The Experts below are selected from a list of 22860 Experts worldwide ranked by ideXlab platform
J V Ortiz - One of the best experts on this subject based on the ideXlab platform.
-
assessment of electron propagator methods for the simulation of vibrationally resolved valence and core photoionization spectra
Journal of Chemical Theory and Computation, 2017Co-Authors: Alberto Baiardi, V G Zakrzewski, Lorenzo Paoloni, Vincenzo Barone, J V OrtizAbstract:The analysis of photoelectron spectra is usually facilitated by quantum mechanical simulations. Because of the recent improvement of experimental techniques, the resolution of experimental spectra is rapidly increasing, and the inclusion of vibrational effects is usually mandatory to obtain a reliable reproduction of the spectra. With the aim of defining a robust computational protocol, a general time-independent formulation to compute different kinds of vibrationally resolved electronic spectra has been generalized to also support photoelectron spectroscopy. The electronic structure data underlying the simulation are computed using different electron propagator approaches. In addition to the more standard approaches, a new and robust implementation of the second-order self-energy approximation of the electron propagator based on a Transition Operator reference (TOEP2) is presented. To validate our implementation, a series of molecules has been used as test cases. The result of the simulations shows that,...
-
interpreting bonding and spectra with correlated one electron concepts from electron propagator theory
Annual Reports in Computational Chemistry, 2017Co-Authors: J V OrtizAbstract:Abstract Electron propagator theory provides a strategy with computational and interpretive advantages for the prediction of electron attachment and detachment energies and other properties of molecules and molecular ions. Although the effects of electron correlation may be systematically included up to the exact limit, transparent generalizations of one-electron concepts also are procured by the electron propagator approach to molecular electronic structure. Generalized molecular-orbital concepts emerge from the Dyson quasiparticle equation, including correlated electron binding energies and their Dyson orbitals. This information suffices to predict Transition probabilities which are probed in various kinds of spectroscopic and scattering experiments. Relationships between correlated Transition and reference-state properties are discussed. Approximations in the self-energy Operator, wherein relaxation and correlation effects on electron binding energies reside, are described. Emphasis is placed on approaches that employ a separation between occupied and virtual spin-orbitals such as the renormalized partial third order, the nondiagonal renormalized second order, the second-order Transition Operator and the Brueckner-doubles, triple-index ionization Operator methods. Computational characteristics of these methods are compared with those of older precedents, including the second order, outer valence green function, and GW self-energies. Results of numerical tests on molecules of general interest and improved strategies for treating basis-set effects are reviewed. Recent and noteworthy applications to molecular wires, solvated molecules and ions, gas-phase anions, super-halogens, positron–molecule complexes, anionic resonances, and photoionization cross sections are summarized.
-
electron propagator theory an approach to prediction and interpretation in quantum chemistry
Wiley Interdisciplinary Reviews: Computational Molecular Science, 2013Co-Authors: J V OrtizAbstract:Electron propagator theory provides a practical means of calculating electron binding energies, Dyson orbitals, and ground-state properties from first principles. This approach to ab initio electronic structure theory also facilitates the interpretation of its quantitative predictions in terms of concepts that closely resemble those of one-electron theories. An explanation of the physical meaning of the electron propagator's poles and residues is followed by a discussion of its couplings to more complicated propagators. These relationships are exploited in superOperator theory and lead to a compact form of the electron propagator that is derived by matrix partitioning. Expressions for reference-state properties, relationships to the extended Koopmans's theorem technique for evaluating electron binding energies, and connections between Dyson orbitals and Transition probabilities follow from this discussion. The inverse form of the Dyson equation for the electron propagator leads to a strategy for obtaining electron binding energies and Dyson orbitals that generalizes the Hartree–Fock equations through the introduction of the self-energy Operator. All relaxation and correlation effects reside in this Operator, which has an energy-dependent, nonlocal form that is systematically improvable. Perturbative arguments produce several, convenient (e.g. partial third order, outer valence Green's function, and second-order, Transition-Operator) approximations for the evaluation of valence ionization energies, electron affinities, and core ionization energies. Renormalized approaches based on Hartree–Fock or approximate Brueckner orbitals are employed when correlation effects become qualitatively important. Reference-state total energies based on contour integrals in the complex plane and gradients of electron binding energies enable exploration of final-state potential energy surfaces. © 2012 John Wiley & Sons, Ltd.
