Quantum Dynamics Calculations on Isotope Effects of Hydrogen Transfer Isomerization in Formic Acid Dimer

We present a quantum dynamics study on the isotope effects of hydro-gen transfer isomerization in the formic acid dimer,and this is achieved by multidimensional dy-namics calculations with an efficient quantum mechanical theoretical scheme developed by our group,on a full-dimensional neural network ab initio potential energy surface.The ground-state and fundamental tun-neling splittings for four deuterium isotopologues of formic acid dimer are considered,and the calculated results are in very good general agreement with the avail-able experimental measurements.Strong isotope effects are revealed,the mode-specific funda-mental excitation effects on the tunneling rate are evidently influenced by the deuterium sub-stitution of H atom with the substitution on the OH bond being more effective than on the CH bond.Our studies are helpful for acquiring a better understanding of isotope effects in the double-hydrogen transfer processes.

Quantum dynamics of charge transfer on the one-dimensional lattice:Wave packet spreading and recurrence

The wave function temporal evolution on the one-dimensional （ID） lattice is considered in the tight-binding approxi- mation. The lattice consists of N equal sites and one impurity site （donor）. The donor differs from other lattice sites by the on-site electron energy E and the intersite coupling C. The moving wave packet is formed from the wave function initially localized on the donor. The exact solution for the wave packet velocity and the shape is derived at different values E and C. The velocity has the maximal possible group velocity v = 2. The wave packet width grows with time -t1/3 and its amplitude decreases ,- t-1/3. The wave packet reflects multiply from the lattice ends. Analytical expressions for the wave packet front propagation and recurrence are in good agreement with numeric simulations.

A typical slow reaction H(~2S) + S_2(X^3-Σ_g^-) → SH(X^2Π)+S(~3P) on a new surface:Quantum dynamics calculations

Quantum dynamics calculations for the title reaction H（2S） ＋ S2（X3∑g） → SH（X2П） ＋S（3P） are performed byusing a globally accurate double many-body expansion potential energy surface [J. Phys. Chem. A 115 5274 （2011）]. The Chebyshev real wave packet propagation method is employed to obtain the dynamical information, such as reaction probability, initial state-specified integral cross section, and thermal rate constant. It is found not only that there is a reaction threshold near 0.7 eV in both reaction probabilities and integral cross section curves, but also that both the probability and cross section increase firstly and then decrease as the collision energy increases. The existence of the resonance structure in both the probability and cross section curves is ascribed to the deep potential well. The calculation of the rate constant reveals that the reaction occurring on the potential energy surface of the ground-state HS2 is slow to take place.

Dynamical learning of non-Markovian quantum dynamics

We study the non-Markovian dynamics of an open quantum system with machine learning.The observable physical quantities and their evolutions are generated by using the neural network.After the pre-training is completed,we fix the weights in the subsequent processes thus do not need the further gradient feedback.We find that the dynamical properties of physical quantities obtained by the dynamical learning are better than those obtained by the learning of Hamiltonian and time evolution operator.The dynamical learning can be applied to other quantum many-body systems,non-equilibrium statistics and random processes.

State-to-state integral cross sections and rate constants for the N^(+)(3P)+HD→NH^(+)/ND^(+)+D/H reaction:Accurate quantum dynamics studies

The reactive collisions of nitrogen ion with hydrogen and its isotopic variations have great significance in the field of astrophysics.Herein,the state-to-state quantum time-dependent wave packet calculations of N^(+)(3P)+HD→NH^(+)/ND^(+)+D/H reaction are carried out based on the recently developed potential energy surface[Phys.Chem.Chem.Phys.2122203(2019)].The integral cross sections(ICSs)and rate coefficients of both channels are precisely determined at the state-to-state level.The results of total ICSs and rate coefficients present a dramatic preference on the ND+product over the NH^(+)product,conforming to the long-lived complex-forming mechanism.Product state-resolved ICSs indicate that both the product molecules are difficult to excite to higher vibrational states,and the ND^(+)product has a hotter rotational state distribution.Moreover,the integral cross sections and rate coefficients are precisely determined at the state-to-state level and insights are provided about the differences between the two channels.The present results would provide an important reference for the further experimental studies at the finer level for this interstellar chemical reaction.The datasets presented in this paper,including the ICSs and rate coefficients of the two products for the title reaction,are openly available at https://www.doi.org/10.57760/sciencedb.j00113.00034.

