Double Wells Research Articles

Spin-orbit coupling in wurtzite heterostructures

Effective spin-orbit (SO) Hamiltonians for conduction electrons in wurtzite heterostructures are lacking in the literature, in contrast to zincblende structures. Here we address this issue by deriving such an effective Hamiltonian valid for quantum wells, wires, and dots with arbitrary confining potentials and external magnetic fields. We start from an 8$\times$8 Kane model accounting for the $s$--$p_z$ orbital mixing important to wurtzite structures, but absent in zincblende, and apply both quasi-degenerate perturbation theory (L\"owdin partitioning) and the folding down approach to derive an effective 2$\times$2 electron Hamiltonian. We obtain the usual $k$-linear Rashba term arising from the structural inversion asymmetry of the wells and, differently from zincblende structures, a bulk Rashba-type term induced by the inversion asymmetry of the wurtzite lattice. We also find linear- and cubic-in-momentum Dresselhaus contributions. Both the bulk Rashba-type term and the Dresselhaus terms originate exclusively from the admixture of $s$- and $p_z$-like states in wurtzites structures. Interestingly, in these systems the linear Rashba and the Dresselhaus terms have the same symmetry and can in principle cancel each other out completely, thus making the spin a conserved quantity. We determine the intrasubband (intersubband) Rashba $\alpha_\nu$ ($\eta$) and linear Dresselhaus $\beta_\nu$ ($\Gamma$) SO strengths of GaN/AlGaN single and double wells with one and two occupied subbands ($\nu=1,2$). We believe our general effective Hamiltonian for electrons in wurtzite heterostructures put forward here, should stimulate additional theoretical works on wurtzite quantum wells, wires, and dots with variously defined geometries and external magnetic fields.

Transfer efficiency enhancement and eigenstate properties in locally symmetric disordered finite chains

The impact of local reflection symmetry on wave localization and transport within finite disordered chains is investigated. Local symmetries thereby play the role of a spatial correlation of variable range in the finite system. We find that, on ensemble average, the chain eigenstates become more fragmented spatially for intermediate average symmetry domain sizes, depending on the degree of disorder. This is caused by the partial formation of states with approximate local parity confined within fictitious, disorder-induced double wells and perturbed by the coupling to adjacent domains. The dynamical evolution of wave-packets shows that the average site-resolved transfer efficiency is enhanced between regions connected by local symmetry. The transfer may further be drastically amplified in the presence of spatial overlap between the symmetry domains, and in particular when global and local symmetry coexist. Applicable to generic discrete models for matter and light waves, our work provides a perspective to understand and exploit the impact of local order at multiple scales in complex systems.

Exploration and production practice of oil sands in Fengcheng oilfield of Junggar Basin, China

Oil sands are characterized by shallow burial and extremely high viscosity, whose exploration technologies and production methods are quite different from that of conventional oil and gas. Oil sands with the largest reserve scale and best quality in China are developed in Fengcheng area of Junggar Basin. This paper presents the forming conditions and enrichment rules of oil sands in Fengcheng area. The dividing standards for effective thickness of oil sands are established with exploration technologies like high-density drilling, whole well section coring and the method of weight percentage of bitumen. The geologic reserves of oil sands are calculated with the method of weight percentage of bitumen. Open-pit mining practices and SAGD double horizontal well development tests are carried out, and good effects are obtained in SAGD production. At present, Fengcheng oil sands have been developed on a large scale with SAGD technology.

