Landau-Zener Approximation Research Articles

Nonadiabatic Kinetics in the Intermediate Coupling Regime: Comparing Molecular Dynamics to an Energy-Grained Master Equation.

We propose and test an extension of the energy-grained master equation (EGME) for treating nonadiabatic (NA) hopping between different potential energy surfaces, which enables us to model the competition between stepwise collisional relaxation and kinetic processes which transfer population between different electronic states of the same spin symmetry. By incorporating Zhu-Nakamura theory into the EGME, we are able to treat NA passages beyond the simple Landau-Zener approximation, along with the corresponding treatments of zero-point energy and tunneling probability. To evaluate the performance of this NA-EGME approach, we carried out detailed studies of the UV photodynamics of the volatile organic compound C6-hydroperoxy aldehyde (C6-HPALD) using on-the-fly ab initio molecular dynamics and trajectory surface hopping. For this multichromophore molecule, we show that the EGME is able to capture important aspects of the dynamics, including kinetic timescales, and diabatic trapping. Such an approach provides a promising and efficient strategy for treating the long-time dynamics of photoexcited molecules in regimes which are difficult to capture using atomistic on-the-fly molecular dynamics.

Density matrix calculation of the dark matter abundance in the Higgs induced right-handed neutrino mixing model

We present new results on the calculation of the dark matter relic abundance within the Higgs induced right-handed neutrino mixing model, solving the associated density matrix equation. For a benchmark value of the dark matter mass MDM = 220 TeV, we show the evolution of the abundance and how this depends on reheat temperature, dark matter lifetime and source right-handed neutrino mass MS, with the assumption MS < MDM. We compare the results with those obtained within the Landau-Zener approximation, showing that the latter largely overestimates the final abundance giving some analytical insight. However, we also notice that since in the density matrix formalism the production is non-resonant, this allows source right-handed neutrino masses below the W boson mass, making dark matter more stable at large mass values. This opens an allowed region for initial vanishing source right-handed neutrino abundance. For example, for MS ≳ 1 GeV, we find MDM≳ 20 PeV. Otherwise, for MS > MW∼ 100 GeV, one has to assume a thermalisation of the source right-handed neutrinos prior to the freeze-in of the dark matter abundance. This results into a large allowed range for MDM, depending on MS. For example, imposing MS ≳ 300 GeV, allowing also successful leptogenesis, we find 00.5 ≲ MDM/TeV ≲ 50. We also discuss in detail leptogenesis with two quasi-degenerate right-handed neutrinos, showing a case when observed dark matter abundance and matter-antimatter asymmetry are simultaneously reproduced. Finally, we comment on how an initial thermal source right-handed neutrino abundance can be justified and on how our results suggest that also the interesting case where MDM < MS, embeddable in usual high scale two right-handed neutrino seesaw models, might be viable.

Nonadiabatic dynamics with intersystem crossings: A time-dependent density functional theory implementation

In this work, we derive a method to perform trajectory-based nonadiabatic dynamics that is able to describe both nonadiabatic transitions and intersystem crossing events (transitions between states of different spin-multiplicity) at the same level of theory, namely, time-dependent density functional theory (TDDFT). To this end, we combined our previously developed TDDFT-based trajectory surface hopping scheme with an accurate and efficient algorithm for the calculation of the spin-orbit coupling (SOC) matrix elements. More specifically, we designed two algorithms for the calculation of intersystem crossing transitions, one based on an extended Tully's surface hopping scheme including SOC and the second based on a Landau-Zener approximation applied to the spin sector of the electronic Hilbert space. This development allows for the design of an efficient on-the-fly nonadiabatic approach that can handle, on an equal footing, nonadiabatic and intersystem crossing transitions. The method is applied to the study of the photophysics of sulfur dioxide (SO2) in gas and liquid phases.

