Horacio Grinberg

Atomic orbitals of the nonrelativistic hydrogen atom in a four‐dimensional Riemann space through the path integral formalism

The Kustaanheimo–Stiefel transformation together with the well‐known expansion of the kernel of an isotropic harmonic oscillator is used to generate the atomic orbitals of the nonrelativistic hydrogen atom in a four‐dimensional Riemann space through the path integral formalism. Group theoretical implications of the present problem are briefly discussed.

Three‐dimensional analytic quantum theory for triatomic photodissociations. II. Angle dependent dissociative surfaces and rotational infinite order sudden approximation for bent triatomics

We extend to triatomic molecules with bent initial bound states our analytical quantum theory of triatomic photodissociations. The theory uses basis functions for the initial bound state wave function that are product functions in the natural normal (or local) modes appropriate to that state and a continuum wave function that is a product function in the natural scattering coordinates appropriate to the dissociative surface. This choice of wave functions produces three‐dimensional nonseparable transition amplitudes which are reduced to analytical forms by introduction of the infinite order sudden and Airy approximations for the continuum wave function and a quadrature formula for the integral over bending motions. The present theory also lifts some assumptions that had been introduced previously to simplify the theory for isotropic repulsive potentials. Thus, we use the exact nonlinear relation between the bound state bending angle and the scattering angle to remove the previous small angle approximation ...

Path integral of spin models

Abstract A path-integral representation of 1D Ising and XY spin models is investigated. Short-time propagator algorithms and a discrete time formalism are used in combination with Grassmann variables non-orthogonal coherent states to get a many-body analytic propagator. Fermion operators satisfying the canonical anticommutation relations are constructed from the rising and lowering spin operators via the Jordan–Wigner transformation. Computation of the partition function and thermodynamic properties follows from an appropriate tracing over Grassmann variables in the imaginary time domain.

Self-energies for the particle-hole propagator from Feynman-Dyson equations

Abstract Correlation-relaxation corrections to electronic transition energies are obtained through the self-energy fields for the particle-hole propagator. These objects are generated from Feynman-Dyson like equations within the scenario of the superoperator algebra. A Hartree-Fock reference state and a partition of the operator space along with a particle conserving manifold are used to recast the lower order perturbative expressions for the self-energies. Correlated states are used to make explicit the appearance of higher order correction terms to the self-energy. It is explicitly shown that the present scheme leads to a proper classification of the order of the contribution from both the intrinsic interaction operator and the improved reference state.

An ansatz for the decoupling of the electron-propagator equation of motion via superoperator algebra

Abstract An alternative and direct procedure for the decoupling of the electron-propagator equation of motion within the superoperator formalism is presented. The present approach, based on inversion of the perturbation series for the (energy) Greens function, does not require inner projection of the superoperator resolvent or renormalization theory and it is shown to yield, through an appropriate partitioning of the operator space, the lower-order corrections (ring and ladder diagrams) to the Tamm-Dancoff approximation (TDA).

A Liouville-space method for the decoupling of the polarization propagator equation of motion

Abstract Statistical ensemble averages based on Liouville space matrix elements are used to introduce an alternative approach to the decoupling of the polarization propagator equation of motion. To this end, an appropriate ansatz for the (energy) propagator is introduced in the scenario of the superoperator algebra. The perturbation series which arises from the iteration of the (energy) Green function hierarchy allows, upon further expansion of the inverse of such series, to get the lower-order corrections to the Dyson self-energies. This procedure does not require inner projection of the superoperator resolvent or renormalization theory.

ALGEBRAIC RELATIONS BETWEEN DYSON AND LIOUVILLIAN SELF-ENERGY FIELD APPROACHES

Through the superoperator algebraic formalism it is shown that Liouvillian self-energies derived from the equations of motion hierarchy for two-time propagators in stationary states of time independent Hamiltonians of N-particle systems are closely related to those obtained from the solution of the super-operator approach to Dyson equations (Dyson self-energies). It probes the quasi-equivalence of the two formulae, namely, they are equivalent to lower orders in the perturbative series expansion, a result valid for any kind of reference state used in the evaluation of the propagators leading to the self-energy fields. The relations obtained for the one-particle propagator are generalized p-particle propagators (p < N). Thus, it shows the existence, as in the case of one-particle propagators, of Dyson like equations and consequently that the Liouvillian formulation is adequate to solve the decoupling problem in many-body physics allowing extensions to be made to other related fields such as the solution of the reduced Liouville quantum equation.

Density matrix of fermionic systems from coherent states via functional integrals

Abstract A complete system of states, closely related to the coherent states, and which incorporates the necessary algebra of fermion states, is used to derive an expression for the corresponding propagator via functional integrals. The calculation, based on a product expansion of the evolution operator, leads to an exact Feynman propagator from which the expectation value of the density matrix is obtained.

Semiempirical quantum mechanical calculation of the electronic structure of DNA. Molecular orbitals correlation and orbital energy shifts in the double hydrogen bonding of the adenine—thymine base pair

Abstract The double hydrogen bonding in the adenine—thymine nucleotide base pair has been investigated in the CNDO/S semiempirical approximation. Correlation of the molecular orbitals for the double proton transfer in the normal and tautomeric configurations shows that the π molecular orbitals are only slightly perturbed, whereas the σ molecular orbitals are delocalized on both units of the base pair. Analysis via perturbation theory in order to elucidate the formation of the hydrogen-bonded complex has been performed. The results suggest that an unsymmetrical charge transfer is involved in the double proton transfer process. The first-order contribution to the perturbed orbital energies of the σ and π molecular orbitals localized on the same unit of the base pair, is predominantly from exchange repulsion energy, whereas the second-order contributor is mainly polarization energy. In the normal configuration of the base pair, the contribution of the deepest σ molecular orbitals (up to −30 eV) to the energy of formation of the hydrogen-bonded complex shows a stabilizing character, whereas at higher energies the opposite trend predominates. The behaviour of the molecular orbitals of the tautomeric configuration is quite different since only some of the σ orbitals (those laying between −40 and −30 eV) localized on thymine help stabilize the complex, whereas the remainder contribute to destabilization of the configuration. Hence the normal configuration of the base pair is more stable than the tautomeric configuration.

On the evolution equations for reduced density operators in quantum open systems

Abstract Evolution equations for transition probabilities of reduced density operators in quantum open systems are derived. Information contained in such equations is obtained from spectral resolutions and the role of memory kernels is elucidated within the scenario of many body theory as a function of the self-energy fields. As an analytical example of this formulation relaxation times for dissipative systems are evaluated in terms of the interaction between subsystems.