451 research outputs found
Effects of initial correlations on the dynamics of dissipative systems
No full textThe time correlation functions for a Gaussian wave-packet preparation of the dissipative harmonic oscillator evolving from three initial conditions for the heat bath are calculated and compared with each other for Ohmic heat baths. The three initial distributions for the bath are the factorized, partially factorized, and unfactorized distributions. Explicit analytical formulas are derived and then used to study the effect of the three initial distributions on the subsequent dynamics. We find that the transient behavior does not depend sensitively on the initial condition as long as the initial Gaussian wave function of the system is centered at the equilibrium point. Differences become noticeable as the center of the wave packet is significantly shifted from the equilibrium point. These observations justify to some extent the prevalent use of factorized initial conditions for studying real time quantum dynamics in dissipative systems. The total energy in the system is also calculated for the three initial states and its relation to features in the decay is pointed out
Multidimensional generalization of the Pollak–Grabert–Hänggi turnover theory for activated rate processes
No full textIs Quantum Above-Barrier Reflection Important for Molecular Barrier Crossing Rates?
No full textUnderstanding quantum tunneling and above-barrier reflection effects on unimolecular and bimolecular reaction rate constants remains challenging to this very day. In many applications, especially when considering moderate-to-high temperatures, the "standard" procedure is to use the parabolic barrier approximation. Recent work has shown though that this may be insufficient, and one cannot ignore anharmonicity. In this work, we study the analytic theory, including anharmonicity obtained when expanding the thermal rate up to order (sic)(4). Such theories need high-order derivatives of the potential at the barrier top. We show that such derivatives are computed straightforwardly for six different reactions. We suggest a straightforward methodology for assessing whether the parabolic barrier approximation is valid and show that when the reaction asymmetry is large, this may lead to significant quantum above-barrier reflection and transmission coefficients, which are less than unity
Lower Bounds for Nonrelativistic Atomic Energies
No full textA recently developed lower bound theory for Coulombic problems (E. Pollak, R. Martinazzo, J. Chem. Theory Comput. 2021, 17, 1535) is further developed and applied to the highly accurate calculation of the ground-state energy of two- (He, Li+, and H-) and three- (Li) electron atoms. The method has been implemented with explicitly correlated many-particle basis sets of Gaussian type, on the basis of the highly accurate (Ritz) upper bounds they can provide with relatively small numbers of functions. The use of explicitly correlated Gaussians is developed further for computing the variances, and the necessary modifications are here discussed. The computed lower bounds are of submilli-Hartree (parts per million relative) precision and for Li represent the best lower bounds ever obtained. Although not yet as accurate as the corresponding (Ritz) upper bounds, the computed bounds are orders of magnitude tighter than those obtained with other lower bound methods, thereby demonstrating that the proposed method is viable for lower bound calculations in quantum chemistry applications. Among several aspects, the optimization of the wave function is shown to play a key role for both the optimal solution of the lower bound problem and the internal check of the theory
From Eggs to the Stars
No full textJane Pollak is a Westport, Connecticut, artist who started her career as a high school art teacher. She has now branched out into public speaking, is the author of two books, and embraces the life of entrepreneur as a sole proprietor of her rapidly expanding business of decorating eggs. For Jane, her life path has been one of hope and unexpected personal and business achievements.</jats:p
From Eggs to the Stars
No full textInterview of artist Jane Pollak by Shawn Blau and Laurence Weinstein.