Noise-assisted transport in the Wannier–Stark system

We investigated how the presence of an additional lattice potential, driven by a harmonic noise process, changes the transition rate from the ground band to the first excited band in a Wannier–Stark system. Alongside numerical simulations, we present two models that capture the essential features of the dynamics. The first model uses a noise-driven Landau–Zener approximation and describes the short-time evolution of the full system very well. The second model assumes that the noise process correlation time is much larger than the internal timescale of the system, yet it allows for good estimates of the observed transition rates and gives a simple interpretation of the dynamics. One of the central results is that we obtain a way of controlling the interband transitions with the help of the second lattice. This could readily be realized in state-of-the-art experiments using either Bose–Einstein condensates or optical pulses in engineered potentials.

Ab Initio Excited State Properties and Dynamics of a Prototype σ-Bridged-Donor−Acceptor Molecule

The photophysical and dynamical properties of the donor-(sigma-bridge)-acceptor molecule N-phenylpiperindone-malondinitrile are investigated by second-order approximate coupled cluster (CC2) and time-dependent density functional theory (TDDFT). The study is based on optimized equilibrium geometries for ground and excited states as well as on ab initio molecular dynamics simulations. While CC2 and DFT both predict ground state geometries that are consistent with the crystal structure, equilibrium geometries for the fluorescent charge transfer (CT) state are qualitatively different between CC2 and TDDFT. CC2 reproduces the experimental results for vertical excitations (within 0.3 eV) and provides an orbital assignment of the experimental absorption bands that is supported by experiments. Using CC2, a good agreement is also found for fluorescence energies (within 0.1-0.6 eV). At contrast, CT absorption and fluorescence energies are strongly underestimated by TDDFT using the semi-local functional PBE but improved agreement is found for the hybrid functional PBE0. However, for both functionals, TDDFT fails to predict an equilibrium geometry of the intradonor excited state because of mixing between this state and an artificially low-lying CT state during the optimization. This is an example where the well documented CT failure of TDDFT affects properties of other locally excited states. The minimum of the intradonor locally excited state was therefore only located by the CC2 method. The internal conversion (IC) process from a locally excited donor state to the CT state is simulated by excited state ab initio molecular dynamics based on CC2 and where nonadiabatic transitions are described using the Landau-Zener approximation. We find the IC process to occur a few tens of femtoseconds after excitation. The simulation provides a detailed description of the atomic rearrangements in electron donor and acceptor that drive the interconversion process.

Quantum annealing of an infinite-range transverse-field Ising model

The adiabatic quantum evolution of the Lipkin-Meshkov-Glick (LMG) model across its quantum critical point is studied. The dynamics is realized by linearly switching the transverse field from an initial large value towards zero. We concentrate our attention on the residual energy after the quench in order to estimate the level of diabaticity of the evolution. We discuss a Landau-Zener approximation of the finite size LMG model, that is successful in reproducing the behavior of the residual energy as function of the transition rate in most of the regimes considered. The system proposed is a paradigm of infinite-range interaction or high-dimensional models.

Adiabatic quantum dynamics of the Lipkin-Meshkov-Glick model

The adiabatic quantum evolution of the Lipkin-Meshkov-Glick (LMG) model across its quantum critical point is studied. The dynamics is realized by linearly switching the transverse field from an initial large value towards zero and considering different transition rates. We concentrate our attention on the residual energy after the quench in order to estimate the level of diabaticity of the evolution. We discuss a Landau-Zener approximation of the finite size LMG model, that is successful in reproducing the behavior of the residual energy as function of the transition rate in the most part of the regimes considered. We also support our description through the analysis of the entanglement entropy of the evolved state. The system proposed is a paradigm of infinite-range interaction or high-dimensional models.