-
Efficient and Accurate Electron Propagator Methods and Algorithms
Practical Aspects of Computational Chemistry, 2009Co-Authors: Roberto Flores-moreno, J V OrtizAbstract:Recent developments in electron propagator methods that employ the quasiparticle approximation can facilitate calculations on molecules of unprecedented size. Reductions of arithmetic and storage requirements are considered. New and reliable approximations that offer a better compromise of accuracy and feasibility are proposed. Transition Operator orbitals, in combination with the second-order self-energy, provide reliable predictions for valence and core electron binding energies with algorithms that are comparable in efficiency to their counterparts that employ ordinary Hartree–Fock orbitals. Quasiparticle virtual orbitals enable accurate evaluation of third-order self-energy contributions, while significantly reducing storage and arithmetic requirements. Algorithms that employ the resolution-of-the-identity approach to the evaluation of electron repulsion integrals require less memory but retain the accuracy of ordinary calculations. Numerical tests confirm the promise of these new approaches.
-
assessment of Transition Operator reference states in electron propagator calculations
Journal of Chemical Physics, 2007Co-Authors: Roberto Floresmoreno, V G Zakrzewski, J V OrtizAbstract:The Transition Operator method combined with second-order, self-energy corrections to the electron propagator (TOEP2) may be used to calculate valence and core-electron binding energies. This method is tested on a set of molecules to assess its predictive quality. For valence ionization energies, well known methods that include third-order terms achieve somewhat higher accuracy, but only with much higher demands for memory and arithmetic operations. Therefore, we propose the use of the TOEP2 method for the calculation of valence electron binding energies in large molecules where third-order methods are infeasible. For core-electron binding energies, TOEP2 results exhibit superior accuracy and efficiency and are relatively insensitive to the fractional occupation numbers that are assigned to the Transition orbital.
V K B Kota - One of the best experts on this subject based on the ideXlab platform.
-
bivariate q normal distribution for Transition strengths distribution from many particle random matrix ensembles generated by k body interactions
arXiv: Mathematical Physics, 2020Co-Authors: V K B Kota, Manan VyasAbstract:Recently it is established, via lower order moments, that the univariate q-normal distribution, which is the weight function for $q$-Hermite polynomials, describes the ensemble averaged eigenvalue density from many-particle random matrix ensembles generated by $k$-body interactions [Manan Vyas and V.K.B. Kota, J. Stat. Mech. {\bf 2019}, 103103 (2019)]. These ensembles are generically called embedded ensembles of $k$-body interactions [EE($k$)] and their GOE and GUE versions are called EGOE($k$) and EGUE($k$) respectively. Going beyond this work, the lower order bivariate reduced moments of the Transition strength densities, generated by EGOE($k$) [or EGUE($k$)] for the Hamiltonian and an independent EGOE($t$) for the Transition Operator ${\cal O}$ that is $t$-body, are used to establish that the ensemble averaged bivariate Transition densities follow the bivariate $q$-normal distribution. Presented are also formulas for the bivariate correlation coefficient $\rho$ and the $q$ values as a function of the particle number $m$, number of single particle states $N$ that the particles are occupying and the body ranks $k$ and $t$ of $H$ and ${\cal O}$ respectively. Finally, using the bivariate $q$ normal form a formula for the chaos measure number of principal components (NPC) in the Transition strengths from a state with energy $E$ is presented.
