Activated dissociation of H_(2) on the Cu(001)surface:The role of quantum tunneling

The activation and dissociation of hydrogen molecules(H_(2))on the Cu(001)surface are studied theoretically.Using first-principles calculations,the activation barrier for the dissociation of H_(2) on Cu(001)is determined to be~0.59 eV in height.It is found that the electron transfer from the copper substrate to H_(2) plays a key role in the activation and breaking of the H–H bond,and the formation of the Cu–H bonds.Two stationary states are identified at around the critical height of bond breaking,corresponding to the molecular and the dissociative states,respectively.Using the transfer matrix method,we also investigate the role of quantum tunneling in the dissociation process along the minimum energy pathway(MEP),which is found to be significant at or below room temperature.At a given temperature,the tunneling contributions due to the translational and the vibrational motions of H_(2) are quantified for the dissociation process.Within a wide range of temperature,the effects of quantum tunneling on the effective barriers of dissociation and the rate constants are observed.The deduced energetic parameters associated with the thermal equilibrium and non-equilibrium(molecular beam)conditions are comparable to experimental data.In the low-temperature region,the crossover from classical to quantum regime is identified.

Quantum tunneling in the surface diffusion of single hydrogen atoms on Cu(001)

The adsorption and diffusion of hydrogen atoms on Cu(001)are studied using first-principles calculations.By taking into account the contribution of zero-point energy(ZPE),the originally identical barriers are shown to be different for H and D,which are respectively calculated to be~158 me V and~139 me V in height.Using the transfer matrix method(TMM),we are able to calculate the accurate probability of transmission across the barriers.The crucial role of quantum tunneling is clearly demonstrated at low-temperature region.By introducing a temperature-dependent attempting frequency prefactor,the rate constants and diffusion coefficients are calculated.The results are in agreement with the experimental measurements at temperatures from~50 K to 80 K.

Concrete quantum tunneling spectrum of Schwarzschild black holes

In this paper,a canonical ensemble model for black hole quantum tunneling radiation is introduced.We find that the probability distribution function is the same as the emission rate of a spherical shell in the Parikh-Wilczek tunneling framework.With this model,the probability distribution function corresponding to the emission shell system is calculated.Therefore,the concrete quantum tunneling spectrum of the Schwarzschild black hole is obtained.

Thermodynamics in a quantum corrected Reissner-Nordstr?m-AdS black hole and its GUP-corrections

We calculate the thermodynamic quantities in the quantum corrected Reissner-Nordstr?m-AdS(RN-AdS)black hole,and examine their quantum corrections.By analyzing the mass and heat capacity,we give the critical state and the remnant state,respectively,and discuss their consistency.Then,we investigate the quantum tunneling from the event horizon of massless scalar particle by using the null geodesic method,and charged massive boson W^(±)and fermions by using the Hamilton-Jacob method.It is shown that the same Hawking temperature can be obtained from these tunneling processes of different particles and methods.Next,by using the generalized uncertainty principle(GUP),we study the quantum corrections to the tunneling and the temperature.Then the logarithmic correction to the black hole entropy is obtained.

Quantum tunneling of ultracold atoms in optical traps

We review our theoretical advances in quantum tunneling of BoseEinstein condensates in optical traps and in microcavities. By employing a real physical system, the frequencies of the pseudo Goldstone modes in different phases between two optical traps are studied respectivdy, which are tile crucial feature of the non-Abelian Joseptmon effect. When the optical lattices are under gravity, we investigate the quantum tummling in the ＂Wannier-Stark localization＂ regime and ＂Lan（lau Zener tunneling＂ regime. We finally get the total decay rate and the rate is valid over the entire range of temperatures. At high temperatures, we show how the decay rate reduces to the appropriate results for the classical thermal activation. At hltermediate temperatures, the results of tile total decay rate are consistent with the thermally assisted tunneling. At low temperatures, we obtain the pure quantmn tunneling ultimately. And we study the alternating-current and direct-current （ac and de） photonic 3osephson effects in two weakly linked microcavities containing ultracold two-level atones, which allows for direct observation of the effects. This enables new investigations of the effect of maw-body physics in strongly coupled atom-cavity systems and provides a strategy for constructing novel interference devices of coherent photons. In addition, we propose the experimental protocols to observe these quantmn tunneling of Bose- Einstein condensates.

