Entangled trajectory molecular dynamics in multidimensional systems: two-dimensional quantum tunneling through the Eckart barrier

In this paper, we extend the entangled trajectory molecular dynamics (ETMD) method to multidimensional systems. The integrodifferential form of the evolution equation for the Wigner function is employed, allowing general potentials not represented as a polynomial to be treated. As the example, the method is applied to a two-dimensional model of scattering from an Eckart barrier. The results of ETMD are in good agreement with quantum hydrodynamics and exact quantum simulations. By comparing the quantum and classical trajectory in phase space, the quantum tunneling phenomenon is interpreted vividly.     

Quantum tunneling effect in entanglement dynamics

Quantum tunneling effect in entanglement dynamics between two coupled particles with separable Gaussian initial state is investigated using entangled trajectory molecular dynamics method in terms of the reduced‐density linear entropy. It has been presented through showing distinguish contribution of single trajectory to linear entropy between classical trajectory and entangled trajectory with same initial state. We find that quantum tunneling effect makes single trajectory's contribution remarkably decrease under quantum dynamics compared to classical dynamics. The nonlocality of quantum entanglement is presented, and the energy transfer between two coupled particles through quantum correlations and classical ones is also discussed in the end. © 2015 Wiley Periodicals, Inc.     

Quantum tunneling in a periodically driven double well system: Entangled trajectory molecular dynamics method

We study a wavepacket tunneling in one‐dimensional periodically driven double‐well system using entangled trajectory molecular dynamics method. The tunneling dynamics dependents on the amplitude and frequency of the driven force are present. Both resonant and nonresonant tunneling process are enhanced by the driven force when the system is chaotic under classical dynamics. We give entangled trajectory in phase space compared to corresponding classical trajectory with same initial state to visually show quantum tunneling process. The average values of quantum tunneling probability after long time evolution have been shown in the parameter spaces, the effect of resonance and chaos on the tunneling dynamics are present. The relation between chaos and the uncertainly product is discussed in the end. © 2016 Wiley Periodicals, Inc.     

Quantum conditions on dynamics and control in open systems

Quantum conditions on the control of dynamics of a system coupled to an environment are obtained. Specifically, consider a system initially in a system subspace H(0) of dimensionality M(0), which evolves to populate system subspaces H(1), H(2) of dimensionalities M(1), M(2). Then, there always exists an initial state in H(0) that does not evolve into H(2) if M(0)>dM(2), where 2相似文献   

Quantum wave packet ab initio molecular dynamics: an approach to study quantum dynamics in large systems

A methodology to efficiently conduct simultaneous dynamics of electrons and nuclei is presented. The approach involves quantum wave packet dynamics using an accurate banded, sparse and Toeplitz representation for the discrete free propagator, in conjunction with ab initio molecular dynamics treatment of the electronic and classical nuclear degree of freedom. The latter may be achieved either by using atom-centered density-matrix propagation or by using Born-Oppenheimer dynamics. The two components of the methodology, namely, quantum dynamics and ab initio molecular dynamics, are harnessed together using a time-dependent self-consistent field-like coupling procedure. The quantum wave packet dynamics is made computationally robust by using adaptive grids to achieve optimized sampling. One notable feature of the approach is that important quantum dynamical effects including zero-point effects, tunneling, as well as over-barrier reflections are treated accurately. The electronic degrees of freedom are simultaneously handled at accurate levels of density functional theory, including hybrid or gradient corrected approximations. Benchmark calculations are provided for proton transfer systems and the dynamics results are compared with exact calculations to determine the accuracy of the approach.     

