Tunneling Transitions Research Articles

Study on Large Deformation Characteristics and Secondary Lining Supporting Time of Tunnels in Carbonaceous Schist Stratum under High Geo-Stress

The deformation characteristics and the timing for secondary lining support in high geo-stress soft rock tunnels have drawn significant attention. In carbonaceous shale formations, tunnel construction deformations are very pronounced under construction disturbances due to the development of joints, dense fractures, and poor interlayer bonding. With the Xishuangbanna tunnel as our research backdrop, this study meticulously analyzed the deformation patterns and characteristics inherent to high geo-stress tunnels constructed within carbonaceous schist formations. Employing a comprehensive approach involving full displacement analysis and on-site construction mechanics testing, we utilized the displacement release rate and structural safety factors as key indicators to determine the secondary lining supporting time. Employing this innovative approach, we successfully identified the ideal junctures for implementing secondary lining support in tunnels excavated through high geo-stress carbonaceous schist. The research findings indicate that the primary damage modes in high geo-stress carbonaceous schist tunnels are initial support failure and extensive early support deformation. These vulnerabilities are primarily attributed to weak and fragmented strata, elevated ground stress levels, and inadequate support strength. During the early stages of tunnel construction, substantial deformations are observed, exhibiting high rates of change. Horizontal convergence, notably, significantly surpasses the settlement at the tunnel’s crown. When employing the three-bench method for construction, the deformation occurring before the excavation of the middle bench contributes the most to the total deformation monitored, whereas the deformation generated after the excavation of the inverted arch constitutes a minor proportion. The tunnel’s crown and invert experience tension while the secondary lining undergoes compression. The internal forces are most significant at the tunnel’s hance and knee, with the left tunnel knee being the weakest section of the secondary lining. The findings of our study are poised to guide the design and execution of tunnels constructed within high geo-stress carbonaceous schist formations.

Electroluminescence from Er-doped GeO2 nanofilms fabricated by atomic layer deposition on silicon: Effect of annealing temperature on film properties

Er-doped GeO2 (GeO2:Er) nanofilms are fabricated by atomic layer deposition on silicon, from which the 1530 nm electroluminescence (EL) is achieved. The GeO2:Er nanofilms maintain the amorphous structure after annealing at 600–1000 °C, while the annealing above 800 °C results in the loss of Ge due to the volatile GeOx (x < 2) species. These GeO2:Er nanofilms could withstand the wet lithography process and the prototype devices could operate under the constant current. The 650 °C annealed GeO2:Er devices manifest the threshold of ∼40 V and 10−7 A, while the maximum injection current is 0.28 A/cm2. The EL power density from the device doped with 3.09 mol% Er reaches to 2.2 mW/cm2, with the external quantum efficiency of 7.3% and power efficiency of 0.17%. The conduction mechanism for the excitation of Er emission confirms to the trap-assisted tunneling mode within the amorphous GeO2:Er nanolaminates. This work demonstrates the potential of GeO2:Er nanofilms in the utilization of Si-based optoelectronics.

Influence of Quantum Effects on Dielectric Relaxation in Functional Electrical and Electric Energy Elements Based on Proton Semiconductors and Dielectrics

Using the quasi-classical kinetic theory of dielectric relaxation, in addition to existing methods, fundamental mathematical expressions are built, which make it possible to more strictly consider the effects of the main charge carriers’ (protons’) tunneling on the numerical values of the molecular parameters (activation energy, equilibrium concentration) of protons in HBC. The formulas for calculating the statistically averaged non-stationary quantum transparency of a parabolic potential barrier for protons have been modernized by more stringent consideration of the effects of corrections caused by an external electric field. For the model of a double-symmetric potential well, a generalized nonlinear solution of the quasi-classical kinetic equation of dielectric relaxation in HBC was built. The phenomenological Bucci-Rive formula for thermally stimulated depolarization current density (TSDC) was first investigated, taking into account quantum transparency, for the case of a parabolic potential barrier. The choice of the parabolic shape of the potential barrier allowed, at a theoretical level, for the mathematical model of relaxation polarization to be brought closer to the conditions of the real spatial structure of the crystal potential field, in comparison with the rectangular potential barrier model. It has been found that quantum effects due to proton tunnel transitions significantly affect the mechanism of thermally stimulated depolarization currents in HBC, over a wide temperature range (50–550 K) and external field parameters (0.1–1 MV/m). Generalized solutions of the nonlinear kinetic equation, recorded considering the effects of field parameters on proton tunnel transitions, made it possible to significantly approximate the theoretical values of activation energies, equilibrium concentrations of protons and amplitudes of the theoretical maxima of the current density of thermally stimulated depolarization, according to their experimental values in the field of low-temperature (50–100 K) and high-temperature (350–550 K) maxima of TSDC density in HBC. For the first time, precision measurements of TSDC temperature spectra were carried out for chalcanthite crystals. The effects of alloying impurities concentrations and crystal calcination temperatures on the parameters of experimental maxima in the TSDC spectrum of chalcanthite were established. A physical mechanism of the quantum tunnel motion of protons in HBC with a complex crystal structure (crystalline hydrates, layered silicates, ferroelectric HBC (KDP, DKDP)) is described. The patterns found in this article indicate a fairly high degree of applied scientific significance for the obtained theoretical results, allowing for the further development of electrophysics and optoelectronics of heterogeneous structures (MIS, MSM) based on proton semiconductors and dielectrics (PSD) and their composites.

