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.     

Tunneling and quantum localization in chaos‐driven symmetric triple well potential: An approach using quantum theory of motion

For a symmetric triple well potential, driven by the forces associated with the bifurcation diagram of a logistic map, the tunneling and quantum localization are studied using quantum theory of motion and time‐dependent Fourier grid Hamiltonian methods. Detailed analysis reveals that application of only asymmetric or symmetric perturbation results into either quantum localization or over‐barrier transition and no tunneling while application of mixed symmetry perturbation gives either tunneling or over‐barrier transition, depending on temporal nature and initial position of the particle. For bifurcative and chaotic symmetric‐asymmetric perturbation, with truncation of mixed symmetry perturbation, a sudden jump in energy causes a transition from the tunneling phenomenon to the over‐barrier transition. With particle located initially near to either of the minima of the unperturbed well, quantum localization, or over‐barrier transition is observed, depending on types of perturbation used.     

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.     

Massively parallel spin–orbit configuration interaction

We describe a new approach to incorporating quantum effects into chemical reaction rate theory using quantum trajectories. Our development is based on the entangled trajectory molecular dynamics method for simulating quantum processes using trajectory integration and ensemble averaging. By making dynamical approximations similar to those underlying classical transition state theory, quantum corrections are incorporated analytically into the quantum rate expression. We focus on a simple model of quantum decay in a metastable system and consider the deep tunneling limit where the classical rate vanishes and the process is entirely quantum mechanical. We compare our approximate estimate with the well-known WKB tunneling rate and find qualitative agreement.     

Bohmian mechanics with complex action: a new trajectory-based formulation of quantum mechanics

In recent years there has been a resurgence of interest in Bohmian mechanics as a numerical tool because of its local dynamics, which suggest the possibility of significant computational advantages for the simulation of large quantum systems. However, closer inspection of the Bohmian formulation reveals that the nonlocality of quantum mechanics has not disappeared-it has simply been swept under the rug into the quantum force. In this paper we present a new formulation of Bohmian mechanics in which the quantum action, S, is taken to be complex. This leads to a single equation for complex S, and ultimately complex x and p but there is a reward for this complexification-a significantly higher degree of localization. The quantum force in the new approach vanishes for Gaussian wave packet dynamics, and its effect on barrier tunneling processes is orders of magnitude lower than that of the classical force. In fact, the current method is shown to be a rigorous extension of generalized Gaussian wave packet dynamics to give exact quantum mechanics. We demonstrate tunneling probabilities that are in virtually perfect agreement with the exact quantum mechanics down to 10(-7) calculated from strictly localized quantum trajectories that do not communicate with their neighbors. The new formulation may have significant implications for fundamental quantum mechanics, ranging from the interpretation of non-locality to measures of quantum complexity.     

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 evolution speed and its limit in the driven double-well system

We investigate quantum evolution speed in the driven double-well system using the entangled trajectory molecular dynamics method. We emphasize not only the evolution speed of the quantum state but also its limit according to different definitions. The Wasserstein 1-distance is used to quantify the distance between distinguishable quantum states in the phase space, the quantum speed limit based on the geometry has been shown to be the strictest one. The single trajectory's contribution to the quantum speed limit is discussed, which is related to both the time evolution of the trajectory and its position in the total Wigner function. The resonance and chaos strongly enhance the evolution speed and its limit in the driven double-well system. The resonance effect makes a large proportion of representative points pass through the well as a whole, nevertheless, the chaos makes the Wigner function disperse in the phase space.     

ac-Driven quantum decay

We study the enhancement of the quantum decay rate out of a metastable state, via tunneling, in presence of an external sinusoidal force. It is shown that the Floquet picture of quantum mechanics, together with the complex scaling method, provides an adequate methodology to describe the periodically driven decay process in a nonperturbative way. In the limiting cases of extremely slow and fast external forces the numerical results are compared with simple semiclassical estimates. The decay near the fundamental resonance assumes a Lorentzian line shape in agreement with recent experiments on Josephson junctions in the deep quantum regime. For small forces the enhancement grows proportional to the square of the forcing strength and saturates above a threshold value. Additionally our results also exhibit secondary resonances: at higher frequency corresponding roughly to a second harmonic induced by the nonlinear potential shape, and at lower frequency, exactly at the half of the first resonance, revealing a two-photon transition.     