Association of Cl with C2H2 by unified variable-reaction-coordinate and reaction-path variational transition-state theory

Barrierless unimolecular association reactions are prominent in atmospheric and combustion mechanisms but are challenging for both experiment and kinetics theory. A key datum for understanding the pressure dependence of association and dissociation reactions is the high-pressure limit, but this is often available experimentally only by extrapolation. Here we calculate the high-pressure limit for the addition of a chlorine atom to acetylene molecule (Cl + C2H2→C2H2Cl). This reaction has outer and inner transition states in series; the outer transition state is barrierless, and it is necessary to use different theoretical frameworks to treat the two kinds of transition state. Here we study the reaction in the high-pressure limit using multifaceted variable-reaction-coordinate variational transition-state theory (VRC-VTST) at the outer transition state and reaction-path variational transition state theory (RP-VTST) at the inner turning point; then we combine the results with the canonical unified statistical (CUS) theory. The calculations are based on a density functional validated against the W3X-L method, which is based on coupled cluster theory with single, double, and triple excitations and a quasiperturbative treatment of connected quadruple excitations [CCSDT(Q)], and the computed rate constants are in good agreement with some of the experimental results. The chlorovinyl (C2H2Cl) adduct has two isomers that are equilibrium structures of a double-well C≡C-H bending potential. Two procedures are used to calculate the vibrational partition function of chlorovinyl; one treats the two isomers separately and the other solves the anharmonic energy levels of the double well. We use these results to calculate the standard-state free energy and equilibrium constant of the reaction.

MCTDH-X: The multiconfigurational time-dependent Hartree method for indistinguishable particles software

We introduce and describe the multiconfigurational time-depenent Hartree for indistinguishable particles (MCTDH-X) software, which is hosted, documented, and distributed at http://ultracold.org. This powerful tool allows the investigation of ground state properties and dynamics of interacting quantum many-body systems in different spatial dimensions. The MCTDH-X software is a set of programs and scripts to compute, analyze, and visualize solutions for the time-dependent and time-independent many-body Schrödinger equation for indistinguishable quantum particles. As the MCTDH-X software represents a general solver for the Schrödinger equation, it is applicable to a wide range of problems in the fields of atomic, optical, molecular physics, and condensed matter systems. In particular, it can be used to study light–matter interactions, correlated dynamics of electrons in the solid state as well as some aspects related to quantum information and computing. The MCTDH-X software solves a set of nonlinear coupled working equations based on the application of the time-dependent variational principle to the Schrödinger equation. These equations are obtained by using an ansatz for the many-body wavefunction that is a expansion in a set of time-dependent, fully symmetrized bosonic (X = B) or fully anti-symmetrized fermionic (X = F) many-body basis states. It is the time-dependence of the basis set that enables MCTDH-X to deal with quantum dynamics at a superior accuracy as compared to, for instance, exact diagonalization approaches with a static basis, where the number of basis states necessary to capture the dynamics of the wavefunction typically grows rapidly with time. Herein, we give an introduction to the MCTDH-X software via an easy-to-follow tutorial with a focus on accessibility. The illustrated exemplary problems are hosted at http://ultracold.org/tutorial and consider the physics of a few interacting bosons or fermions in a double-well potential. We explore computationally the position-space and momentum-space density, the one-body reduced density matrix, Glauber correlation functions, phases, (dynamical) phase transitions, and the imaging of the quantum systems in single-shot images. Although a few particles in a double well potential represent a minimal model system, we are able to demonstrate a rich variety of phenomena with it. We use the double well to illustrate the fermionization of bosonic particles, the crystallization of fermionic particles, characteristics of the superfluid and Mott-insulator quantum phases in Hubbard models, and even dynamical phase transitions. We provide a complete set of input files and scripts to redo all computations in this paper at http://ultracold.org/data/tutorial_input_files.zip, accompanied by tutorial videos at https://tinyurl.com/tjx35sq. Our tutorial should guide the potential users to apply the MCTDH-X software also to more complex systems.