Influence of the transition section shape on the cavitation characteristics at the bottom outlet

Abstract The hydraulic characteristics of the lock chamber section in a bottom outlet are complex. Particularly, cavitation is a prominent problem when the flow in the tunnel transitions from pressurized to unpressurized conditions. As a countermeasure, sidewall contractions are often installed at the end of the pressurized section. In this paper, with numerical simulations and vacuum tank experiments, we analyzed the design parameters of several prototype projects and studied the flow properties and cavitation characteristics of the transition section. The four main factors that influence cavitation risks are the contraction ratio of the transition section, the top press slope, the length of the transition section, and the shape of the orifice. The study of a real-world project demonstrates that by implementing a severe constriction degree, the top press slope can be slowed down, and the pressurized transition section can be extended, thereby reducing cavitation risks and improving flow patterns. These research results provide a reference for the optimal design of hydraulic structures.

Ionization transition rates in the intermediate regime of the Keldysh parameter for a (0,1)*LG spiral amplitude modulated laser field

The mechanisms of the tunnel and multiphoton ionization transitions of hydrogen-like atoms and noble gas atoms are discussed. Atoms potassium and argon, with ionization energy of 4.34 and 15.76 eV, were chosen as the target. The atoms are exposed to Ti:Sapphire, (0,1)*LG, spiral amplitude modulated, laser beam at λ = 800 nm wavelength in a broad intensity range 1012 to 1015 W/cm2. The computational approach to describe tunnel and multiphoton processes was based on using the ADK theory. Stark and ponderomotive effects are also included to study their influence on the transition rate. Obtained results show that, for the lower γ values, the contribution of multiphoton ionization was less significant than the tunnel ionization contribution. In comparison, for higher γ values, multiphoton ionization dominated over tunnel ionization in a total transition rate. It is found that, in this particular case of spiral amplitude modulated mode, the intermediate regime, where both processes equally contribute, strongly depends on the atom selection and laser field intensity. Ionization in the intermediate regime occurs for γ ≈ 10 and 12 for low laser intensities, as γ ≈ 2 and 2.5 for the higher values, in the case of potassium and argon respectively. Our analysis indicated that the Stark and ponderomotive effects have a significant influence on the total transition rate. It is shown that these effects decrease the transition rate value and move the intermediate regime’s position toward lower values of the γ parameter, mainly in the case of higher laser field intensity.

The symmetry in the model of two coupled Kerr oscillators leads to simultaneous multi-photon transitions

We consider the model of two coupled oscillators with Kerr nonlinearities in the rotating-wave approximation. We demonstrate that for a certain set of parameters of the model, the multi-photon transitions occur between many pairs of the oscillator states simultaneously. Also, the position of the multi-photon resonances does not depend on the coupling strength between two oscillators. We prove rigorously that this is a consequence of a certain symmetry of the perturbation theory series for the model. In addition, we analyse the model in the quasi-classical limit by considering the dynamics of the pseudo-angular momentum. We identify the multi-photon transitions with the tunnelling transitions between the degenerate classical trajectories on the Bloch sphere.