-
random matrix theory for Transition strength densities in finite quantum systems results from embedded unitary ensembles
Annals of Physics, 2015Co-Authors: V K B Kota, Manan VyasAbstract:Abstract Embedded random matrix ensembles are generic models for describing statistical properties of finite isolated interacting quantum many-particle systems. For the simplest spinless fermion (or boson) systems, with say m fermions (or bosons) in N single particle states and interacting via k -body interactions, we have EGUE( k ) [embedded GUE of k -body interactions] with GUE embedding and the embedding algebra is U ( N ) . A finite quantum system, induced by a Transition Operator, makes Transitions from its states to the states of the same system or to those of another system. Examples are electromagnetic Transitions (then the initial and final systems are same), nuclear beta and double beta decay (then the initial and final systems are different), particle addition to or removal from a given system and so on. Towards developing a complete statistical theory for Transition strength densities (Transition strengths multiplied by the density of states at the initial and final energies), we have derived formulas for the lower order bivariate moments of the strength densities generated by a variety of Transition Operators. Firstly, for a spinless fermion system, using EGUE( k ) representation for a Hamiltonian that is k -body and an independent EGUE( t ) representation for a Transition Operator that is t -body and employing the embedding U ( N ) algebra, finite- N formulas for moments up to order four are derived, for the first time, for the Transition strength densities. Secondly, formulas for the moments up to order four are also derived for systems with two types of spinless fermions and a Transition Operator similar to beta decay and neutrinoless beta decay Operators. In addition, moments formulas are also derived for a Transition Operator that removes k 0 number of particles from a system of m spinless fermions. In the dilute limit, these formulas are shown to reduce to those for the EGOE version derived using the asymptotic limit theory of Mon and French (1975). Numerical results obtained using the exact formulas for two-body ( k = 2 ) Hamiltonians (in some examples for k = 3 and 4 ) and the asymptotic formulas clearly establish that in general the smoothed (with respect to energy) form of the bivariate Transition strength densities take bivariate Gaussian form for isolated finite quantum systems. Extensions of these results to bosonic systems and EGUE ensembles with further symmetries are discussed.
-
random matrix theory for Transition strength densities in finite quantum systems results from embedded unitary ensembles
arXiv: Quantum Physics, 2015Co-Authors: V K B Kota, Manan VyasAbstract:Embedded random matrix ensembles are generic models for describing statistical properties of finite isolated interacting quantum many-particle systems. For the simplest spinless systems, with say $m$ particles in $N$ single particle states and interacting via $k$-body interactions, we have EGUE($k$) and the embedding algebra is $U(N)$. A finite quantum system, induced by a Transition Operator, makes Transitions from its states to the states of the same system or to those of another system. Examples are electromagnetic Transitions (same initial and final systems), nuclear beta and double beta decay (different initial and final systems), particle addition to/removal from a given system and so on. Towards developing a complete statistical theory for Transition strength densities, we have derived formulas for lower order bivariate moments of the strength densities generated by a variety of Transition Operators. For a spinless fermion system, using EGUE($k$) representation for Hamiltonian and an independent EGUE($t$) representation for Transition Operator, finite-$N$ formulas for moments up to order four are derived, for the first time, for the Transition strength densities. Formulas for the moments up to order four are also derived for systems with two types of spinless fermions and a Transition Operator similar to beta decay and neutrinoless beta decay Operators. Moments formulas are also derived for Transition Operator that removes $k_0$ number of particles from $m$ fermion system. Numerical results obtained using the exact formulas for two-body ($k=2$) Hamiltonians (in some examples for $k=3,4$) and the asymptotic formulas clearly establish that in general the smoothed form of the bivariate Transition strength densities take bivariate Gaussian form for isolated finite quantum systems. Extensions of these results to bosonic systems and EGUE ensembles with further symmetries are discussed.