Jane Pollak is a Westport, Connecticut, artist who started her career as a high school art teacher. She has now branched out into public speaking, is the author of two books, and embraces the life of entrepreneur as a sole proprietor of her rapidly expanding business of decorating eggs. For Jane, her life path has been one of hope and unexpected personal and business achievements
Recent Developments in Kramers’ Theory of Reaction Rates
No full text16 pags., 4 figs. -- An invited contribution to a Special Collection dedicated to Pablo Villarreal Herrán on the occasion of his 70th birthdayIn this short review, we provide an update of recent developments in Kramers' theory of reaction rates. After a brief introduction stressing the importance of this theory initially developed for chemical reactions, we briefly present the main theoretical formalism starting from the generalized Langevin equation and continue by showing the main points of the modern Pollak, Grabert and Hänggi theory. Kramers' theory is then sketched for quantum and classical surface diffusion. As an illustration the surface diffusion of Na atoms on a Cu(110) surface is discussed showing escape rates, jump distributions and diffusion coefficients as a function of reduced friction. Finally, some very recent applications of turnover theory to different fields such as nanoparticle levitation, microcavity polariton dynamics and simulation of reaction in liquids are presented. We end with several open problems and future challenges faced up by Kramers turnover theory.EP thanks the Israel Science Foundation and the Minerva Foundation for their generous support of this work. SMA would like to thank the Fundación Humanismo y Ciencia for its financial support. It is a pleasure and honor for us to contribute to this Special Issue devoted to Prof. Pablo Villarreal. Pablo has always
been a leader in the field of dynamics of molecular systems, whether on the national Spanish scene or internationally.Peer reviewe
Modified vibrational perturbation theory as applied to the collinear H + H2 and D + H2 reactions
No full textA multidimensional version of the modification to vibrational perturbation theory is developed in this article. The modifications to the action are of two types: one is by shifting the energy scale with the VPT2 zero point energy E0 (mVPT2) and the other is by shifting the action by a constant VPT2-based action ΔS and is denoted mYF. These modifications give a continuous “modified” action over the whole energy range. The multidimensional versions of the mVPT2 and mYF theories have been applied to the collinear H + H2 and D + H2 reactions to calculate thermal reaction rates. The results show that the rates computed using the mVPT2 theory are marginally better than those computed by the mYF theory. The corresponding kinetic isotopic effects have also been computed. Both the theories account for the correct ħ2 limit at high temperature and not the parabolic barrier limit as in various other theories. The mVPT2 and mYF theories also improve upon the thermal rates in the low temperature limit due to the shifting of the action by the zero point energy shift E0. The resulting theory is more accurate than the ring polymer molecular dynamics based approximation over the whole temperature range probed. The results presented here indicate that the multidimensional version of the modified VPT2 theory may be the recommended method for computing thermal tunneling rates in multidimensional systems
Frozen Gaussian series representation of the imaginary time propagator theory and numerical tests
No full textThawed Gaussian wavepackets have been used in recent years to compute approximations to the thermal density matrix. From a numerical point of view, it is cheaper to employ frozen Gaussian wavepackets. In this paper, we provide the formalism for the computation of thermal densities using frozen Gaussian wavepackets. We show that the exact density may be given in terms of a series, in which the zeroth order term is the frozen Gaussian. A numerical test of the methodology is presented for deep tunneling in the quartic double well potential. In all cases, the series is observed to converge. The convergence of the diagonal density matrix element is much faster than that of the antidiagonal one, suggesting that the methodology should be especially useful for the computation of partition functions. As a by product of this study, we find that the density matrix in configuration space can have more than two saddle points at low temperatures. This has implications for the use of the quantum instanton theory
Talking Trade: China's Super Consumers: Changing China, Changing the World
No full textFIT's International Trade and Marketing Department, in partnership with the New York District Export Council at World Trade Week, presents Talking Trade: China's Super Consumers. Distinguished speakers discuss how marketing to China has been transformed, how China's consumers themselves are influencing marketing around the world, and how companies can enhance their sales and exports to the burgeoning Chinese market.Master of Ceremonies: Thomas Pollak, President, Tally-Ho Creations, Pollak Import/Export Corp. and ITM Advisory Board member. Speakers: Mr. Michael A. Zakkour, Vice President, China/Asia Pacific Practice Leader, Tompkins International and co-author of book, China's Super Consumers; Mr. Jason Merritt, Assistant Vice President, Corporate Foreign Exchange Sales, HSBC Bank USA, N
- …