Tunneling-induced fractal transmission in valley Hall waveguides

The Valley Hall effect provides a popular route to engineer robust waveguides for bosonic excitations such a photons and phonons. The almost complete absence of backscattering in many experiments has its theoretical underpinning in a smooth-envelope approximation that neglects large momentum transfer and is accurate only for small bulk band gaps and/or smooth domain walls. For larger bulk band gaps and hard domain walls backscattering is expected to become significant. Here, we show that in this experimentally relevant regime, the reflection of a wave at a sharp corner becomes highly sensitive on the orientation of the outgoing waveguide relative to the underlying lattice. Enhanced backscattering can be understood as being triggered by resonant tunneling transitions in quasimomentum space. Tracking the resonant tunneling energies as a function of the waveguide orientation reveals a self-repeating fractal pattern that is also imprinted in the density of states and the backscattering rate at a sharp corner.

Model of DC Tunneling Conductivity via Hydrogen‐Like Impurities in Heavily Doped Compensated Semiconductors

Herein, a theoretical model is proposed for the weakly temperature‐dependent electrical conductivity of compensated crystalline semiconductors with hydrogen‐like impurities near the insulator–metal concentration phase transition (Mott transition). The model uses a simple non‐stoichiometric cubic “impurity lattice” formed by the doping and compensating impurities in crystal matrix. A shift of the c‐band bottom (v‐band top) into the bandgap due to overlap of the excited states of neighboring impurities is considered. The distribution of electron (and hole) density of states in the band of ground (unexcited) states of impurities is assumed to be Gaussian. Tunneling transitions of electrons between nearest donors in the charge states () and (), and tunneling transitions of holes between acceptors in the charge states () and () are considered. It is shown that, at low temperatures, transitions of electrons (holes) near the Fermi level in the impurity band lead to electrical conductivity that weakly depends on temperature (in the form of a characteristic plateau). The results of calculating electrical resistivity in the zero‐temperature limit for the plateau region agree with the known experimental data for moderately compensated n‐ and p‐type Ge, Dia, Si, ZnSe, GaAs, InSb, and InP crystals.

Inelastic Neutron Scattering Measurement of the Ground State Tunneling Gap in Tb and Ho Analogues of a Dy Field-Induced Single-Molecule Magnet.

Recent advances in single-molecule magnet (SMM) research have placed great value on interpretation of inelastic neutron scattering (INS) data for rare earth (RE)-containing SMMs. Here, we present the synthesis of several rare earth complexes where combined magnetic and INS studies have been performed, supported by ab initio calculations. The reaction of rare earth nitrate salts with 2,2'-bipyridine (2,2'-bpy) and tetrahalocatecholate (X4Cat2-, X = Br, Cl) ligands in methanol (MeOH) afforded two new families of compounds [RE(2,2'-bpy)2(X4Cat)(X4CatH)(MeOH)] (X = Br and RE = Y, Eu, Gd, Tb, Dy, Ho, Yb for 1-RE; X = Cl and RE = Y, Tb, Dy, Ho, and Yb for 2-RE). Addition of triethylamine (Et3N) to the reaction mixture delivered Et3NH[RE(2,2'-bpy)2(Br4Cat)2] (3-RE, RE = Er and Yb). Interestingly, cerium behaves differently to the rest of the series, generating (2,2'-bpyH)2[Ce(Br4Cat)3(2,2'-bpy)] (4-Ce) with tetravalent Ce(IV) in contrast to the trivalent metal ions in 1-3. The static magnetic properties of 1-RE (RE = Gd, Tb, Dy and Ho) were investigated in conjunction with INS measurements on 1-Y, 1-Tb, and 1-Ho to probe their ground state properties and any crystal field excitations. To facilitate interpretation of the INS spectra and provide insight into the magnetic behavior, ab initio calculations were performed using the single-crystal X-ray diffraction structural data of 1-RE (RE = Tb, Dy and Ho). The ab initio calculations indicate ground doublets dominated by the maximal angular momentum projection states of Kramers type for 1-Dy and Ising type for 1-Tb and 1-Ho. Dynamic magnetic susceptibility measurements indicate that 1-Dy exhibits slow magnetic relaxation in the presence of a small applied magnetic field mainly through Raman pathways. Inelastic neutron scattering spectra exhibit distinct transitions corresponding to crystal field-induced tunneling gaps between the pseudo-doublet ground state components for 1-Tb and 1-Ho, which is one of the first direct experimental measurements with INS of such tunneling transitions in a molecular nanomagnet. The power of high-resolution INS is demonstrated with evidence of two distinct tunneling gaps measurable for the two crystallographically unique Tb coordination environments observed in the single crystal X-ray structure.