-
convergence of moment expansions for expectation values with embedded random matrix ensembles and quantum chaos
Annals of Physics, 2003Co-Authors: V K B KotaAbstract:Abstract Smoothed forms for expectation values 〈 K 〉 E of positive definite Operators K follow from the K-density moments either directly or in many other ways each giving a series expansion (involving polynomials in E). In large spectroscopic spaces one has to partition the many particle spaces into subspaces. Partitioning leads to new expansions for expectation values. It is shown that all the expansions converge to compact forms depending on the nature of the Operator K and the operation of embedded random matrix ensembles and quantum chaos in many particle spaces. Explicit results are given for occupancies 〈ni〉E, spin-cutoff factors 〈JZ2〉E and strength sums 〈 O † O 〉 E , where O is a one-body Transition Operator.
Manan Vyas - One of the best experts on this subject based on the ideXlab platform.
-
bivariate q normal distribution for Transition strengths distribution from many particle random matrix ensembles generated by k body interactions
arXiv: Mathematical Physics, 2020Co-Authors: V K B Kota, Manan VyasAbstract:Recently it is established, via lower order moments, that the univariate q-normal distribution, which is the weight function for $q$-Hermite polynomials, describes the ensemble averaged eigenvalue density from many-particle random matrix ensembles generated by $k$-body interactions [Manan Vyas and V.K.B. Kota, J. Stat. Mech. {\bf 2019}, 103103 (2019)]. These ensembles are generically called embedded ensembles of $k$-body interactions [EE($k$)] and their GOE and GUE versions are called EGOE($k$) and EGUE($k$) respectively. Going beyond this work, the lower order bivariate reduced moments of the Transition strength densities, generated by EGOE($k$) [or EGUE($k$)] for the Hamiltonian and an independent EGOE($t$) for the Transition Operator ${\cal O}$ that is $t$-body, are used to establish that the ensemble averaged bivariate Transition densities follow the bivariate $q$-normal distribution. Presented are also formulas for the bivariate correlation coefficient $\rho$ and the $q$ values as a function of the particle number $m$, number of single particle states $N$ that the particles are occupying and the body ranks $k$ and $t$ of $H$ and ${\cal O}$ respectively. Finally, using the bivariate $q$ normal form a formula for the chaos measure number of principal components (NPC) in the Transition strengths from a state with energy $E$ is presented.
-
random matrix theory for Transition strength densities in finite quantum systems results from embedded unitary ensembles
Annals of Physics, 2015Co-Authors: V K B Kota, Manan VyasAbstract:Abstract Embedded random matrix ensembles are generic models for describing statistical properties of finite isolated interacting quantum many-particle systems. For the simplest spinless fermion (or boson) systems, with say m fermions (or bosons) in N single particle states and interacting via k -body interactions, we have EGUE( k ) [embedded GUE of k -body interactions] with GUE embedding and the embedding algebra is U ( N ) . A finite quantum system, induced by a Transition Operator, makes Transitions from its states to the states of the same system or to those of another system. Examples are electromagnetic Transitions (then the initial and final systems are same), nuclear beta and double beta decay (then the initial and final systems are different), particle addition to or removal from a given system and so on. Towards developing a complete statistical theory for Transition strength densities (Transition strengths multiplied by the density of states at the initial and final energies), we have derived formulas for the lower order bivariate moments of the strength densities generated by a variety of Transition Operators. Firstly, for a spinless fermion system, using EGUE( k ) representation for a Hamiltonian that is k -body and an independent EGUE( t ) representation for a Transition Operator that is t -body and employing the embedding U ( N ) algebra, finite- N formulas for moments up to order four are derived, for the first time, for the Transition strength densities. Secondly, formulas for the moments up to order four are also derived for systems with two types of spinless fermions and a Transition Operator similar to beta decay and neutrinoless beta decay Operators. In addition, moments formulas are also derived for a Transition Operator that removes k 0 number of particles from a system of m spinless fermions. In the dilute limit, these formulas are shown to reduce to those for the EGOE version derived using the asymptotic limit theory of Mon and French (1975). Numerical results obtained using the exact formulas for two-body ( k = 2 ) Hamiltonians (in some examples for k = 3 and 4 ) and the asymptotic formulas clearly establish that in general the smoothed (with respect to energy) form of the bivariate Transition strength densities take bivariate Gaussian form for isolated finite quantum systems. Extensions of these results to bosonic systems and EGUE ensembles with further symmetries are discussed.
