Analytical properties of mean two-particle density matrix

The analytical properties of the mean two-particle density matrixZ(t)=d R ₁ d R ₂ <_c(R ₁:R ₂;t)(R ₁,R ₂;t)> in the right-hand halfplane of the complex variable t is considered; herec,v(R₁,R ₂; t) are single-particle density matrices. It is proven that, in the case of a Gaussian field, the function Z(t) is analytical in the region Ret > 0. It is shown that the frequency dependence of the light-absorption coefficient in disordered semiconductors is determined by the asymptote of the function Z(t) as t.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 46–50, June, 1987.     

Asymptotic behavior of the density for two-particle annihilating exclusion

We consider a stochastic process which presents an evolution of particles of two types,A andB, onZ ^d with annihilations between particles of opposite types. Initially, at each site ofZ ^d, independently of the other sites, we put a particle with probability 2<1 and assign to it one of two types with equal chances. Each particle evolves onZ ^d in the following manner: independently from the others, it waits an exponential time with mean 1, chooses one of its neighboring sites on the latticeZ ^d with equal probabilities, and jumps to the site chosen. If the site to which a particle attempts to move is occupied by another particle of the same type, the jump is suppressed; if it is occupied by a particle of the opposite type, then both are annihilated and disappear from the system. The considered process may serve as a model for the chemical reactionA+Binert. Let (t) denote the density of particles in this process at timet. We prove that there exist absolute finite constantsc(d) andC(d) such that for all sufficiently larget,c(d)t ^–d/4 (t)C(d)t ^–d/4 in the dimensionsd4 andc(d)t ^–1 (t)C(d)t ^–1 in all higher dimensions. This completes and makes more precise the results obtained by us earlier and shows that asymptotically the density behaves like that in a similar process called two-particle annihilating random walks which was studied by Bramson and Lebowitz. Our proofs are based on the approach developed in their and our works. We use the basic properties of random walk and various tools which have been designed to study simple symmetric exclusion processes.     

Asymptotic upper bound of density for two-particle annihilating exclusion

We consider a stochastic process which presents an evolution of particles of two types on ^d with annihilations between particles of opposite types. Initially, at each site of ^d , independently of the other sites, we put a particle with probability 21 and assign to it one of two types with equal chances. Each particle, independently from the others, waits an exponential time with mean 1, chooses one of its neighboring sites on the lattice ^d with equal probabilities, and jumps to the site chosen. If the site to which a particle attempts to move is occupied by another particle of the same type, the jump is suppressed; if it is occupied by a particle of the opposite type, then both are annihilated and disappear from the system. The considered process may serve as a model for the chemical reaction A+B inert. The paper concerns an upper bound of(t), the density of particles in the system at timet. We prove that(t)<t -d/ when t>t() for all>0 in the dimensionsd4 and asymptotically(t) ^–1 in the higher dimensions. In our proofs, we used the ideas and the technique developed by Bramson and Lebowitz and the tools which are customarily used to study a symmetric exclusion process.     

Active-space N-representability constraints for variational two-particle reduced density matrix calculations

The ground-state energy of a system of fermions can be calculated by minimizing a linear functional of the two-particle reduced density matrix (2-RDM) if an accurate set of N-representability conditions is applied. In this Letter we introduce a class of linear N-representability conditions based on exact calculations on a reduced active space. Unlike wave-function-based approaches, the 2-RDM methodology allows us to combine information from calculations on different active spaces. By adding active-space constraints, we can iteratively improve our estimate for the ground-state energy. Applying our methodology to a 1D Hubbard model yields a significant improvement over traditional 2-positivity constraints with the same computational scaling.     

Reactions of excited atoms and molecules with atoms and molecules

Penning electron distributions arising from the ionization of Na and K by He (1s 2s ^1,3 S)-metastables in thermal collisions, as well as the absolute cross section for Penning ionization of Na by He (2³ S) and relative cross sections for ionization of Na and K by He(2¹ S) and He(2³ S) are measured. It is shown that under fairly general conditions the well depth ε* of the interaction potential between the metastable and the target particle can be obtained directly from the measured electron distributions. ε*-values are reported for the moleules He(1s 2s ^1,3 S)-Na(² S), K(² S) (^2,2Ω), and for He(1s 2s ^1,3 S)-Hg(¹ S)(^1,3Ω). These latter values are obtained from previously published measurements and are to be considered preliminary. Further, additional evidence is given, that Penning ionization with metastables is an electron exchange process.     