Towards modelling, and analysis of differential pressure and air velocity in a mechanical ventilation poultry house: Application for hot climates

Due to the broiler house's needs for a healthy environment, efficient control system, and appropriate air, several studies were interested in microclimate and air quality characteristics. However, limited studies are conducted to investigate pressure and air velocity within poultry buildings, which are also significant parameters that impact the breeding environment and productivity. As a reason, the objective of this work was to develop a mathematical model exploring the differential pressure and air velocity inside the house. The peculiarity of this research is the use of thermal balance and air properties to propose a model related to birds' weight which can be translated to birds' age and thermal conditions. The proposed approach acquired experimental measurements (e.g., indoor air temperature and humidity, air velocity, and differential pressure) and performed simulations in a mechanically ventilated Mediterranean broiler house over a summer production cycle. The findings revealed that the observed and modelled differential pressure ranged from a negative to a positive pressure (−5 to 39 Pa), with broilers subjected to air velocity varying from 0.09 to 1.641 m s−1 depending on three distinct modes of regulation: nature, power, and tunnel mode. These results confirmed the model's predictive capacity with a relative error of 1.03% of differential pressure and 0.68% of air velocity and a normalised mean square error (NMSE) of −1.06 Pa and 0.19 m s−1, respectively. Consequently, the methodology applied in this paper may be extended to various species of breeding structures in other seasons, allowing simulation tools and system control improvement.

Effect of formic acid on O2 + OH˙CHOH → HCOOH + HO2 reaction under tropospheric condition: kinetics of cis and trans isomers.

Formic acid (HCOOH) is one of the highly abundant acids in the troposphere. It is important in the formation of atmospheric aerosols and impacts the acidity of rainwater. In the present scenario, the model chemistry of HCOOH(FA) sources and sinks is poorly understood. In this work, we apply quantum chemical methods coupled with advanced statistical rate theories to understand the production of FA and its catalytic behavior under tropospheric conditions. The potential energy surfaces (PES) for O2 + OH˙CHOH and O2 + OH˙CHOH(+FA) reactions were constructed using the CCSD(T)/6-311++G(3df,3pd)//M06-2X/6-311++G(3df,3pd) level and rate constants for the production of FA were predicted using Rice-Ramsperger-Kassel-Marcus (RRKM)/master equation (ME) simulation with Eckart tunnelling and canonical variational transition state theory (CVT) with small curvature tunnelling (SCT) between the temperature range of 200-320 K and pressure range of 0.001 to 10 bar. The reaction follows the formation of cis and trans intermediates followed by spontaneous decomposition via concerted HO2 elimination to form stable post intermediates, which then leads to the straight formation of cis and trans formic acid. The current study also helps understand the role of cis and trans contribution to the total rate constants. The results show that O2 + OH˙CHOH is dominated by both cis and trans isomers; however, the trans isomer plays a more important role in the catalytic reaction. This result is due to the formation of a strong hydrogen-bonded complex in the trans isomer, which is dominated by the enthalpy factor rather than the entropy factor. The results predict that the catalytic effect of FA on the O2 + OH˙CHOH reaction is important when the concentration of FA is not included in the calculations; however, it has no effect under tropospheric conditions, when the FA concentration is included in the calculation. As a result, the total effective reaction rate constants are smaller. This work provides experimental/theoretical confirmation of Franco et al. who predicted that methanediol is the precursor for the FA formation, resolving an open problem in the kinetics of the gas phase reaction. O2 + OH˙CHOH and O2 + OH˙CHOH(+FA) probably explain other diol systems, which can help explain the formation of other atmospheric acids that affect aerosol formation and cloud evolution.

Application of 5G Communication Technology Based on Intelligent Sensor Network in Coal Mining

Intelligent mining provides an indispensable, strong technical support for the construction of intelligent mines. Intelligent tunneling technology is an inevitable requirement for safe and efficient production of coal and a fundamental way to solve the imbalance of mining in order to improve the deficiency of data transmission in light of intelligent coal tunneling technology. Based on intelligent sensor and 5G technology, this paper puts forward a kind of intelligent tunneling support transportation integrated technology. According to the geological conditions of the surrounding rock in different coal seams, the anchor road header and 5G continuous intelligent tunneling mode are adopted. At the same time, the data communication network coverage suitable for underground unmanned driving is expounded, and the performance indexes that need to be met for accessing WLAN network are given based on the actual engineering experience. The breakthrough of underground unmanned driving application that 5G new communication network will bring is analyzed. And the construction mode of 5G platform of underground coal mine sensor network is given.