-
random matrix theory for Transition strength densities in finite quantum systems results from embedded unitary ensembles
arXiv: Quantum Physics, 2015Co-Authors: V K B Kota, Manan VyasAbstract:Embedded random matrix ensembles are generic models for describing statistical properties of finite isolated interacting quantum many-particle systems. For the simplest spinless systems, with say $m$ particles in $N$ single particle states and interacting via $k$-body interactions, we have EGUE($k$) and the embedding algebra is $U(N)$. A finite quantum system, induced by a Transition Operator, makes Transitions from its states to the states of the same system or to those of another system. Examples are electromagnetic Transitions (same initial and final systems), nuclear beta and double beta decay (different initial and final systems), particle addition to/removal from a given system and so on. Towards developing a complete statistical theory for Transition strength densities, we have derived formulas for lower order bivariate moments of the strength densities generated by a variety of Transition Operators. For a spinless fermion system, using EGUE($k$) representation for Hamiltonian and an independent EGUE($t$) representation for Transition Operator, finite-$N$ formulas for moments up to order four are derived, for the first time, for the Transition strength densities. Formulas for the moments up to order four are also derived for systems with two types of spinless fermions and a Transition Operator similar to beta decay and neutrinoless beta decay Operators. Moments formulas are also derived for Transition Operator that removes $k_0$ number of particles from $m$ fermion system. Numerical results obtained using the exact formulas for two-body ($k=2$) Hamiltonians (in some examples for $k=3,4$) and the asymptotic formulas clearly establish that in general the smoothed form of the bivariate Transition strength densities take bivariate Gaussian form for isolated finite quantum systems. Extensions of these results to bosonic systems and EGUE ensembles with further symmetries are discussed.
Yoshua Bengio - One of the best experts on this subject based on the ideXlab platform.
-
variational walkback learning a Transition Operator as a stochastic recurrent net
arXiv: Machine Learning, 2017Co-Authors: Anirudh Goyal, Surya Ganguli, Yoshua BengioAbstract:We propose a novel method to directly learn a stochastic Transition Operator whose repeated application provides generated samples. Traditional undirected graphical models approach this problem indirectly by learning a Markov chain model whose stationary distribution obeys detailed balance with respect to a parameterized energy function. The energy function is then modified so the model and data distributions match, with no guarantee on the number of steps required for the Markov chain to converge. Moreover, the detailed balance condition is highly restrictive: energy based models corresponding to neural networks must have symmetric weights, unlike biological neural circuits. In contrast, we develop a method for directly learning arbitrarily parameterized Transition Operators capable of expressing non-equilibrium stationary distributions that violate detailed balance, thereby enabling us to learn more biologically plausible asymmetric neural networks and more general non-energy based dynamical systems. The proposed training objective, which we derive via principled variational methods, encourages the Transition Operator to "walk back" in multi-step trajectories that start at data-points, as quickly as possible back to the original data points. We present a series of experimental results illustrating the soundness of the proposed approach, Variational Walkback (VW), on the MNIST, CIFAR-10, SVHN and CelebA datasets, demonstrating superior samples compared to earlier attempts to learn a Transition Operator. We also show that although each rapid training trajectory is limited to a finite but variable number of steps, our Transition Operator continues to generate good samples well past the length of such trajectories, thereby demonstrating the match of its non-equilibrium stationary distribution to the data distribution. Source Code: this http URL
-
variational walkback learning a Transition Operator as a stochastic recurrent net
