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Benjamin G Levine  One of the best experts on this subject based on the ideXlab platform.

Wave Function continuity and the diagonal born oppenheimer correction at conical intersections
Journal of Chemical Physics, 2016CoAuthors: Garrett A Meek, Benjamin G LevineAbstract:We demonstrate that though exact in principle, the expansion of the total molecular Wave Function as a sum over adiabatic BornOppenheimer (BO) vibronic states makes inclusion of the secondderivative nonadiabatic energy term near conical intersections practically problematic. In order to construct a wellbehaved molecular Wave Function that has density at a conical intersection, the individual BO vibronic states in the summation must be discontinuous. When the secondderivative nonadiabatic terms are added to the Hamiltonian, singularities in the diagonal BO corrections (DBOCs) of the individual BO states arise from these discontinuities. In contrast to the wellknown singularities in the firstderivative couplings at conical intersections, these singularities are nonintegrable, resulting in undefined DBOC matrix elements. Though these singularities suggest that the exact molecular Wave Function may not have density at the conical intersection point, there is no physical basis for this constraint. Inste...

Wave Function continuity and the diagonal born oppenheimer correction at conical intersections
Journal of Chemical Physics, 2016CoAuthors: Garrett A Meek, Benjamin G LevineAbstract:We demonstrate that though exact in principle, the expansion of the total molecular Wave Function as a sum over adiabatic BornOppenheimer (BO) vibronic states makes inclusion of the secondderivative nonadiabatic energy term near conical intersections practically problematic. In order to construct a wellbehaved molecular Wave Function that has density at a conical intersection, the individual BO vibronic states in the summation must be discontinuous. When the secondderivative nonadiabatic terms are added to the Hamiltonian, singularities in the diagonal BO corrections (DBOCs) of the individual BO states arise from these discontinuities. In contrast to the wellknown singularities in the firstderivative couplings at conical intersections, these singularities are nonintegrable, resulting in undefined DBOC matrix elements. Though these singularities suggest that the exact molecular Wave Function may not have density at the conical intersection point, there is no physical basis for this constraint. Instead, the singularities are artifacts of the chosen basis of discontinuous Functions. We also demonstrate that continuity of the total molecular Wave Function does not require continuity of the individual adiabatic nuclear Wave Functions. We classify nonadiabatic molecular dynamics methods according to the constraints placed on Wave Function continuity and analyze their formal properties. Based on our analysis, it is recommended that the DBOC be neglected when employing mixed quantumclassical methods and certain approximate quantum dynamical methods in the adiabatic representation.
Y Kuramashi  One of the best experts on this subject based on the ideXlab platform.

relation between scattering amplitude and bethe salpeter Wave Function in quantum field theory
Physical Review D, 2017CoAuthors: Takeshi Yamazaki, Y KuramashiAbstract:We reexamine the relations between the BetheSalpeter (BS) Wave Function of two particles, the onshell scattering amplitude, and the effective potential in quantum filed theory. It is emphasized that there is an exact relation between the BS Wave Function inside the interaction range and the scattering amplitude, and the reduced BS Wave Function, which is defined in this article, plays an essential role in this relation. Based on the exact relation, we show that the solution of Schr\"odinger equation with the effective potential gives us a correct onshell scattering amplitude only at the momentum where the effective potential is calculated, while wrong results are obtained from the Schr\"odinger equation at general momenta. We also discuss about a momentum expansion of the reduced BS Wave Function and an uncertainty of the scattering amplitude stemming from the choice of the interpolating operator in the BS Wave Function. The theoretical conclusion obtained in this article could give hints to understand the inconsistency observed in lattice QCD calculation of the twonucleon channels with different approaches.

relation between scattering amplitude and bethe salpeter Wave Function in quantum field theory
Physical Review D, 2017CoAuthors: Takeshi Yamazaki, Y KuramashiAbstract:We discuss an exact relation between the twoparticle scattering amplitude and the BetheSalpeter (BS) Wave Function inside the interaction range in quantum field theory. In the relation the reduced BS Wave Function defined by the BS Wave Function plays an essential role. Through the relation the onshell and half offshell amplitudes can be calculated. We also show that the solution of Schrodinger equation with the effective potential determined from the BS Wave Function gives a correct onshell scattering amplitude only at the momentum where the effective potential is determined. Furthermore we discuss a derivative expansion of the reduced BS Wave Function and a condition to obtain results independent of the interpolating operators in the timedependent HALQCD method.
Hsiangnan Li  One of the best experts on this subject based on the ideXlab platform.