Nuclear spin driven quantum tunneling of magnetization in a new lanthanide single-molecule magnet: bis(phthalocyaninato)holmium anion

The first measurements of magnetization hysteresis loops on a diluted single crystal of [(Pc)2Ho]-.TBA+ (Pc = phthalocyaninato, TBA = tetrabutylammonium) in the subkelvin temperature range are reported. Characteristic staircase-like structure was observed, indicating the occurrence of the quantum tunneling of magnetization (QTM), which is a characteristic feature of SMMs. The quantum process in the new lanthanide SMMs is due to resonant quantum tunneling between entangled states of the electronic and nuclear spin systems, which is an essentially different mechanism from those of the known transition-metal-cluster SMMs. Evidence of the two-body quantum process was also observed for the first time in lanthanide complex systems.     

Very fast tunneling in the early stage of reaction dynamics

The difference between quantum and classical survival probabilities for molecular dissociation dynamics in the time domain, which arises mainly from quantum mechanical tunneling, has interesting characteristics that are not noticed through the counterpart in energy domain. It is shown that the early stage undergoes a fast tunneling, while the later stage is characterized with a long-lasting slow tunneling. The mechanism of this behavior is analyzed in terms of a quasi-semiclassical theory featuring the geometrical distribution of the so-called tunneling points. In particular, the role of dynamical tunneling is discussed as a phenomenon that typifies the time dependence of tunneling dynamics. It is predicted that these tunneling characteristics will be reflected in the isotope effect and should be experimentally observable.     

Tunneling through a fluctuating barrier in the presence of a periodically driving field

The zero and finite temperature tunneling dynamics of a periodically driven particle moving in a bistable potential with a fluctuating barrier is studied. We have focused on the influence of barrier fluctuation and thermal modulation on the tunneling processes in the presence of a driving field. At zero temperature, for a fixed strength of the driving field, both the tunneling probability and rate passes through a well-defined minimum when plotted as a function of fluctuation frequency while it reveals a clear maximum as a function of driving frequency. However, at T > 0 the tunneling probability and rate show two maxima as a function of both fluctuation frequency and driving frequency. In both zero and finite temperature, the tunneling rate constant decreases with increasing fluctuation strength. So, the barrier fluctuation may enhance the stability of a periodically driven system. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Analysis of Hydrogen Tunneling in an Enzyme Active Site using von Neumann Measurements

We build on our earlier quantum wavepacket study of hydrogen transfer in the biological enzyme, soybean lipoxygenase-1, by using von Neumann quantum measurement theory to gain qualitative insights into the transfer event. We treat the enzyme active site as a measurement device which acts on the tunneling hydrogen nucleus via the potential it exerts at each configuration. A series of changing active site geometries during the tunneling process effects a sequential projection of the initial, reactant state onto the final, product state. We study this process using several different kinds of von Neumann measurements and show how a discrete sequence of such measurements not only progressively increases the projection of the hydrogen nuclear wavepacket onto the product side but also favors proton over deuteron transfer. Several qualitative features of the hydrogen tunneling problem found in wavepacket dynamics studies are also recovered here. These include the shift in the "transition state" towards the reactant as a result of nuclear quantization, greater participation of excited states in the case of deuterium, and presence of critical points along the reaction coordinate that facilitate hydrogen and deuterium transfer and coincide with surface crossings. To further "tailor" the dynamics, we construct a perturbation to the sequence of measurements, that is a perturbation to the dynamical sequence of active site geometry evolution, which leads us to insight on the existence of sensitive regions of the reaction profile where subtle changes to the dynamics of the active site can have an effect on the hydrogen and deuterium transfer process.     