Neural Information Processing Systems, 2017Co-Authors: Anirudh Goyal, Surya Ganguli, Yoshua BengioAbstract:We propose a novel method to {\it directly} learn a stochastic Transition Operator whose repeated application provides generated samples. Traditional undirected graphical models approach this problem indirectly by learning a Markov chain model whose stationary distribution obeys detailed balance with respect to a parameterized energy function. The energy function is then modified so the model and data distributions match, with no guarantee on the number of steps required for the Markov chain to converge. Moreover, the detailed balance condition is highly restrictive: energy based models corresponding to neural networks must have symmetric weights, unlike biological neural circuits. In contrast, we develop a method for directly learning arbitrarily parameterized Transition Operators capable of expressing non-equilibrium stationary distributions that violate detailed balance, thereby enabling us to learn more biologically plausible asymmetric neural networks and more general non-energy based dynamical systems. The proposed training objective, which we derive via principled variational methods, encourages the Transition Operator to "walk back" (prefer to revert its steps) in multi-step trajectories that start at data-points, as quickly as possible back to the original data points. We present a series of experimental results illustrating the soundness of the proposed approach, Variational Walkback (VW), on the MNIST, CIFAR-10, SVHN and CelebA datasets, demonstrating superior samples compared to earlier attempts to learn a Transition Operator. We also show that although each rapid training trajectory is limited to a finite but variable number of steps, our Transition Operator continues to generate good samples well past the length of such trajectories, thereby demonstrating the match of its non-equilibrium stationary distribution to the data distribution. Source Code:http://github.com/anirudh9119/walkback_nips17
T Sato - One of the best experts on this subject based on the ideXlab platform.
-
a next to next to leading order pp ppπ0 Transition Operator in chiral perturbation theory
Nuclear Physics, 2000Co-Authors: V Dmitrasinovic, K Kubodera, F Myhrer, T SatoAbstract:We present a systematic analysis of next-to-next-to-leading-order diagrams that contribute to the pp" ppp 0 production at threshold. Analytic expressions are given for the effective Transition Operators, and the relative importance of various types of diagrams is discussed. The vertex-correction-type graphs are found to give only small corrections to lower order graphs in conformity with expectations. By contrast, we find very large contributions from two-pion exchange graphs that can be interpreted as a part of effective s-meson exchange diagrams. The recoil correction to the pion rescattering diagram also turns out to be large. q 1999 Published by Elsevier Science B.V. All rights reserved.
-
a next to next to leading order pp ppπ0 Transition Operator in chiral perturbation theory
Physics Letters B, 1999Co-Authors: V Dmitrasinovic, K Kubodera, F Myhrer, T SatoAbstract:Abstract We present a systematic analysis of next-to-next-to-leading-order diagrams that contribute to the pp→ppπ0 production at threshold. Analytic expressions are given for the effective Transition Operators, and the relative importance of various types of diagrams is discussed. The vertex-correction-type graphs are found to give only small corrections to lower order graphs in conformity with expectations. By contrast, we find very large contributions from two-pion exchange graphs that can be interpreted as a part of effective σ-meson exchange diagrams. The recoil correction to the pion rescattering diagram also turns out to be large.
-
a next to next to leading order pp to pp pi 0 Transition Operator in chiral perturbation theory
arXiv: Nuclear Theory, 1999Co-Authors: V Dmitrasinovic, K Kubodera, F Myhrer, T SatoAbstract:We present a systematic analysis of next-to-next-to-leading-order diagrams that contribute to the $pp \to pp\pi^0$ production at threshold. Analytic expressions are given for the effective Transition Operators, and the relative importance of various types of diagrams is discussed. The vertex-correction-type graphs are found to give only small corrections to lower order graphs in conformity with expectations. By contrast, we find very large contributions from the two-pion graphs which can be interpreted as a part of effective $\sigma$-meson exchange diagrams. The recoil correction to the pion rescattering diagram also turns out to be large.