Entanglement-assisted tunneling dynamics of impurities in a double well immersed in a bath of lattice trapped bosons

We unravel the correlated tunneling dynamics of an impurity trapped in a double well and interacting repulsively with a majority species of lattice trapped bosons. Upon quenching the tilt of the double well it is found that the quench-induced tunneling dynamics depends crucially on the interspecies interaction strength and the presence of entanglement inherent in the system. In particular, for weak couplings the impurity performs a rather irregular tunneling process in the double well. Increasing the interspecies coupling it is possible to control the response of the impurity which undergoes a delayed tunneling while the majority species effectively acts as a material barrier. For very strong interspecies interaction strengths the impurity exhibits a self-trapping behavior. We showcase that a similar tunneling dynamics takes place for two weakly interacting impurities and identify its underlying transport mechanisms in terms of pair and single-particle tunneling processes.

Superexponential self-interacting oscillator

The superexponential self-interacting oscillator (SSO) is introduced and analyzed. Its power law potential is characterized by the dependence of both the base and the exponent on the dynamical variable of the oscillator. Opposite to standard oscillators such as the (an-)harmonic oscillator the SSO combines both scattering and confined periodic motion with an exponentially varying nonlinearity. The SSO potential exhibits a transition point with a hierarchy of singularities of logarithmic and power law character leaving their fingerprints in the agglomeration of its phase space curves. The period of the SSO consequently undergoes a crossover from decreasing linear to a nonlinearly increasing behaviour when passing the transition energy. We explore its dynamics and show that the crossover involves a kick-like behaviour. A symmetric double well variant of the SSO is briefly discussed.

Experimental realization of Mott insulator of ultracold <sup>87</sup>Rb atoms in two-dimensional optical lattice

Quantum phase transition of ultracold atomic gas is one of the core contents in the study of quantum correlational many-body systems. In this paper, two-dimensional (2D) optical lattices are generated by a single fold retroreflected laser beam, and this scheme is used to experimentally design and implement the 2D optical lattice of double wells suitable for isolating and manipulating an array of individual pairs of atoms and predict a topological semimetal in the high orbital bands in this 2D lattice. Two types of optical lattice structures are produced by controlling the laser polarization. One type is the usual 2D optical lattice, which is formed by two independent one-dimensional(1D) optical lattices in two directions and named in-plane lattice, and the other type is the lattice that is formed by the interference between two one-dimensional optical lattices in two directions and called out-plane lattice. When <sup>87</sup>Rb BEC (Bose-Einstein condensation) is loaded into the 2D optical lattice, the quantum phase transition between superfluid state and Mott insulator state is observed by controlling the tunneling and in-site interaction. And the phase transition from superfluid state to Mott insulator is judged by observing whether there are interferential lattice points in momentum space. The lattice depths of two cases can be calibrated by Kapitza-Dirac scattering in the ultracold atomic experiment through the time-of-flight absorption imaging. In the in-plane optical lattice, some incorrect points appear in the 45° direction, because the linear polarization degree of beam is impure after being reflected by mirrors and two direction of beam are not completely orthogonal to each other. It is obvious that the two cases have different phase transition points, which is due mainly to the difference in structure. For the in-plane lattice, there are two independent 1D optical lattices, and for the out-plane lattice, the two direction beams mutually interfere with each other, therefore, two optical lattices are not independent of each other. The atoms come back to BEC by reducing the potentials of optical lattice to zero; the temperature of system is slightly higher, because of the jitter of the light lattice. The different behaviors of quantum phase transition are analyzed for two types of optical lattices. This work will provide a platform for the future study of large spin system and strong correlation physics in optical lattices.

Atop‐the‐barrier localization in periodically driven double wells: A minimization of information entropic sums in conjugate spaces

AbstractThe spatio‐temporal localization of a system in the presence of an oscillating electric field for a symmetric double‐well potential is examined via numerical simulations of the time‐dependent Schrödinger equation. For an initial state with equal probability densities in both the wells, stabilized localization atop the barrier can be achieved on a periodic high‐frequency driving. The barrier localization is characterized using Shannon information entropies in position and momentum spaces, defined as Sρ = − ∫ |ψ|2 ln |ψ|2 dx and Sγ = − ∫ |ϕ|2 ln |ϕ|2 dp, where ψ and ϕ refer to position and momentum space wave functions, respectively. The information entropy sum, Sρ + Sγ, goes through a minimum indicating the formation of the barrier‐localized state, when the peak intensity of the oscillating field is reached. The generalized uncertainty via the Białynicki‐Birula‐Mycielski inequality ( Sρ + Sγ ≥ 1 + lnπ) is saturated upon this minimization. This serves as a signature of the formation of the barrier‐atop localized state, in terms of Shannon entropies of measurable densities.