Time-dependent probability of quantum tunneling in terms of the quasisemiclassical method

In view of the rapid progress in experiments of the tunneling dynamics in the time domain, we develop a quasisemiclassical method that is aimed at a study of the proton-transfer dynamics in a large system such as tropolone and its interesting derivatives, to which not only full quantum mechanics, but even a standard semiclassical theory is never easy to apply. In our very tractable method for multidimensional systems, the tunneling paths are generated in terms of the generalized classical mechanics, but the quantum phases arising from the action integral, the Maslov index, and the semicalssical amplitude factor as well in the semiclassical kernels are entirely neglected. This approach is called the quasisemiclassical method. One of the technical issues involved in the general semiclassical scheme is how to locate points from which a tunneling path emanates. Hence the studies of such tunneling points and the quasisemiclassical method should be examined collectively. We test several ways of determining the tunneling point, including those already proposed in the literature and a newly proposed one. It is shown numerically that the quasisemiclassical method with an appropriate choice of tunneling points reproduces the full quantum mechanical tunneling probability reasonably well. This case study indicates that the present conventional approach is promising to the study of large systems. The role of tunneling points in the initial process of tunneling is also discussed.     

The generalized transition state method

Current theories of unimolecular reaction rates are based on the transition state method which replaces internal reactant dynamics by an assumption of internal equilibrium. The present work is devoted to the development of generalized transition state method which allows effects such as nonergodicity and non-exponential decay to be accounted for within a simple theoretical framework. The derivation is quantum mechanical and not limited by any weak perturbation assumption. An effective hamiltonian is constructed for the reactant dynamics. The loss of amplitude due to reaction is accounted for by a dissipative term in the hamiltonian which is obtained on a phenomenological basis. The diagonalization of the hamiltonian allows the decay of reactant state to be predicted. The decay information is then used to set up a non-markovian master equation which in turn yields the rate coefficient for the reaction. The accuracy of the method is tested in one-dimensional model calculations in which particular attention is paid to decay by quantum mechanical tunneling through a potential barrier.     

A hybrid hydrodynamic-Liouvillian approach to mixed quantum-classical dynamics: application to tunneling in a double well

The hybrid quantum-classical approach of Burghardt and Parlant [Burghardt, I.; Parlant, G. J. Chem. Phys. 2004, 120, 3055], referred to here as the quantum-classical moment (QCM) approach, is demonstrated for the dynamics of a quantum double well coupled to a classical harmonic coordinate. The approach combines the quantum hydrodynamic and classical Liouvillian representations by the construction of a particular type of moments (that is, partial hydrodynamic moments) whose evolution is determined by a hierarchy of coupled equations. For pure states, which are at the center of the present study, this hierarchy terminates at the first order. In the Lagrangian picture, the deterministic trajectories result in dynamics which is Hamiltonian in the classical subspace, while the projection onto the quantum subspace evolves under a generalized hydrodynamic force. Importantly, this force also depends upon the classical (Q, P) variables. The present application demonstrates the tunneling dynamics in both the Eulerian and Lagrangian representations. The method is exact if the classical subspace is harmonic, as is the case for the systems studied here.     

A rational approach to the modulation of the dynamics of the magnetisation in a dysprosium-nitronyl-nitroxide radical complex

A control of the dynamics of the magnetisation is chemically achieved in a ring-like Dy-radical based molecule, allowing the estimation of the quantum tunneling frequency with a (4)He-cooled susceptometer.     

The use of magnetic dilution to elucidate the slow magnetic relaxation effects of a Dy2 single-molecule magnet

The magnetic dilution method was employed in order to elucidate the origin of the slow relaxation of the magnetization in a Dy(2) single-molecule magnet (SMM). The doping effect was studied using SQUID and micro-SQUID measurements on a Dy(2) SMM diluted in a diamagnetic Y(2) matrix. The quantum tunneling of the magnetization that can occur was suppressed by applying optimum dc fields. The dominant single-ion relaxation was found to be entangled with the neighboring Dy(III) ion relaxation within the molecule, greatly influencing the quantum tunneling of the magnetization in this complex.     