Fragmentation of Protonated Peptide Ions via Interaction with Metastable Atoms

Fragmentation of protonated peptide ions via interaction with low kinetic energy electronicallyexcited metastable argon atoms was studied in a linear trap-time-of-flight mass spectrometer. Metastable argon atoms were generated using a glow discharge-type source. Protonated peptide ions of substance P, bradykinin, fibrinopetide A, and insulin oxidized chain B were produced by electrospray ionization and trapped in a quadrupole ion guide for 100-400 ms. Intensive series of c- and z-ions were observed in all cases. The kinetic measurements of the fragmentation rates are consistent with calculations of the reaction cross section based on the Landau-Zener approximation.

Model study of the Landau–Zener approximation

We reexamine the accuracy of the Landau–Zener approximation, whose analytic simplicity has made it often cited and applied over the past 70years in describing nonadiabatic transitions. We find that this approximation may be in substantial disagreement with exact numerical results for a model physical system and a wide range of coupling strengths and relative velocities. We conclude that the Landau–Zener approximation should be used with caution for quantitative estimates of nonadiabatic transition probabilities or cross sections.

Active-sterile neutrino oscillations in the early Universe: Asymmetry generation at low|δm2|and the Landau-Zener approximation

It is well established that active-sterile neutrino oscillations generate large neutrino asymmetries for very small mixing angles $({\mathrm{sin}}^{2}2{\ensuremath{\theta}}_{0}\ensuremath{\lesssim}{10}^{\ensuremath{-}4}),$ negative values of $\ensuremath{\delta}{m}^{2},$ provided that $|\ensuremath{\delta}{m}^{2}|\ensuremath{\gtrsim}{10}^{\ensuremath{-}4} {\mathrm{eV}}^{2}.$ By numerically solving the quantum kinetic equations, we show that the generation still occurs at much lower values of $|\ensuremath{\delta}{m}^{2}|.$ We also describe the borders of the generation at small mixing angles and show how our numerical results can be analytically understood within the framework of the Landau-Zener approximation thereby extending previous work based on the adiabatic limit. This approximate approach leads to a fair description of the MSW dominated regime of the neutrino asymmetry evolution and is also able to correctly reproduce its final value. We also briefly discuss the impact that neutrino asymmetry generation could have on big bang nucleosynthesis, CMBR and relic neutrinos.

Inelastic transitions in slow heavy-particle atomic collisions

It is a generally held belief that inelastic transition probabilities and cross sections in slow, nearly adiabatic atomic collisions decrease exponentially with the inverse of the collision velocity $v$ [i.e., $\ensuremath{\sigma}\ensuremath{\propto}\mathrm{exp}(\ensuremath{-}\mathrm{const}/v)].$ This notion is supported by the Landau-Zener approximation and the hidden crossings approximation. We revisit the adiabatic limit of ion-atom collisions and show that for very slow collisions radial transitions are dominated by the topology of the branch points of the radial velocity rather than the branch points of the energy eigensurface. This can lead to a dominant power-law dependence of inelastic cross sections, $\ensuremath{\sigma}\ensuremath{\propto}{v}^{n}.$ We illustrate the interplay between different contributions to the transition probabilities in a one-dimensional collision system for which the exact probabilities can be obtained from a direct numerical solution of the time-dependent Sch\"odinger equation.

Selective field ionization in Li and Rb: Theory and experiment

We present a direct comparison between calculated and measured ionization in Li and Rb when an initially bound Rydberg electron is stripped from the atom by ramping an electric field@0.415 V/~cm ns!#. We describe the method used to calculate the field dependence of the ionization; the method can be used to evolve the population from field strengths where three or more n manifolds cross to the fields where the electron is stripped from the atom. The essential feature of the method is the repeated application of the Landau-Zener approximation for all of the level crossings as the field is ramped. We also give a description of the dynamics of Li and Rb in the ramping field. We observe that the Li selective field ionization is sensitive to the Stark levels within an n manifold, while for Rb only an n dependence is observed. Selective field ionization ~SFI! has been used as an experimental tool to measure the character and population of highly excited states of atoms and molecules. In SFI, the atom is subjected to an electric field that ramps to higher strengths over times that are very long compared to the classical period of the electron. Eventually the field strength is large enough to rip the electron from the atom. Often the field at which the electron is removed from the atom is when the energy of the state is greater than the classical ionization threshold, in atomic units E522AF or equivalently F 51/16n 4 ; in other units, this relationship is often expressed