A feedback model for relaxors

The transition from a ferroelectric to a relaxor is described. Asymmetric double-well potentials for fluctuating charges, dipoles or polar nanoregions and a feedback between these double wells are employed. Tuning the intrinsic asymmetry it is possible to describe either a ferroelectric state or a relaxor behavior. While in ferroelectrics with an ordered crystal lattice the intrinsic asymmetry is small, disorder in the amorphous state can result in double wells with higher asymmetry causing a relaxor response.

Reducing formation damage by artificially controlling the fluid-rock chemical interaction in a double-well geothermal heat production system

Direct heat production by double wells is widely used to extract thermal energy from geothermal reservoirs. However, geothermal water is often type of brine with high dissolved salts. Injection and extraction of the geothermal fluid may cause strong chemical reactions, leading to scaling in the wellbore and reservoir. Such process was seldom considered in the heat production optimization. This study numerically investigated the mechanism of chemical damage to the reservoir in the Zhacang geothermal field, China, and optimized the heat production with constraint of weakening chemical damage. It was found that direct injection of the tail geothermal water can lead the porosity to reduce by 0.06%. The degree of precipitation can be controlled by artificial factors, including injection temperature and mixing ratio of the geothermal water with river water. The comparative computation indicated that at an injection temperature of 35 °C, and a mixing ratio of the river to the geothermal water of 6:4, the reservoir porosity was unaffected by chemical reactions in 100 years and geothermal energy production can be maintained above 0.11 MW. The methodology can be applied in other geothermal fields for sustainable geothermal energy production regarding the formation damage in geothermal reservoirs due to fluid-rock interaction.

Coordination bonding in dicopper and dichromium tetrakis(μ-acetato)-diaqua complexes: Nature, strength, length, and topology.

Geometry optimization, energetics, electronic structure, and topology of electron density of dicopper (I) and dichromium (II) tetrakis(μ-acetato)-diaqua complexes are studied focusing on the metal-metal interactions. The performance of broken symmetry (BS) single-determinant ab initio (Hartree-Fock, Møller-Plesset perturbation theory to the second and third orders, coupled clusters singles and doubles) and density functional theory (BLYP, B3LYP, B3LYP-D3, B2PLYP, MPW2PLYP) methods is compared to multideterminant ab initio (CASSCF, NEVPT2) methods as well as to the multipole model of charge density from a single-crystal X-ray diffraction experiment (Herich et al., Acta Cryst. 2018, B74, 681-692). In vacuo DFT geometry optimizations (improper axial water ligand orientation) are compared against the periodic ones. The singlet state is found to be energetically preferred. J coupling of (I) becomes underestimated for all ab initio methods used, when compared to experiment. It is concluded that the strength of the direct M─M interactions correlates closely with the J coupling magnitude at a given level of theory. The double potential well character of (II) and of the dehydrated form of (II) are considered with respect to the Cr─Cr distance. The physical effective bond order of the metal-metal interaction is small (below 0.1 e) in (I) and moderate (0.4 e) in (II). The CASSCF results overestimate the electron density of the metal-metal bond critical point by 20% and 50% in (I) and (II), respectively, when compared to the multipole model. © 2019 Wiley Periodicals, Inc.