Quantum Mechanical Tunneling of Dislocations: Quantization and Depinning from Peierls Barrier

Theories of Mott and Weertmann pertaining to quantum mechanical tunneling of dislocations from Peierls barrier in cubic crystals are revisited. Their mathematical calculations about logarithmic creep rate and lattice vibrations as a manifestation of Debye temperature for quantized thermal energy are found correct but they can not ascertain to choose the mass of phonon or “quanta” of lattice vibrations. The quantum mechanical yielding in metals at relatively low temperatures, where Debye temperatures operate, is resolved and the mathematical formulas are presented. The crystal plasticity is studied with stress relaxation curves instead of logarithmic creep rate. With creep rate formulas of Mott and Weertmann, a new formula based on logarithmic profile of stress relaxation curves is proposed which suggests simultaneous quantization of dislocations with their stress, i.e., and depinning of dislocations, i.e., , where is quantum action, σ is the stress, N is the number of dislocations, A is the area and t is the time. The two different interpretations of “quantum length of Peierls barrier”, one based on curvature of space, i.e., yields quantization of Burgers vector and the other based on the curvature of time, i.e., yields depinning of dislocations from Peierls barrier in cubic crystals, are presented. , i.e., the unitary operator on shear modulus yields the variations in the curvature of time due to which simultaneous quantization, and depinning of dislocations occur from Peierls barrier in cubic crystals.

Analytical Solution to the Density-Gradient Equation for MOS Quantum Tunneling

Engineering-oriented simulations of quantum mechanical tunneling are often based on density-gradient （DG） theory. This paper presents an analytical solution to the DG equation for quantum tunneling through an ultra-thin oxide in a MOS capacitor with an n＋ poly-silicon gate obtained using the method of matched asymptotic expansions. Tunneling boundary conditions extend the approximation into the entire region of the poty-silicon gate, oxide barrier, and substrate. An analytical solution in the form of an asymptotic series is obtained in each region by treating each part of the domain as a separate singular perturbation problem. The solutions are then combined through ＇matching＇ to obtain an approximate solution for the whole domain. Analytical formulae are given for the electrostatic potential and the electron density profiles. The results capture the features of the quantum effects which are quite different from classical physics pre- dictions. The analytical results compare well with exact numerical solutions over a broad range of voltages and different oxide thicknesses. The analytical results predict the enhancement of the quantum tunneling effect as the oxide thickness is reduced.

Shot noise of the spin inelastic tunneling through a quantum dot with single molecule-magnet

We have studied the quantum fluctuations of inelastic spin-electron scattering in quantum dot with an embedded biaxial single molecule-magnet and particularly investigated the zero-frequency shot noise and Fano factor in different magnetic fields. It is found that the shot noise and Fano factor exhibit a stepwise behaviour as bias increases in the presence of interaction between the electron and molecule-magnet for a weak magnetic field. As magnetic field becomes strong, a dip is displayed in the shot-noise-bias curve due to the suppression of inelastic shot noise caused by the quantum tunneling of magnetisation. Because of the spontaneous inelastic tunneling at zero bias, a small shot noise occurs, which results in the case of Fano factor F ≥ 1. Moreover, our results show that the sweeping speed can also influence the shot noise and Fano factor obviously.

Macroscopic Quantum Tunneling and Coherence of the Néel Vector in Small Antiferromagnets

The tunneling behavior of the Néel vector out of metastable easy directions or between degenerate easy directions is studied for a small single\|domain antiferromagnetic particle at low temperature. The quantum tunneling rates for these processes are evaluated for two examples of macroscopic quantum tunneling and one example of macroscopic quantum coherence. The calculations are performed by using the two sublattice model and the instanton method in the spin coherent state path integral. Quantum interference or the spin parity effect is also discussed for each case.

Lorentz violation, quantum tunneling, and information conservation

In this paper, by introducing the Lorentz-invariance-violation(LIV) class of dispersion relations(DR)suppressed by the second power(E/EQG)2, we investigated the effect of the LIV on the Hawking radiation of a charged Dirac particle based on tunneling from a Reissner-Nordstrom(RN) black hole. It was determined that the LIV speeds up black hole evaporation. As a result, the induced Hawking temperature was very sensitive to changes in the energy of the radiation particle. However, at the same energy level, it was insensitive to changes in the charge of the radiation particle. This is phenomenological evidence in support of the LIV-DR as a candidate for describing the effect of quantum gravity. Moreover, when the effect of the LIV was included, we discovered that the statistical correlations with the Planck-scale corrections between successive emissions could leak out information via radiation.We also determined that black hole radiation via tunneling is an entropy conservation process, and no information loss occurred during radiation, where the interpretation of the entropy of a black hole is addressed. Finally, we concluded that black hole evaporation is still a unitary process in the context of quantum gravity.