Reactions of excited atoms and molecules with atoms and molecules

Ionizing collisions of long lived excited particles with atoms and molecules are studied by a cross beam technique. For the first time reactions of atoms in high Rydberg states are included in the investigation. In this paper we report relative cross sections for the production of the ions RH⁺, RH ₂ ⁺ , and H ₂ ⁺ by collisions of excited rare gas atoms R^* with H₂. With HD as the target molecule the isotope effect for the production of RD⁺ and RH⁺ has been determined. In the case of argon and krypton, ions are produced only by the high Rydberg states, whereas in the case of helium and neon only the metastable states contribute to a measurable extent. The data indicate, that the reaction mechanism is different in principle for metastable and highly excited atoms. Simple models are proposed to explain the experimental results.     

Reactions of excited atoms and molecules with atoms and molecules

From a He-beam excited by electron impact we eliminated the He(2¹ S) component to better than 0.5% by irradiating light from a He discharge. The quenching process ishv(2¹ P→2¹ S)+He(2¹ S)→He(2¹ P)→He(1¹ S +hv) (2¹ P 1)¹ S. By measuring the ions produced in collisions of the He-metastables with various target gases in a mass spectrometer, singlet to triplet Penning-cross section ratios were obtained. These ratios are without exception close to one, which is taken as evidence for the previously proposed electron exchange mechanism of the Penning ionization. In the case that more ions are produced in the collision of He (2¹ S) and He(2³ S) with a target gas, separate relative production cross sections are obtained for the two metastables. For the rare gases the measurements are performed at two temperatures of the He-beam, 320 and 90 °K. It is found that the cross section ratio of associative — to Penning ionization increases considerably as the temperature is decreased for both, He(2¹ S) and He(2³ S), the effect being much more pronounced for He(2¹ S). The results of this work are found to confirm conclusions drawn from measured energy distributions of the electrons ejected in the Penning process.     

Asymptotic behavior of densities for two-particle annihilating random walks

Consider the system of particles on ^d where particles are of two types—A andB—and execute simple random walks in continuous time. Particles do not interact with their own type, but when anA-particle meets aB-particle, both disappear, i.e., are annihilated. This system serves as a model for the chemical reactionA+B inert. We analyze the limiting behavior of the densities _A (t) and _B (t) when the initial state is given by homogeneous Poisson random fields. We prove that for equal initial densities _A (0)= _B (0) there is a change in behavior fromd4, where _A (t)= _B (t)C/t ^d /4, tod4, where _A (t)= _B (t)C/tast. For unequal initial densities _A (0)< _B (0), _A (t)e ^–cl ind=1, _A (t)e ^–Ct/logt ind=2, and _A (t)e ^–Ct ind3. The termC depends on the initial densities and changes withd. Techniques are from interacting particle systems. The behavior for this two-particle annihilation process has similarities to those for coalescing random walks (A+AA) and annihilating random walks (A+Ainert). The analysis of the present process is made considerably more difficult by the lack of comparison with an attractive particle system.     

Asymptotic potential coefficients for rare gas and alkali atoms and simple molecules interacting with metallic surfaces

Values of the coefficients C₃ and C₅ which describe the asymptotic potential energy between an atom or molecule and a surface, and the constants C_s1 and C_s2 which characterize the surface mediation of the long-range atom(molecule)-atom(molecule) interaction, are calculated for rare gas and alkali or simple molecules, such as NO, H₂, and H₂O, adsorbed on noble and transition metals. These calculated results are obtained using analytic representations of the atomic polarizability and a numerical treatment of the substrate dielectric response obtained from measured optical constants.     