Nonadiabatic wave packet dynamics: Experiment and theory in IBr

We present an experimental and a theoretical study of nonadiabatic wave packet dynamics in the intermediate coupling regime as exhibited by the IBr molecule. Using a femtosecond pump–probe molecular beam technique, we generated a wave packet which evolves on the electronically excited B 3Π0+/Y(0+) coupled states. The wave packet dynamics was detected by a time-delayed probe pulse which induced two photon ionization to the ground state of the IBr+ ion. The study consisted of a systematic variation of the pump laser wavelength from the crossing point of the two coupled states to the dissociation limit of the bound diabatic state. The theoretical study is based on the convolution of the products of the energy resolved X 1Σ+→B 3Π0+/Y(0+) bound–free dipole matrix elements and the free–bound two-photon ionization amplitudes (calculated exactly using the artificial channel method) with the profiles of the pump and probe pulses. The theoretical calculations reproduce the general decay, recurrence, and revivals observed experimentally. The importance of treating nonadiabatic dynamics beyond the Landau–Zener approximation, as well as the utility of femtosecond pump–probe techniques in probing simultaneously short and long lived resonances is demonstrated.

Electronic to vibrational and rotational energy transfer in S(1D)+CO quenching reaction: Ab initio MO and surface hopping trajectory studies

The collisional energy transfer reaction, S(1D)+CO→S(3P)+CO(v,J), has been studied by means of the ab initio MO (molecular orbital) and surface-hopping trajectory calculations. The potential-energy surfaces (PESs) calculated by the ab initio MO calculations showed that the singlet and triplet PESs [S(1D)+CO and S(3P)+CO] are composed of the attractive and repulsive potential curves, respectively. The strongly bond intermediate corresponding to SCO(1∑) is found on the collision region on the singlet PES. The singlet and triplet PESs are crossed each other at region of around r(S−C)=2.4 Å with the seam of the conical intersection. By using the fitted ab initio PESs, three-dimensional surface-hopping trajectory calculations are performed under the Landau–Zener approximation. The calculated rotational and vibrational state distributions of the product CO(v,J) are composed of two components due to the contributions from both direct and complex channels. The calculations show that the quenching probability decreases gradually with increasing collision energy. This decrease is due to the fact that the branching ratio of direct to complex channels is varied as a function of collision energy. The mechanism of the energy transfer was discussed on the basis of the theoretical results.

Incomplete optical shielding in cold atom traps: three-dimensional Landau-Zener theory

Ultracold atom collisions in the presence of a linearly polarized blueshifted laser field are studied theoretically. An analytical solution is presented within the framework of the Landau-Zener approximation. The effect of incomplete shielding is mostly accounted for by incorporating the three-dimensional character of the collisions, using a partial-wave analysis with space degeneracy. A model of two electronic states, including effects of indistinguishability of the colliding atoms, is used. The model associates the incomplete shielding with a process involving two crossing points. The theory is applied to the case of metastable xenon traps, obtaining a fair agreement with the experimental data. {copyright} {ital 1997} {ital The American Physical Society}

Theoretical charge-transfer cross-sections for from a diatomics-in-molecules effective Hamiltonian

Abstract A projection matrix technique is used to construct a two-state effective Hamiltonian matrix from a diatomics-in-molecules model (10 × 10 matrix) for the H 2 Cl + molecule. This is applied to the computation of the dependence on collision energy of the cross-section for the charge-transfer process H + + HCl(X 1 Σ + ) → H ( 2 S g ) + HCl + ( A 2 Σ + ) . The reaction probabilities are estimated by the Landau-Zener approximation within the context of simple straight-line trajectories. The results, which in general overestimate the experimentally measured cross-sections, are discussed in terms of the properties at the crossing of the diabatic states and are compared with earlier calculations.