Intrasubband-related linear and nonlinear optical absorption in single, double and triple QW: the compositions, temperature and QW’s number effects

ABSTRACT This paper exhibits a numerical simulation study of the 1s→2p ISB-related linear and nonlinear optical absorption in single, double, and triple QWs considering the effects of the compositions, temperature, and QW’s number. Our calculations were performed numerically as part of the effective mass approximation using finite element analysis. Our results reveal that for different nanostructures, optical absorption in quantum wells strongly depends on geometry, compositions, and temperature. Furthermore, we have found that optical absorption is greater and more sensitive to compositions and temperature variations in single QW than in double and triple QWs. In addition, a red-shift (blue-shift) associated with an enhancement (fall) of the resonance peaks of the optical absorption spectrum was obtained under the variation of composition, temperature, and number of QW per structure. However, we noticed that adding a QW causes a dramatic decrease in optical absorption due to the high loss rate due to oblique tunnelling and non-radiative optical transitions in double and multiple QWs compared to a single QW. We hope that this study will make a modest contribution to the field of theoretical and computational condensed matter physics.

Study of an asymmetry tunnel FET biosensor using junctionless heterostructure and dual material gate

In recent years, label-free sensors have been studied extensively for biomolecule detections. Label-free biosensors based on MOSFETs could achieve high detection sensitivity, the subthreshold swing of such sensors cannot break the limitation of 60 mV Dec−1 due to the physical mechanism of thermal electron emission. However, subthreshold swing less than 60 mV Dec−1 can be achieved in biosensors based on tunnel FETs working in band to band tunneling (BTBT) mode. Usually, label-free biosensors have a nanogap under the gate electrode both in MOSFET and tunnel FET (TFET), which can electrically sense the characteristics of biomolecules by dielectric constant modulation effect. In this article, we propose a novel nanogap embedded and dielectric modulated asymmetry tunnel FET biosensor with junctionless heterostructure and dual material gate, where different biomolecules can be detected effectively by adjusting the workfunctions for gate electrodes. Influences of tunnel gate, auxiliary gate and back gate workfunctions on sensitivities are explored. In addition, device-level gate effects are simulated by considering neutral and charged biomolecules. The influence of different dielectric constant at fixed charge density is also studied. Simulation results show that asymmetry dual material gate junctionless heterostructure tunnel FET (ADMG-HJLTFET) biosensor can provide higher switch ratio and higher sensitivity.

Study on the smoke back-layering length in a tilted tunnel with vertical shaft under natural ventilation

By varying tunnel slope, shaft height and fire source location, a series of numerical simulations were conducted to investigate the smoke back-layering length in a tilted tunnel with a vertical shaft. The simulation results were verified by corresponding reduced-scale experiments. Five possible smoke exhaust modes in tilted tunnels with single shaft were concluded through the flow field analysis. The dimensionless relationships between tunnel slope, shaft height, fire source distance and back-layering length were analyzed. When the fire source is located upstream of the shaft, smoke back-layering occurs when the tunnel slope is less than 1.5%. When the fire source is located downstream of the shaft, smoke back-layering disappears until the tunnel slope is bigger than 2.5%. The dimensionless analysis shows that the back-layering length is related to the fire source location and the tunnel slope, but has no significant dependency on the shaft height. Using the Froude number, the location of hot smoke is identified, when Frc < 1, part of the high-temperature smoke below the shaft cannot enter the shaft but spread to the tunnel exit. Dimensionless correlations between smoke back-laying length and Richardson number (Ri) were proposed. Moreover, the critical conditions that changes the smoke exhaust mode of the tunnel were determined only by the tunnel slope and the shaft height.

Peierls Instability of the Lieb Lattice

It is shown that the energy of the electron system in the two-dimensional Lieb lattice decreases owing to displacements of the edge atoms from the lattice sites along the edges. This decrease in the electron energy gives rise to soft phonon modes, anharmonic phonons, and to a lattice instability. Under certain conditions, the decrease in the electron energy can exceed the increase in the elastic energy of the ion lattice, and the total energy as a function of the displacements of edge atoms takes the form of a double-well potential. As a result, in the case of a pronounced instability, a partially ordered sublattice of edge atoms arises with the number of equilibrium positions twice as large as the number of atoms. The quantum tunneling of edge atoms between equilibrium positions results in the formation of quantum tunneling modes. The possible experimental manifestations of such instability and the extension of the model under study to the three-dimensional lattices are discussed.