Least energy nodal solution for Kirchhoff type problem with an asymptotically 4-linear nonlinearity

In the present paper, we consider the following Kirchhoff type problem −(a+b∫R3|∇u|2dx)Δu+V(x)u=f(u)inR3,where a,b>0 and the potential V has double potential well. With an asymptotically 4-linear nonlinearity f, we prove that the Kirchhoff type problem has one least energy nodal solution by variational methods.

Mica Dehydroxylation Mechanism

The dehydroxylation mechanism of mica is studied using IR spectroscopy; x-ray structure and thermodynamic analysis; and kinetic, quantum-mechanical, and quantum-chemical methods. Dehydroxylation is shown to involve localization of a proton between two O atoms. A model in which the hydroxyl proton is placed in a double potential well is proposed. The model allows the basic features of mineral dehydroxylation to be revealed. The proton energy increases if the mineral is heated so that the barrier becomes more transparent. The probability of a particle transitioning through the barrier owing to a tunnel effect is considered. The change of this probability defines the dehydroxylation process.

Unidirectional flow of solitons with nonlinearity management.

Unidirectional flow of solitons is obtained with a localized modulation of the nonlinearity strength. The modulation takes the shape of an asymmetric double well with a slight difference between the potential depths. The results were established using numerical computations and then verified qualitatively using a variational approach. Our results suggest that the most important physics at the origin of the unidirectional flow is the excitation of the breathing modes in the scattering region. Simplified variational equations of motion suggested that the phenomenon can be observed if the soliton is scattered by a generic asymmetric effective double potential well.

Many-body quantum dynamics of an asymmetric bosonic Josephson junction

The out-of-equilibrium quantum dynamics of an interacting Bose gas trapped in a one-dimensional asymmetric double-well potential is studied by solving the many-body Schrödinger equation numerically accurately. We examine how the gradual loss of symmetry of the confining trap affects the macroscopic quantum tunneling dynamics of the system between the two wells. In an asymmetric double well, the two wells are not equivalent anymore, say, the left well is deeper than the right one. Accordingly, we analyze the dynamics by initially preparing the condensate in both the left and the right wells. The dynamics of the system is characterized by the time evolution of a few physical quantities of increasing many-body complexity, namely, the survival probability, depletion and fragmentation, and the many-particle position and momentum variances. In particular, we have examined the frequencies and amplitudes of the oscillations of the survival probabilities, the time scale for the development of fragmentation and its degree, and the growth and oscillatory behavior of the many-particle position and momentum variances. There is an overall suppression of the oscillations of the survival probabilities in an asymmetric double well, except for resonant values of asymmetry for which the one-body ground state energy in the right well matches with one of the one-body excited states in the left well, thereby resulting in resonantly enhanced tunneling from the right well ground state. Overall, depending on whether the condensate is initially prepared in the left or right well, the repulsive inter-atomic interactions affect the survival probabilities differently. For a sufficiently strong repulsive interaction, the system is found to become fragmented. The degree of fragmentation depends both on the asymmetry of the trap and the initial well in which the condensate is prepared in a non-trivial manner. Furthermore, we show that the phenomenon of resonantly enhanced tunneling can be accompanied by a large degree of fragmentation (depletion) for the strong (weak) interaction. The many-particle position and momentum variances follow the density oscillations of the system in the asymmetric double well and bears prominent signatures of the degree of depletion or fragmentation, depending on the strength of the interactions. These quantities further exhibit a fine structure signifying a breathing-mode oscillation. Finally, a universality of fragmentation for systems made of different numbers of particles but the same interaction parameter is also found and its dependence on the asymmetry is investigated. The phenomenon is robust despite the asymmetry of the junction and admits a macroscopically-large fragmented condensate characterized by a diverging many-particle position variance. This is as far as one can get from the dynamics of the density in the junction.

Atom-pair tunneling and quantum phase transition in asymmetry double-well trap in strong-interaction regime**Project supported by the National Natural Science Foundation of China (Grant No. 11075099).