Cross section for the mutual neutralization reaction H2++H-, calculated in a multiple-crossing Landau-Zener approximation.

A multiple-crossing Landau-Zener model is applied to calculate mutual neutralization cross sections for the reactions ${\mathrm{H}}^{+}$+${\mathrm{H}}^{\mathrm{\ensuremath{-}}}$ and ${\mathrm{H}}_{2}^{+}$+${\mathrm{H}}^{\mathrm{\ensuremath{-}}}$ as a function of the principal quantum number n of the resulting H atom. For low-energy collisions (E\ensuremath{\le}10 eV), the total cross section for ${\mathrm{H}}_{2}^{+}$+${\mathrm{H}}^{\mathrm{\ensuremath{-}}}$ is a factor of 8 larger than the one for ${\mathrm{H}}^{+}$+${\mathrm{H}}^{\mathrm{\ensuremath{-}}}$. The cross section for the process including ${\mathrm{H}}_{2}^{+}$, in which the H atom is excited to the quantum state n (2\ensuremath{\le}n\ensuremath{\le}8), has a nonmonotonic behavior as a function of the atomic quantum state. Comparison of the calculated results with newly received experimental data is made.

Two-photon absorption of dissociating TLI in strong laser fields

In a strong laser field (I=2 GW/cm2) TlI is dissociated by a two-photon process and the Tl fragment is detected state specifically. The yield of Tl 6p 2 P 3/2 (Tl*) is measured as a function of the dissociation wavelength (480 nm–540 nm). If the dissociation wavelength is close to two-photon transitions of the Tl atom from 6p 2 P 3/2 to np2 P 1/2,3/2 or mf2 F 5/2,7/2,n=10 ... 15,m=7 ... 12 dips in the yield are observed. These dips show a significant asymmetric broadening, compared to a free atomic transition and the observation is interpreted as an absorption process of the transient state of dissociating TlI during the laser pulse. By applying the Landau-Zener approximation for the potential crossing of dressed molecular states, we are able to describe the broadening and the power density dependence of the observations. Simulations show that the asymmetry is determined by the difference potential of the electronic states which are coupled by the laser field.

Cross Section Measurement of C-2 and C2H- Ion Formation by Double Electron Transfer in One Collision.

Using a beam-gas technique, double electron transfer cross sections of non-dissociative C2- and C2H- ion formations with a Cs target were evaluated to be 7.03 × 10-18 and 1.87 × 10-18 cm2 at laboratory energy of 3.0 keV, respectively. The cross sections of C2- and C2H- ion formation decreased with the decrease of the laboratory energy, becoming 2.15×10-18 and 3.41 × 10-19 cm2 at 0.7 keV, respectively. The cross sections of double electron transfer with K or Na targets were estimated to be less than 2 × 10-20 cm2 at collision energy between 0.7 keV and 3.0 keV. The energy dependence and the magnitude of the cross sections were compared with an adiabatic criterion and Landau-Zener approximation. The Landau-Zener approximation gave the cross sections which were one order of magnitude larger than the experimental value. This difference between the calculated value and the experimental value would be explained from the influence of intermediate pseudopotential crossings between an ion pair state and excited ion molecule states.

Wave packet description of laser-induced level crossings

Abstract We discuss the phenomenon of laser-induced level crossings in molecular systems, and we show how such crossings may be created and explored. The problem is formulated in terms of Born-Oppenheimer states coupled by electric dipole transitions. We specify the problem to a pair of crossing levels, and integrate the coupled motion of wave packets on these levels. The results of the calculation are compared with the Landau-Zener approximation; agreement is found for most parameter ranges, when the classically calculated velocity at the crossing is introduced into the Landau-Zener adiabaticity parameter. For cases when no actual crossing is encountered we observe features characteristic of the wave mechanical nature of the situation, namely: tunneling, split up of the packets and interference.