joint resummation for pion Wave Function and pion transition form factor
Journal of High Energy Physics, 2014CoAuthors: Yuelong Shen, Hsiangnan Li, Yuming WangAbstract:We construct an evolution equation for the pion Wave Function in the k T factorization formalism, whose solution sums the mixed logarithm ln x ln k T to all orders, with x (k T ) being a parton momentum fraction (transverse momentum). This joint resummation induces strong suppression of the pion Wave Function in the small x and large b regions, b being the impact parameter conjugate to k T , and improves the applicability of perturbative QCD to hard exclusive processes. The above effect is similar to those from the conventional threshold resummation for the double logarithm ln2 x and the conventional k T resummation for ln2 k T . Combining the evolution equation for the hard kernel, we are able to organize all large logarithms in the γ * π 0 → γ scattering, and to establish a schemeindependent k T factorization formula. It will be shown that the significance of nexttoleadingorder contributions and saturation behaviors of this process at high energy differ from those under the conventional resummations. It implies that QCD logarithmic corrections to a process must be handled appropriately, before its data are used to extract a hadron Wave Function. Our predictions for the involved pion transition form factor, derived under the joint resummation and the input of a nonasymptotic pion Wave Function with the second Gegenbauer moment a 2 = 0.05, match reasonably well the CLEO, BaBar, and Belle data.
Yuki Yamazaki  One of the best experts on this subject based on the ideXlab platform.

de broglie bohm interpretation for Wave Function of reissner nordstrom de sitter black hole
International Journal of Modern Physics A, 2000CoAuthors: Masakatsu Kenmoku, Hiroto Kubotani, Eiichi Takasugi, Yuki YamazakiAbstract:We study the canonical quantum theory of the spherically symmetric geometry with the cosmological constant and the electromagnetic field. We obtain a solution of the Wheeler–DeWitt equation for the geometrical variables and investigate the Wave Function from a viewpoint of the de Broglie–Bohm interpretation of the ordinary quantum mechanics. The de Broglie–Bohm interpretation introduces deterministic rigid trajectories on the minisuperspace without any outside observers nor the collapse of the Wave Function. It is shown that the Wave Function does not only correspond to the classical Reissner–Nordstrom–de Sitter black hole in the semiclassical region, but it also represents quantum geometrical fluctuations near the black hole horizon and the cosmological one. The result suggests that the semiclassical gravity on which the Hawking radiation is based is broken near the horizons.

de broglie bohm interpretation for Wave Function of reissner nordstrom de sitter black hole
arXiv: General Relativity and Quantum Cosmology, 1998CoAuthors: Masakatsu Kenmoku, Hiroto Kubotani, Eiichi Takasugi, Yuki YamazakiAbstract:We study the canonical quantum theory of the ReissnerNordstromde Sitter black hole(RNdS). We obtain an exact general solution of the WheelerDeWitt equation for the spherically symmetric geometry with electromagnetic field. We investigate the Wave Function form a viewpoint of the de BroglieBohm interpretation. The de BroglieBohm interpretation introduces a rigid trajectory on the minisuperspace without assuming an outside observer or causing collapse of the Wave Function. In our analysis, we obtain the boundary condition for the Wave Function which corresponds to the classical RNdS black hole and describe the quantum fluctuations near the horizons quantitatively.
Garrett A Meek  One of the best experts on this subject based on the ideXlab platform.

Wave Function continuity and the diagonal born oppenheimer correction at conical intersections
Journal of Chemical Physics, 2016CoAuthors: Garrett A Meek, Benjamin G LevineAbstract:We demonstrate that though exact in principle, the expansion of the total molecular Wave Function as a sum over adiabatic BornOppenheimer (BO) vibronic states makes inclusion of the secondderivative nonadiabatic energy term near conical intersections practically problematic. In order to construct a wellbehaved molecular Wave Function that has density at a conical intersection, the individual BO vibronic states in the summation must be discontinuous. When the secondderivative nonadiabatic terms are added to the Hamiltonian, singularities in the diagonal BO corrections (DBOCs) of the individual BO states arise from these discontinuities. In contrast to the wellknown singularities in the firstderivative couplings at conical intersections, these singularities are nonintegrable, resulting in undefined DBOC matrix elements. Though these singularities suggest that the exact molecular Wave Function may not have density at the conical intersection point, there is no physical basis for this constraint. Inste...

Wave Function continuity and the diagonal born oppenheimer correction at conical intersections
Journal of Chemical Physics, 2016CoAuthors: Garrett A Meek, Benjamin G LevineAbstract:We demonstrate that though exact in principle, the expansion of the total molecular Wave Function as a sum over adiabatic BornOppenheimer (BO) vibronic states makes inclusion of the secondderivative nonadiabatic energy term near conical intersections practically problematic. In order to construct a wellbehaved molecular Wave Function that has density at a conical intersection, the individual BO vibronic states in the summation must be discontinuous. When the secondderivative nonadiabatic terms are added to the Hamiltonian, singularities in the diagonal BO corrections (DBOCs) of the individual BO states arise from these discontinuities. In contrast to the wellknown singularities in the firstderivative couplings at conical intersections, these singularities are nonintegrable, resulting in undefined DBOC matrix elements. Though these singularities suggest that the exact molecular Wave Function may not have density at the conical intersection point, there is no physical basis for this constraint. Instead, the singularities are artifacts of the chosen basis of discontinuous Functions. We also demonstrate that continuity of the total molecular Wave Function does not require continuity of the individual adiabatic nuclear Wave Functions. We classify nonadiabatic molecular dynamics methods according to the constraints placed on Wave Function continuity and analyze their formal properties. Based on our analysis, it is recommended that the DBOC be neglected when employing mixed quantumclassical methods and certain approximate quantum dynamical methods in the adiabatic representation.