Dynamics of mode entanglement induced by particle-tunneling in the extended Bose–Hubbard dimer model

The evolution of mode entanglement is analyzed for a system of two indistinguishable bosons with two accessible modes. Whereas entanglement remains stationary whenever the number of bosons in each mode is left invariant, it exhibits a rich dynamics under the effects of single-and two-particle tunneling. By analyzing such effects in paradigmatic families of states, our results provide guidance for the design and control of specific dynamics of mode entanglement, by varying the tunneling transition rates and the preparation of the initial state.

The reorientation of protonic defects in barium zirconate: Low-temperature tunneling regime and transition to the adiabatic regime

In most proton-conducting oxides, proton conductivity is mediated by a Grotthuss-like mechanism, i.e. the succession of transfers, in which the proton jumps from an oxygen onto another (breaking, and then reforming an ionocovalent hydroxyl bond OH), and reorientations, in which the OH bond simply rotates without breaking. We focus in this work on this second step, i.e. the reorientation of the protonic defect, in barium zirconate, one of the most promising proton-conducting oxides. Considered alone, the rotations of a proton are responsible for a rotational diffusion of this proton around a given oxygen atom. The reorientation of the protonic defect, like transfer, is strongly affected by the quantum effects associated with the protonic motions, and can only take place thanks to two specific lattice vibrations: (i) a reorganization, that symmetrizes the proton potential and puts the proton levels in the initial and final wells in coincidence, and (ii) the increase of the separation between the protonated oxygen and the nearest neighbor barium atom (that forms an obstacle to the reorientation of the protonic defect). The former (necessary step) mostly consists in rotations of the two oxygen octahedra sharing the protonated oxygen, while the latter (facilitating step) helps to overcome the proton‑barium electrostatic repulsion and lowers the proton barrier. We show that the reorientation of the protonic defect in barium zirconate undergoes a transition at about 220 K between a low-temperature and a high-temperature regime. Below ∼ 220 K, it is governed by tunneling, with a reorientation rate having an activation energy of 0.09 eV and a prefactor of ∼ 0.4 THz, due to quasi-non-adiabatic transitions between coincident protonic ground states (GS → GS), and involving an effective proton coupling of 5.7 meV. Above 220 K, two additional contributions, corresponding to transitions between the first excited protonic state (1st) in one of the two wells, and the protonic ground state (GS) in the other well, become dominant. These asymmetric transitions (1st → GS and GS → 1st) are quasi-adiabatic, and their rates are associated with an activation energy of 0.14 eV and a prefactor of 1.7 THz. The contribution due to adiabatic symmetric transitions between first excited protonic states (1st → 1st) should become equivalent to each of the asymmetric ones only at high temperature (above 900 K).

A High-Throughput Hardware Implementation of NAT Traversal For IPSEC VPN

In this paper, we present a high-throughput FPGA implementation of IPSec core. The core supports both NAT and non-NAT mode and can be used in high speed security gateway devices. Although IPSec ESP is very computing intensive for its cryptography process, our implementation shows that it can achieve high throughput and low lantency. The system is realized on the Zynq XC7Z045 from Xilinx and was verified and tested in practice. Results show that the design can gives a peak throughput of 5.721 Gbps for the IPSec ESP tunnel mode in NAT mode and 7.753 Gbps in non-NAT mode using one single AES encrypt core. We also compare the performance of the core when running in other mode of encryption.

Complexified stable and unstable manifolds and chaotic tunneling

Quantum tunneling in nonintegrable systems is studied based on the complex semiclassical analysis in the time domain. The theory of complex dynamical systems predicts that complexified stable and unstable manifolds form the skeleton of the dynamics in phase space, and mixing and ergodicity hold even for the mixed system. After surveying some rigorous results derived for the Hénon map, we numerically verify that some fundamental properties thus predicted can actually be observed, and then investigate natures of complexified stable and unstable manifolds since they guide the complex orbits controlling the tunneling transition in the mixed phase space. In particular, for a properly designed scattering map, we examine the imaginary action associated with the stable manifolds for the periodic orbits in the real plane and find that the orbits tending to the sticky zone of the KAM region provide the most dominant contribution in the semiclassical sum. It is worth emphasizing that the behavior of such dominant orbits is affected by the presence of chaos in the complex plane, which is an aspect far beyond the scope of the dynamics in the real plane.