Quantum wavepacket ab initio molecular dynamics for extended systems

In this paper, we introduce a symmetry-adapted quantum nuclear propagation technique that utilizes distributed approximating functionals for quantum wavepacket dynamics in extended condensed-phase systems. The approach is developed with a goal for implementation in quantum-classical methods such as the recently developed quantum wavepacket ab intio molecular dynamics (QWAIMD) to facilitate the study of extended systems. The method has been numerically benchmarked for extended electronic systems as well as protonic conducting systems that benefit from quantum nuclear treatment. Vibrational properties are computed for the case of the protonic systems through use of a novel velocity-flux correlation function. The treatment is found to be numerically accurate and efficient.     

Quantum trajectories in complex phase space: multidimensional barrier transmission

The quantum Hamilton-Jacobi equation for the action function is approximately solved by propagating individual Lagrangian quantum trajectories in complex-valued phase space. Equations of motion for these trajectories are derived through use of the derivative propagation method (DPM), which leads to a hierarchy of coupled differential equations for the action function and its spatial derivatives along each trajectory. In this study, complex-valued classical trajectories (second order DPM), along which is transported quantum phase information, are used to study low energy barrier transmission for a model two-dimensional system involving either an Eckart or Gaussian barrier along the reaction coordinate coupled to a harmonic oscillator. The arrival time for trajectories to reach the transmitted (product) region is studied. Trajectories launched from an "equal arrival time surface," defined as an isochrone, all reach the real-valued subspace in the transmitted region at the same time. The Rutherford-type diffraction of trajectories around poles in the complex extended Eckart potential energy surface is described. For thin barriers, these poles are close to the real axis and present problems for computing the transmitted density. In contrast, for the Gaussian barrier or the thick Eckart barrier where the poles are further from the real axis, smooth transmitted densities are obtained. Results obtained using higher-order quantum trajectories (third order DPM) are described for both thick and thin barriers, and some issues that arise for thin barriers are examined.     

Electron tunneling dynamics in anharmonic bath

Tunneling transition probability for a particle interacting with an anharmonic bath is found in a time-dependent Hartree approximation. The general expression is presented in terms of medium Keldysh functions that are assumed to be known. Furthermore, the transition probability is calculated in the noninteracting-blip approximation where the rate constant does not exhibit an activation dependence at high temperatures. The reorganization energy E(r) and the renormalized reaction heat epsilon are expressed in terms of the correlation matrix for a solvent and internal modes in both quantum and classical regimes. It is shown that E(r) and epsilon are temperature dependent.     

Quantum mechanical tunneling in synaptic and ephaptic transmission

Quantum mechanical tunneling theory is applied to the problem of synaptic vesicle release and to the problem of electric transmission at the ephaptic junction. In the synapse the tunneling produces conformational changes in macromolecules to open and close vesicle macrogates. Quantum mechanical tunneling as a basis for charge transfer and physical release of vesicles at junction membranes provides a unified concept of ephaptic and synaptic transmission. Details of this model are in agreement with experimental data for miniature endplate potential frequency and delay effects as a function of polarization, osmotic pressure, and temperature. The theory accounts for anatomical specializations at the synaptic cleft and the narrow junction observed for the ephapse.     

Theoretical description of a new analytical technique: comprehensive online multidimensional fast Fourier transform separations

Comprehensive multidimensional separations are today dominated by systems that are fundamentally limited to highly asymmetrical online separations sacrificing separation space, or to lengthy, time consuming offline separations. With the exception of pulse-modulated methods, separations have thus been limited to two dimensions. It is proposed that some of the limitations and shortcomings of these methods may be ameliorated or overcome by employing multi-dimensional detection whereby each analyte is effectively labelled in the frequency domain by a series of pulsed-injections, and a symmetrical, comprehensive online analysis performed with the resulting signal processed by sequential Fourier analysis. A semi-empirical computer model of this system was developed and its feasibility positively demonstrated in simulations of high-efficiency separations in two dimensions. Separations of higher dimensionality were shown to be possible but involved signal-processing challenges beyond the present work. By eliminating wrap-around effects and enabling the separation of physically unseparated peaks, the technique facilitates significant improvements in peak capacity per unit of analysis time as well as greatly improved signal to noise ratios. Because these comprehensive online multidimensional Fourier transform separations depend heavily upon the practical lifetime of imposed injection pulses, it is envisaged that this method will leverage emerging high-efficiency micro- and nanoscale separations technologies.     