The quantum effect of nonlinear co-tunnelling process, which is dependent on atom-pair tunneling and asymmetry of an double-well trap, is studied by using an asymmetrical extended Bose–Hubbard model. Due to the existence of atom-pair tunneling that describes quantum phenomena of ultracold atom-gas clouds in an asymmetrical double-well trap, the asymmetrical extended Bose–Hubbard model is better than the previous Bose–Hubbard model model by comparing with the experimental data cited from the literature. The dependence of dynamics and quantum phase transition on atom-pair tunneling and asymmetry are investigated. Importantly, it shows that the asymmetry of the extended Bose–Hubbard model, corresponding to the bias between double wells, leads to a number of resonance tunneling processes, which tunneling is renamed conditional resonance tunneling, and corrects the atom-number parity effect by controlling the bias between double wells.

Transition dipole moments and probabilities of the CCl radicals

This work studies the transition dipole moments and properties of 12 electronic states. These states are X2Π, A2Δ, B2Σ+, C2Π, 12Σ−, 22Σ−, a4Σ−, b4Π, 14Σ+, 14Δ, 24Π, and 24Σ−; they originate from the first dissociation limit of the carbon monochloride radical. The potential energy curves were calculated using the complete active space self-consistent field method, followed by the valence internally contracted multireference configuration interaction approach. The B2Σ+ state has a double well and C2Π a single barrier. The radiative lifetimes of the vibrational levels are in the order of 10−7 s for the A2Δ state, and 10−7 and 10−5 s for the first and second wells of the B2Σ+ state, respectively, suggesting that the spontaneous emissions originated from the two states can easily occur. The radiative lifetimes are long for C2Π, b4Π, 14Δ, 14Σ+, and 24Π states and the Einstein A coefficients are small for the emissions originated from these states, indicating that the spontaneous emissions generated from these states are difficult to measure through spectroscopy. The 12Σ−, 22Σ−, and 24Σ− states are repulsive. Furthermore, the spectroscopic parameters and vibrational levels were evaluated. For the A2Δ – X2Π and B2Σ+ – X2Π systems, the Einstein A coefficients of the vibronic emissions are large, indicating that the emissions from the two systems can be easily detected by spectroscopy. The spectral range of the spontaneous emissions was evaluated for certain transitions.

Comparative study of different anisotropy and potential formulations of phase-field models for dendritic solidification

Phase-field model formulations with double well and double obstacle potentials, and different anisotropy models are investigated with respect to their potential to simulate (i) tip growth on a quantitative level, (ii) well resolved side-branching. The dilute binary alloy Al-4 at%Cu is used as a model alloy. The effects of the numerical resolution (the ratio of the capillary length to the grid spacing) on the growth velocity are studied by means of convergence tests for isothermal and directional solidification in comparison to the theoretical values calculated by the Green-function method (A. Karma, W.J. Rappel, Phys. Rev. E 57 (1998) 4323). An interface stability parameter is introduced as a measure for the estimation of the maximum value of the grid spacing for effective simulations. We show that predominantly the side-branching occurs at numerical resolution lower than the limit value needed to produce correct results in accordance to the convergence analysis. The best results for dendrite growth at a relevant numerical resolution are obtained for the double well potential.

Three-body constrained bosons in a double-well optical lattice

We analyse the ground-state properties of three-body constrained bosons in a one dimensional optical lattice with staggered hoppings analogous to the double well optical lattice. By considering attractive and repulsive on-site interactions between the bosons, we obtain the phase diagram which exhibits various quantum phases. Due to the double-well geometry and three-body constraint several gapped phases such as the Mott insulators and dimer/bond-order phases emerge at commensurate densities in the repulsive interaction regime. Attractive interaction leads to the pair formation which leads to the pair bond order phase at unit filling which resembles the valence-bond solid phase of composite bosonic pairs. At incommensurate densities we see the signatures of the gapless pair superfluid phase.