Asymptotic coefficients for atoms and ions

We derive convenient analytical formulas in the effective-range approximation for the asymptotic coefficient C _κ of the radial wave function at infinity and for the average radius of the system. A comparison with the results of numerical calculations (done by the Hartree-Fock method) for multi-electron atoms and ions reveals that this approximation has good accuracy for valence s-electrons in all atoms from hydrogen to uranium. We calculate the values of the scattering lengths and the effective ranges for electron-atom and electron-ion scattering. We also examine the quasiclassical approximation for C _κ. Finally, we discuss the logarithmic increase in the effective ranges of ns states as n→∞. Zh. éksp. Teor. Fiz. 115, 521–541 (February 1999)     

Electron correlation in atoms and molecules

Using a modified Rayleigh-Schrödinger perturbation scheme, it is shown that the first order correction to the Hartree-Fock function due to electron correlation effects may be written as Σ_i>j A(χ_ijφ₁...φ_i−1φ_i+1...φ_j−1φ_j+1...φ_N−φ₁...φ_N), where the φ's are the Hartree-Fock SCF orbitals, A is the antisymmetrization operator, χ_ij is an antisymmetrized function of two coordinates. It is also shown that each pair function χ_ij may be evaluated by a variational procedure.     

The spin density matrix for slowly reorienting molecules in zero field

The time evolution of the spin density matrix of a spin embedded in a slowly moving molecule is investigated using Gordon's extended diffusion model for molecular reorientation and allowing the spin to follow the molecular motion. The results for this model are identical with those previously obtained using a jump diffusional model and do not give the adiabatic limit in slow motion. This model is valid provided the molecular angular velocity correlation time is short compared to the spin precession period. The perturbed angular correlation of rays or the spin resonance line shape can be calculated for any value of the rotational diffusion constant by diagonalizing a finite matrix. The necessary matrix elements are given for the 247 keV state of ¹¹¹Cd (I = 5/2).     

Asymptotic behavior of the quasipotential wave function of a two-particle system

The asymptotic behavior of relativistic wave functions of two-particle systems, consisting of spin 0 and 1/2 particles, is found with the help of integral equations derived within the framework of a covariant single-time approach in quantum field theory.Gomel'skii State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 102–105, June, 1993.     

A density functional theory and quantum theory of atoms in molecules study on hydrogen bonding interaction between paracetamol and water molecules

To consider the hydrogen bonding interactions between paracetamol and water molecules, probable complexes of paracetamol from three active sites (carbonyl oxygen atom, hydroxyl oxygen atom, and nitrogen atom) with H₂O molecule were formed. The optimized geometries and total energies have been obtained at the B3PW91/6-31+G(d, p) level of theory. Comparison of hydrogen bond lengths and the energies of complexes showed hydrogen bond that form between the oxygen atom of the carbonyl group and hydrogen atom is stronger than others. Moreover, an increase in the number of hydrogen bonds increases stability of paracetamol-water complexes. At the end, the QTAIM was applied to explain the nature of the hydrogen bonds and confirm the more stability by complexation.     

Phase-sensitive measurements of order parameters for ultracold atoms through two-particle interferometry

Nontrivial symmetry of order parameters is crucial in some of the most interesting quantum many-body states of ultracold atoms as well as condensed matter systems. Examples in cold atoms include p-wave Feshbach molecules and d-wave paired states of fermions that could be realized in optical lattices in the Hubbard regime. Identifying these states in experiments requires measurements of the relative phase of different components of the entangled pair wave function. We propose and discuss two schemes for such phase-sensitive measurements, based on two-particle interference revealed in atom-atom or atomic density correlations. Our schemes can also be used for relative phase measurements for nontrivial particle-hole order parameters, such as d-density wave order.     

Plasmonic atoms and plasmonic molecules

The proposed paradigm of plasmonic atoms and plasmonic molecules allows one to describe and predict the strongly localized plasmonic oscillations in the clusters of nanoparticles and some other nanostructures in uniform way. Strongly localized plasmonic molecules near the contacting surfaces might become the fundamental elements (by analogy with Lego bricks) for the construction of fully integrated opto-electronic nanodevices of any complexity and scale of integration. PACS 78.67.-n; 73.20.Mf; 32.50.+d     

Optomechanical control of atoms and molecules

We briefly review some of our recent and ongoing work on nanoscale optomechanics, an emerging area at the confluence of atomic, condensed matter and gravitational wave physics. A central tenet of optomechanics is the laser cooling of a moving mirror, typically an end mirror of a Fabry-Perot resonator, to a point near its quantum-mechanical ground state of vibration. Following a general introduction we discuss how the motion of such a macroscopic quantum oscillator can be squeezed, and then show how the placement of a ferroelectric tip on the oscillator allows the coherent manipulation and control of the center-of-mass motion of ultracold polar molecules.