Quantum tunneling process for double well potential

Quantum tunneling effects of Gaussian wave packet in one‐ and two‐dimensional double well potentials are investigated using quantum Liouville equation for time evolution of Wigner distribution in phase space. It is shown that a trajectory‐based solution of this problem can be constructed by the entangled trajectory ensemble simulating the evolving quantum state. Quantum effects arise in this approach as a breakdown of the statistical independence of the trajectory ensemble. © 2014 Wiley Periodicals, Inc.     

Quantum molecular dynamics

Electron or ion dynamics are treated using spin‐dependent quantum trajectories. These trajectories are inferred from the Dirac current, which contributes Schroedinger's current and additional spin‐dependent terms, all of which are of order c⁰ in the nonrelativistic regime of particle velocity, where c is the speed of light. The many‐body problem is treated precisely as in classical dynamics. Each electron or ion has its own equation of motion, which is the time‐dependent Dirac or the time‐dependent Schroedinger equation in the relativistic or nonrelativistic regime of particle velocity, respectively. As an example the theory is applied to the electronic structure of the helium atom, in which two electrons with opposite spin states are shown to correlate such that their quantum trajectories keep them on average on opposite sides of the nucleus. As the theory is time dependent, excited states are also generated. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Quantum tunneling in the midrange vibrational fundamentals of tropolone

The Fourier transform infrared spectrum of tropolone(OH) vapor in the 1175-1700 cm(-1) region is reported at 0.0025 and 0.10 cm(-1) spectral resolutions. The 12 vibrational fundamentals in this region of rapidly rising vibrational state density are dominated by mixtures of the CC, CO, CCH, and COH internal coordinates. Estimates based on the measurement of sharp Q branch peaks are reported for 11 of the spectral doublet component separations DS(v) = |Delta(v) +/- Delta(0)|. Delta(0) = 0.974 cm(-1) is the known zero-point splitting, and three a(1) modes show tunneling splittings Delta(v) approximately Delta(0), four b(2) modes show splittings Delta(v) approximately 0.90Delta(0), and the remaining four modes show splittings Delta(v) falling 5-14% from Delta(0.) Significantly, the splitting for the nominal COH bending mode nu(8) (a(1)) is small, that is, 10% from Delta(0). Many of the vibrational excited states demonstrate strong anharmonic behavior, but there are only mild perturbations on the tautomerization mechanism driving Delta(0). The data suggest, especially for the higher frequency a(1) fundamentals, the onset of selective intramolecular vibrational energy redistribution processes that are fast on the time scale of the tautomerization process. These appear to delocalize and smooth out the topographical modifications of the zero-point potential energy surface that are anticipated to follow absorption of the nu(v) photon. Further, the spectra show the propensity for the Delta(v) splittings of b(2) and other complex vibrations to be damped relative to Delta(0).     

One-dimensional description of multidimensional electron transfer reactions in condensed phase

We derive a one-dimensional energy diffusion equation for describing the dynamics of multidimensional electron transfer reactions in condensed phase, which is conceptually simpler and computationally more economic than the conventional approaches. We also obtain an analytical expression for the rate of electron transfer reactions for a general one-dimensional effective potential as well as an energy dependent diffusitivity. As an illustrative example, we consider application to electron transfer in a contact ion pair system modeled through harmonic potentials consisting of two slow classical modes and a high frequency vibrational mode for which the numerical results calculated using the proposed one-dimensional approach are shown to be in good agreement with experimental results. The energy diffusion equation and the rate expression for electron transfer obtained from the present theory, therefore, open up the possibility of describing the dynamics of electron transfer in complex systems, through a simpler approach.