Multidimensional Quantum Tunneling:Direct Instanton Calculation with Application to Polyatomic Molecules

Multidimensional tunneling appears in many problems at nano scale.The high dimensionality of the potential energy surface(e.g.many degrees of freedom)poses a great challenge in both theoretical and numerical description of tunneling.Numerical simulation based on Schrodinger equation is often prohibitively expensive.We propose an accurate,efficient,robust and easy-to-implement numerical method to calculate the ground state tunneling splitting based on imaginary-time path integral(‘instanton’formulation).The method is genuinely multi-dimensional and free from any additional ad hoc assumptions on potential energy surface.It enables us to calculate the effects of all coupling modes on the tunneling degree of freedom without loss.We also review in this paper some theoretical background and survey some recent work from other groups in calculating multidimensional quantum tunneling effects in chemical reactions.

Optimal Performance Analysis of a Three-Terminal Thermoelectric Refrigerator with Ideal Tunneling Quantum Dots

The model of a three-terminal thermoelectric refrigerator with ideal tunneling quantum dots is established. It consists of a cavity connected to two quantum dots embedded between two electron reservoirs at different temperatures and chemical potentials. According to the Landauer formula the expressions for the heat current, the cooling rate and the coefficient of performance （COP） are derived analytically. The performance characteristic curves of the cooling rate versus the coefficient of performance are plotted with numerical calculation. The optimal regions of the cooling rate and the COP are determined. Moreover, we optimize the cooling rate and the COP with respect to the position of energy level of the right quantum dot, respectively. The influence of the width of energy level and the temperature ratio on performance of the three-terminal thermoelectric refrigerator is analyzed. Lastly, when the width of energy level is small enough, the optimal performance of the refrigerator is discussed in detail.

Quantum Coupling Effect between Quantum Dot and Quantum Well in a Resonant Tunneling Photon-Number-Resolving Detector

Excited states of lnAs quantum dots （QDs） can be energetically coupled with the confined level of OaAs quantum wells （QWs） in a thin-barrier resonant tunneling diode （RTD）. Single charge variation in the coupled QD can effectively switch on/off the resonant tunneling current passing through RTD, not only for emcient single-photon detection but also for photon-number-resolving detection. We present the study of the Q,D-QW coupling effect in the quantum dot coupled resonant tunneling diode （QD-cRTD） and figure out important factors for further improving the detector performance.

Controlling the Goos-H?nchen Shift via Incoherent Pumping Field and Electron Tunneling in the Triple Coupled InGaAs/GaAs Quantum Dots

We study the controlling of the Goos-Hanchen （GH） shifts in reflected and transmitted light beams in the triple coupled InGaAs/GaAs quantum dot （QD） nanostructures with electron tunneling and incoherent pumping field. It is shown that the lateral shift can become either large negative or large positive, which can be controlled by the electron tunneling and the rate of incoherent pump field in different incident angles. It is also demonstrated that the properties of the OH shifts are strongly dependent on the probe absorption beam of the intracavity medium due to the switching from superluminal light propagation to subluminal behavior or vice versa. Our suggested system can be considered as a new theoretical method for developing a new nano-optoelectronic sensor.

Left-Handedness with Three Zero-Absorption Windows Tuned by the Incoherent Pumping Field and Inter-Dot Tunnelings in a GaAs/AlGaAs Triple Quantum Dots System

Left-handedness with three zero-absorption windows is achieved in a triple-quantum-dot system. With the typ- ical parameters of a GaAs/AlGaAs heterostructure, the simultaneous negative relative electric permittivity and magnetic permeability are obtained by the adjustable incoherent pumping field and two inter-dot tunnelings. Furthermore, three zero-absorption windows in the left-handedness frequency bands are observed. The left- handedness with zero-absorption in the solid state heterostrueture may solve the challenges not only in the left-handed materials achieved by the photonic resonant scheme but also in the application of negative refractive materials with a large amount of absorption.