Combined QM/MM and path integral simulations of kinetic isotope effects in the proton transfer reaction between nitroethane and acetate ion in water

An integrated Feynman path integral-free energy perturbation and umbrella sampling (PI-FEP/UM) method has been used to investigate the kinetic isotope effects (KIEs) in the proton transfer reaction between nitroethane and acetate ion in water. In the present study, both nuclear and electronic quantum effects are explicitly treated for the reacting system. The nuclear quantum effects are represented by bisection sampling centroid path integral simulations, while the potential energy surface is described by a combined quantum mechanical and molecular mechanical (QM/MM) potential. The accuracy essential for computing KIEs is achieved by a FEP technique that transforms the mass of a light isotope into a heavy one, which is equivalent to the perturbation of the coordinates for the path integral quasiparticle in the bisection sampling scheme. The PI-FEP/UM method is applied to the proton abstraction of nitroethane by acetate ion in water through molecular dynamics simulations. The rule of the geometric mean and the Swain-Schaad exponents for various isotopic substitutions at the primary and secondary sites have been examined. The computed total deuterium KIEs are in accord with experiments. It is found that the mixed isotopic Swain-Schaad exponents are very close to the semiclassical limits, suggesting that tunneling effects do not significantly affect this property for the reaction between nitroethane and acetate ion in aqueous solution.     

DOIT: a program to calculate thermal rate constants and mode‐specific tunneling splittings directly from quantum‐chemical calculations

In this contribution we discuss computational aspects of a recently introduced method for the calculation of proton tunneling rate constants, and tunneling splittings, which has been applied to molecules and complexes, and should apply equally well to bulk materials. The method is based on instanton theory, adapted so as to permit a direct link to the output of quantum‐chemical codes. It is implemented in the DOIT (dynamics of instanton tunneling) code, which calculates temperature‐dependent tunneling rate constants and mode‐specific tunneling splittings. As input, it uses the structure, energy, and vibrational force field of the stationary configurations along the reaction coordinate, computed by conventional quantum‐chemical programs. The method avoids the difficult problem of calculating the exact least‐action trajectory, known as the instanton path, and instead focusses on the corresponding instanton action, because it governs the dynamic properties. To approximate this action for a multidimensional system, the program starts from the one‐dimensional instanton action along the reaction coordinate, which can be obtained without difficulty. It then applies correction terms for the coupling to the other vibrational degrees of freedom, which are treated as harmonic oscillators (transverse normal modes). The couplings are assumed linear in these modes. Depending on the frequency and the character of the transverse modes, they may either decrease or increase the action, i.e., help or hinder the transfer. A number of tests have shown that the program is at least as accurate as alternative programs based on transition‐state theory with tunneling corrections, and is also much less demanding in computer time, thus allowing application to much larger systems. An outline of the instanton formalism is presented, some new developments are introduced, and special attention is paid to the connection with quantum‐chemical codes. Possible sources of error are investigated. To show the program in action, calculations are presented of tunneling rates and splittings associated with triple proton transfer in the chiral water trimer. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 787–801, 2001     

Perturbative treatment of anharmonic vibrational effects on bond distances: An extended langevin dynamics method

In this work, we first review the perturbative treatment of an oscillator with cubic anharmonicity. It is shown that there is a quantum‐classical correspondence in terms of mean displacement, mean‐squared displacement, and the corresponding variance in the first‐order perturbation theory, provided that the amplitude of the classical oscillator is fixed at the zeroth‐order energy of quantum mechanics . This correspondence condition is realized by proposing the extended Langevin dynamics (XLD), where the key is to construct a proper driving force. It is assumed that the driving force adopts a simple harmonic form with its amplitude chosen according to , while the driving frequency chosen as the harmonic frequency. The latter can be improved by using the natural frequency of the system in response to the potential if its anharmonicity is strong. By comparing to the accurate numeric results from discrete variable representation calculations for a set of diatomic species, it is shown that the present method is able to capture the large part of anharmonicity, being competitive with the wave function‐based vibrational second‐order perturbation theory, for the whole frequency range from ～4400 cm^?1 (H₂) to ～160 cm^?1 (Na₂). XLD shows a substantial improvement over the classical molecular dynamics which ceases to work for hard mode when zero‐point energy effects are significant. © 2013 Wiley Periodicals, Inc.