Novel potential energy surface-based quantum dynamics of ion–molecule reaction O^++ D_2→OD^++ D

According to a novel electronic ground-state potential energy surface of H2O^＋（X^4 A″）,we calculate the reaction probabilities and the integral cross section for the titled reaction O^＋＋ D2→OD^＋＋ D by the Chebyshev wave packet propagation method.The reaction probabilities in a collision-energy range of 0.0 e V–1.0 e V show an oscillatory structure for the O^＋＋ D2 reaction due to the existence of the potential well.Compared with the results of Martinez et al.,the present integral cross section is large,which is in line with experimental data.

State-to-state quantum dynamics of the N(~4S)+H_2(X^1Σ^+) → NH(X^3Σ^-)+H(~2S) reaction and its reaction mechanism analysis

Quantum state-to-state dynamics of the N(4S) + H-2(X1+Σ) → NH(X3Σ) + H(2S) reaction is reported in an accurate novel potential energy surface constructed by Zhai et al.(2011 J. Chem. Phys. 135 104314). The time-dependent wave packet method, which is implemented on graphics processing units, is used to calculate the differential cross sections. The influences of the collision energy on the product state-resolved integral cross sections and total differential cross sections are calculated and discussed. It is found that the products NH are predominated by the backward scattering due to the small impact parameter collisions, with only minor components being forward and sideways scattered, and have an inverted rotational distribution and no inversion in vibrational distributions; both rebound and stripping mechanisms exist in the case of high collision energies.

Inverse Square Law in Spectrally Bounded Quantum Dynamics

The object of the paper is to formulate Quantum (Schrödinger) dynamics of spectrally bounded wavefunction. The Nyquist theorem is used to replace the wavefunction with a discrete series of numbers. Consequently, in this case, Schrödinger dynamics can be formalized as a universal set of ordinary differential Equations, with universal coupling between them, which are related to Euler’s formula. It is shown that the coefficient (m, n) is inversely proportional to the distance between the points n and m. As far as we know, this is the first time that this inverse square law was formulated.

A Topological Transformation of Quantum Dynamics

In this work, we discuss the topological transformation of quantum dynamics by showing the wave dynamics of a quantum particle on different types of topological structures in various dimensions from the fundamental polygons of the corresponding universal covering spaces. This is not the view from different perspectives of an observer who simply uses different coordinate systems to describe the same physical phenomenon but rather possible geometric and topological structures that quantum particles are endowed with when they are identified with differentiable manifolds that are embedded or immersed in Euclidean spaces of higher dimension. We present our discussions in the form of Bohr model in one, two and three dimensions using linear wave equations. In one dimension, the fundamental polygon is an interval and the universal covering space is the straight line and in this case the standing wave on a finite string is transformed into the standing wave on a circle which can be applied into the Bohr model of the hydrogen atom. In two dimensions, the fundamental polygon is a square and the universal covering space is the plane and in this case, the standing wave on the square is transformed into the standing wave on different surfaces that can be formed by gluing opposite sides of the square, which include a 2-sphere, a 2-torus, a Klein bottle and a projective plane. In three dimensions, the fundamental polygon is a cube and the universal covering space is the three-dimensional Euclidean space. It is shown that a 3-torus and the manifold K?× S1?defined as the product of a Klein bottle and a circle can be constructed by gluing opposite faces of a cube. Therefore, in three-dimensions, the standing wave on a cube is transformed into the standing wave on a 3-torus or on the manifold K?× S1. We also suggest that the mathematical degeneracy may play an important role in quantum dynamics and be associated with the concept of wavefunction collapse in quantum mechanics.

Quantum dynamics studies on the non-adiabatic effects of H+LiD reaction

After the Big Bang,chemical reactions of hydrogen with LiH and its isotopic variants played an important role in the late stage of recombination.Moreover,these reactions have attracted the attention of experts in the field of molecular dynamics because of its simple structure.Electronically non-adiabatic effects play a key role in many chemical reactions,while the related studies in LiH2 reactive system and its isotopic variants are not enough,so the microscopic mechanism of this system has not been fully explored.In this work,the microscopic mechanism of H+LiD reaction are performed by comparing both the adiabatic and non-adiabatic results to study the non-adiabatic effects.The reactivity of R1(H+LiD→Li+HD)channel is inhibited,while that of R2(H+LiD→D+LiH)channel is enhanced when the non-adiabatic couplings are considered.For R1 channel,a direct stripping process dominates this channel and the main reaction mechanism is not influenced by the non-adiabatic effects.For R2 channel,at relatively low collision energy,the dominance changes from a rebound process to the complex-forming mechanism when the non-adiabatic effects are considered,whereas the rebound collision approach still dominates the reaction at relatively high collision energy in both calculations.The presented results provide a basis for further detailed study on this importantly astrophysical reaction system.