Tunneling effect in cavity-resonator-coupled arrays

The quantum tunneling effect （QTE） in a cavity-resonator-coupled （CRC） array was analytically and numerically investigated. The underlying mechanism was interpreted by treating electromagnetic waves as photons, and then was generalized to acoustic waves and matter waves. It is indicated that for the three kinds of waves, the QTE can be excited by cavity resonance in a CRC array, resulting in sub-wavelength transparency through the narrow splits between cavities. This opens up opportunities for designing new types of crystals based on CRC arrays, which may find potential applications such as quantum devices, micro-optic transmission, and acoustic manipulation.

Dephasing of quantum tunnelling in molecular nanomagnets

Dephasing mechanism of quantum tunnelling in molecular magnets has been studied by means of the spin-coherentstate path integral in a mean field approximation. It is found that the fluctuating uncompensated transverse field from the dipolar-dipolar interaction between molecular magnets contributes a random phase to the quantum interference phase. The resulting transition rate is determined by the average tunnel splitting over the random phase. Such a dephasing process leads to the suppression of quenching due to the quantum phase interference, and to the steps due to odd resonances in hysteresis loop survived, which is in good agreement with experimental observations in molecular nanomagnets Fes and Mn12.

Simplified modeling of frequency behavior in photonic crystal vertical cavity surface emitting laser with tunnel injection quantum dot in active region

In this work, the characteristics of the photonic crystal tunneling injection quantum dot vertical cavity surface emitting lasers（Ph C-TIQD-VCSEL） are studied through analyzing a modified modulation transfer function. The function is based on the rate equations describing the carrier dynamics at different energy levels of dot and injector well. Although the frequency modulation response component associated with carrier dynamics in wetting layer（WL） and at excited state（ES） levels of dots limits the total bandwidth in conventional QD-VCSEL, our study shows that it can be compensated for by electron tunneling from the injector well into the dot in TIQD structure. Carrier back tunneling time is one of the most important parameters, and by increment of that, the bias current dependence of the total bandwidth will be insignificant. It is proved that at high bias current, the limitation of the WL-ES level plays an important role in reducing the total bandwidth and results in rollovers on 3-d B bandwidth-I curves. In such a way, for smaller air hole diameter of photonic crystal, the effect of this reduction is stronger.

Concerted versus stepwise mechanisms of cyclic proton transfer:Experiments, simulations, and current challenges

Proton transfer(PT) is a process of fundamental importance in hydrogen(H)-bonded systems. At cryogenic or moderate temperatures, pronounced quantum tunneling may happen due to the light mass of H. Single PT processes have been extensively studied. However, for PT involving multiple protons, our understanding remains in its infancy stage due to the complicated interplay between the high-dimensional nature of the process and the quantum nature of tunneling. Cyclic H-bonded systems are typical examples of this, where PT can happen separately via a “stepwise” mechanism or collectively via a “concerted” mechanism. In the first scenario, some protons hop first, typically resulting in metastable intermediate states(ISs) and the reaction pathway passes through multiple transition states. Whilst in the concerted mechanism, all protons move simultaneously, resulting in only one barrier along the path. Here, we review previous experimental and theoretical studies probing quantum tunneling in several representative systems for cyclic PT, with more focus on recent theoretical findings with path-integral based methods. For gas-phase porphyrin and porphycene, as well as porphycene on a metal surface, theoretical predictions are consistent with experimental observations, and enhance our understanding of the processes. Yet, discrepancies in the PT kinetic isotope effects between experiment and theory appear in two systems,most noticeably in water tetramer adsorbed on NaCl(001) surface, and also hinted in porphycene adsorbed on Ag(110)surface. In ice Ih, controversy surrounding concerted PT remains even between experiments. Despite of the recent progress in both theoretical methods and experimental techniques, multiple PT processes in cyclic H-bonded systems remain to be mysterious.

Quantum hydrogen tunneling promoting halogen-atom and group transfer chemistry

A quantum-hydrogen-tunneling-controlled halogen-atom and group transfer strategy has been successfully developed to generate carbon radicals by using the substituted cyclohexadiene as the abstractor under mild photochemical conditions,in which alkyl and aryl halides as well as numerous alcohol and thiol analogues can be activated.Mechanism investigation unveiled that this process is inhibited from thermodynamic and kinetic effects but is rendered successful through quantum tunneling.