the two lowest 3P states of the carbon atom with explicitly correlated Gaussian basis functions
(2010) Sharkey, Keeper L.; Bubin, Sergiy; Adamowicz, Ludwik
Variational calculations of ground and excited bound states on atomic and molecular systems performed with basis functions that explicitly depend on the interparticle distances can generate very accurate results provided that the basis function parameters are thoroughly optimized by the minimization of the energy. In this work we have derived the algorithm for the gradient of the energy determined with respect to the nonlinear exponential parameters of explicitly correlated Gaussian functions used in calculating n-electron atomic systems with two p-electrons and n−2 s-electrons. The atomic Hamiltonian we used was obtained by rigorously separating out the kinetic energy of the center of mass motion from the laboratory-frame Hamiltonian and explicitly depends on the finite mass of the nucleus. The advantage of having the gradient available in the variational minimization of the energy is demonstrated in the calculations of the ground and the first excited 3P state of the carbon atom. For the former the lowest energy upper bound ever obtained is reported
Open Access
Analytical investigations of ground modifications assisting the detection of buried object
(Nazarbayev University School of Science and Technology, 2016-08-18) Valagiannopoulos, Constantinos; Tsitsas, Nikolaos L.; Sihvola, Ari H.
A ground-penetrating radar (GPR) antenna excites a perfectly electric conducting inclusion buried inside the ground. The scattering problem is solved semi-analytically via integral equation techniques. The permittivity and thickness of a superstrate deposited atop the ground are determined such that the detectability of the inclusion is significantly increased. Results from numerical simulations are presented exhibiting the effectiveness of the approach. Emphasis is given on the effects that the shape of the buried inclusion has on the scattered field.
Open Access
Anomalous reflection of visible light by all-dielectric gradient metasurfaces
(Journal of the Optical Society of America B, 2017-03-15) Tsitsas, Nikolaos L.; Valagiannopoulos, Constantinos
Plane wave scattering by a planar metasurface composed of two periodically alternating rectangular dielectric rods is considered. A rigorous integral equation methodology is employed for the analysis and the accurate determination of the reflected and transmitted fields. Systematic optimizations with respect to the configuration’s parameters are performed, which reveal that it is possible to obtain significantly enhanced anomalous reflection (with simultaneously suppressed ordinary reflection predicted by Snell’s law) with power varying from 92% to almost 100% of the input one, depending on the color of the incident light. It is shown that these reflection properties are supported by metasurfaces easily realizable with specific low-loss dielectric materials. In this way, several all-dielectric optimal designs are reported that can be used in numerous applications demanding anomalous reflection in the visible range
Open Access
Are Black Holes Springy?
(2014) Good, Michael R.R.; Ong, Yen Chin
A (3+1)-dimensional asymptotically at Kerr black hole angular speed + can be used to de ne an e ective spring constant, k = m2 +. Its maximum value is the Schwarzschild surface gravity, k = , which rapidly weakens as the black hole spins down and the temperature increases. The Hawking temperature is expressed in terms of the spring constant: 2 T = 􀀀 k. Hooke's law, in the extremal limit, provides the force F = 1=4, which is consistent with the conjecture of maximum force in general relativity
Open Access
Assessing performance of modern Brillouin spectrometers
(Optics Express, 2018-02) Coker, Zachary; Troyanova‐Wood, Maria; Traverso, Andrew J.; Yakupov, Talgat; Utegulov, Zhandos; Yakovlev, Vladislav V.
Brillouin spectroscopy and imaging has experienced a renaissance in recent years seeing vast improvements in methodology and increasing number of applications. With this resurgence has come the development of new spontaneous Brillouin instruments that often tout superior performance compared to established conventional systems such as tandem Fabry-Perot interferometers (TFPI). The performance of these new systems cannot always be thoroughly examined beyond the scope of the intended application, as applications often take precedence in reports. We therefore present evaluation of three modern Brillouin spectrometers: two VIPA-based spectrometers with wavelength-specific notch filters, and one scanning 6-pass TFPI. Performance analysis is presented along with a discussion about the dependence of measurements on excitation laser source and the various susceptibilities of each system.
Open Access
Assessment of the accuracy the experimental energies of the 1Po 1s22s6p and 1s22s7p states of 9Be based on variational calculations with explicitly correlated Gaussians
(2012) Bubin, Sergiy; Adamowicz, Ludwik
Benchmark variational calculations are performed for the six lowest states of the 1Po 1s22snp state series of the 9Be atom. The wave functions of the states are expanded in terms of all-particle, explicitly correlated Gaussian basis functions and the effect of the finite nuclear mass is directly included in the calculations. The exponential parameters of the Gaussians are variationally optimized using the analytical energy gradient determined with respect to those parameters. Besides providing reference non-relativistic energies for the considered states, the calculations also allow to assess the accuracy of the experimental energies of the 1Po 1s22s6p and 1s22s7p states and suggest their refinement
Open Access
Band structure of cavity-type hypersonic phononic crystals fabricated by femtosecond laser-induced two-photon polymerization
(Applied Physics Letters, 2016-05) Rakhymzhanov, A. M.; Gueddida, A.; Alonso-Redondo, E.; Utegulov, Zhandos; Perevoznik, D.; Kurselis, K.; Chichkov, B. N.; El Boudouti, E. H.; Djafari-Rouhani, B.; Fytas, G.
The phononic band diagram of a periodic square structure fabricated by femtosecond laser pulseinduced two photon polymerization is recorded by Brillouin light scattering (BLS) at hypersonic (GHz) frequencies and computed by finite element method. The theoretical calculations along the two main symmetry directions quantitatively capture the band diagrams of the air- and liquid-filled structure and moreover represent the BLS intensities. The theory helps identify the observed modes, reveals the origin of the observed bandgaps at the Brillouin zone boundaries, and unravels direction dependent effective medium behavior.