A Branching Random Walk Method for Many-Body Wigner Quantum Dynamics

A branching random walk algorithm for many-body Wigner equations and its numerical applications for quantum dynamics in phase space are proposed and ana-lyzed in this paper.Using an auxiliary function,the truncated Wigner equation and its adjoint form are cast into integral formulations,which can be then reformulated into renewal-type equations with probabilistic interpretations.We prove that the first mo-ment of a branching random walk is the solution for the adjoint equation.With the help of the additional degree of freedom offered by the auxiliary function,we are able to produce a weighted-particle implementation of the branching random walk.In contrast to existing signed-particle implementations,this weighted-particle one shows a key ca-pacity of variance reduction by increasing the constant auxiliary function and has no time discretization errors.Several canonical numerical experiments on the 2D Gaussian barrier scattering and a 4D Helium-like system validate our theoretical findings,and demonstrate the accuracy,the efficiency,and thus the computability of the proposed weighted-particle Wigner branching random walk algorithm.

Quantum dynamics of an impurity-doped Bose–Einstein condensate system

We study the quantum dynamics of an impurity-doped Bose–Einstein condensate(BEC) system.We show how to generate the macroscopic quantum superposition states(MQSSs) of the BEC by the use of projective measurements on impurity atoms. It is found that the nonclassicality of MQSSs can be manipulated by changing the number of the impurities and their interaction with the BEC. It is shown that the BEC matter-wave field exhibits a collapse and revival phenomenon which reveals the quantum nature of the BEC matter-wave field. We investigate the micro-macro entanglement between the impurities and the BEC, and find enhancement of the micro-macro entanglement induced by the initial quantum coherence of the impurity atoms.

Quantum and quasiclassical dynamics of C(^(3)P)+H_(2)(^(1Σ_(g)^(+)))→H(^(2)S)+CH(^(2)Ⅱ)reaction:Coriolis coupling effects and stereodynamics

The dynamics of C+H_(2)→H+CH reaction is theoretically studied using the quasiclassical trajectory and quantum mechanical wave packet methods.The analysis of reaction probabilities,integral cross sections,and rate coefficients reveal the essential Coriolis coupling effects in the quantum mechanical wave packet calculations.The calculated polarizationdependent differential cross section,P(θ_(r))and P(Φ_(r))show that the j'of product rotational angular momentum is not only aligned along the y axis and the direction of the vector x+z,but also strongly oriented along the positive y axis.

Quantum Dynamics in Continuum for Proton Transport I:Basic Formulation

Proton transport is one of the most important and interesting phenomena in living cells.The present work proposes a multiscale/multiphysics model for the understanding of the molecular mechanism of proton transport in transmembrane proteins.We describe proton dynamics quantum mechanically via a density functional approach while implicitly model other solvent ions as a dielectric continuum to reduce the number of degrees of freedom.The densities of all other ions in the solvent are assumed to obey the Boltzmann distribution.The impact of protein molecular structure and its charge polarization on the proton transport is considered explicitly at the atomic level.We formulate a total free energy functional to put proton kinetic and potential energies as well as electrostatic energy of all ions on an equal footing.The variational principle is employed to derive nonlinear governing equations for the proton transport system.Generalized Poisson-Boltzmann equation and Kohn-Sham equation are obtained from the variational framework.Theoretical formulations for the proton density and proton conductance are constructed based on fundamental principles.The molecular surface of the channel protein is utilized to split the discrete protein domain and the continuum solvent domain,and facilitate the multiscale discrete/continuum/quantum descriptions.A number of mathematical algorithms,including the Dirichlet to Neumann mapping,matched interface and boundary method,Gummel iteration,and Krylov space techniques are utilized to implement the proposed model in a computationally efficient manner.The Gramicidin A(GA)channel is used to demonstrate the performance of the proposed proton transport model and validate the efficiency of proposed mathematical algorithms.The electrostatic characteristics of the GA channel is analyzed with a wide range of model parameters.The proton conductances are studied over a number of applied voltages and reference concentrations.A comparison with experimental data verifies the present model predictions and validates the proposed model.

Numerical Path Integral Approach to Quantum Dynamics and Stationary Quantum States

Applicability of Feynman path integral approach to numerical simulations of quantum dynamics of an electron in real time domain is examined.Coherent quantum dynamics is demonstrated with one dimensional test cases(quantum dot models)and performance of the Trotter kernel as compared with the exact kernels is tested.Also,a novel approach for finding the ground state and other stationary sates is presented.This is based on the incoherent propagation in real time.For both approaches the Monte Carlo grid and sampling are tested and compared with regular grids and sampling.We asses the numerical prerequisites for all of the above.

Quantum correlation dynamics of three non-coupled two-level atoms in different reservoirs

Time evolution dynamics of three non-coupled two-level atoms independently interacting with their reservoirs is solved exactly by considering a damping Lorentzian spectral density.For three atoms initially prepared in Greenberger-Horne-Zeilinger-type state,quantum correlation dynamics in a Markovian reservoir is compared with that in a nonMarkovian reservoir.By increasing detuning quantity in the non-Markovian reservoir,three-atom correlation dynamics measured by negative eigenvalue presents a trapping phenomenon which provides long-time quantum entanglement.Then we compare the correlation dynamics of three atoms with that of two atoms,measured by quantum entanglement and quantum discord for an initial robuster-entangled type state.The result further confirms that quantum discord is indeed different from quantum entanglement in identifying quantum correlation of many bodies.

Combined Effect of Classical Chaos and Quantum Resonance on Entanglement Dynamics

We use linear entropy of an exact quantum state to study the entanglement between internal electronic states and external motional states for a two-level atom held in an amplitude-modulated and tilted optical lattice. Starting from an unentangled initial state associated with the regular ＇island＇ of classical phase space, it is demonstrated that the quantum resonance leads to entanglement generation, the chaotic parameter region results in the increase of the generation speed, and the symmetries of the initial probability distribution determine the final degree of entanglement. The entangled initial states are associated with the classical ＇chaotic sea＇, which do not affect the final entanglement degree for the same initial symmetry. The results may be useful in engineering quantum dynamics for quantum information processing.

Dynamics of Quantum State and Effective Hamiltonian with Vector Differential Form of Motion Method

Effective Hamiltonians in periodically driven systems have received widespread attention for realization of novel quantum phases, non-equilibrium phase transition, and Majorana mode. Recently, the study of effective Hamiltonian using various methods has gained great interest. We consider a vector differential equation of motion to derive the effective Hamiltonian for any periodically driven two-level system, and the dynamics of the spin vector are an evolution under the Bloch sphere. Here, we investigate the properties of this equation and show that a sudden change of the effective Hamiltonian is expected. Furthermore, we present several exact relations, whose expressions are independent of the different starting points. Moreover, we deduce the effective Hamiltonian from the high-frequency limit, which approximately equals the results in previous studies. Our results show that the vector differential equation of motion is not affected by a convergence problem, and thus, can be used to numerically investigate the effective models in any periodic modulating system. Finally, we anticipate that the proposed method can be applied to experimental platforms that require time-periodic modulation, such as ultracold atoms and optical lattices.

Motion-Enhanced Quantum Entanglement in the Dynamics of Excitation Transfer

We investigate the dynamics of entanglement in the excitation transfer through a model consisting of three interacting molecules coupled to environments. It is shown that the entanglement can be further enhanced if the distance between the molecules is oscillating. Our results demonstrate that the motional effect plays a constructive role on quantum entanglement in the dynamics of excitation transfer. This mechanism might provide a useful guideline for designing artificial systems to battle against decoherence.

Preservation of Quantum Coherence for Gaussian-State Dynamics in a Non-Markovian Process

Coherence is a key resource in quantum information science.Exactly understanding and controlling the variation of coherence are vital for implementation in realistic quantum systems.Using P-representation of density matrix,we obtain the analytical solution of the master equation for the classical states in the non-Markovian process and investigate the coherent dynamics of Gaussian states.It is found that quantum coherence can be preserved in such a process if the coupling strength between system and environment exceeds a threshold value.We also discuss the characteristic function of the Gaussian states in the non-Markovian process,which provides an inevitable bridge for the control and operation of quantum coherence.