Solving ground eigenvalue and eigenfunction of spheroidal wave equation at low frequency by supersymmetric quantum mechanics method

The spheroidal wave functions are found to have extensive applications in many branches of physics and mathematics. We use the perturbation method in supersymmetric quantum mechanics to obtain the analytic ground eigenvalue and the ground eigenfunction of the angular spheroidal wave equation at low frequency in a series form. Using this approach, the numerical determinations of the ground eigenvalue and the ground eigenfunction for small complex frequencies are also obtained.

The Study of Alcoholysis of 1,2-Thiazetidine-l,l-dioxide with Quantum Chemical Method

The alcoholysis mechanism of 1,2-thiazetidine-1,1-dioxide with methanol, in which the relatively stable product is sulfonate ester, has been investigated by quantum chemical method. Our calculations indicate the reaction for alcoholysis of 1,2-thiazetidine-1,1-dioxide proceeds via two possible mechanisms: concerted and stepwise. In the stepwise mechanism, two possible reaction pathways can be followed while only one possible reaction pathway can be followed in the concerted mechanism.

Quantum Boltzmann equation solved by Monte Carlo method for nano-scale semiconductor devices simulation

A two-dimensional （2D） full band self-consistent ensemble Monte Carlo （MC） method for solving the quantum Boltzmann equation, including collision broadening and quantum potential corrections, is developed to extend the MC method to the study of nano-scale semiconductor devices with obvious quantum mechanical （QM） effects. The quantum effects both in real space and momentum space in nano-scale semiconductor devices can be simulated. The effective mobility in the inversion layer of n and p channel MOSFET is simulated and compared with experimental data to verify this method. With this method 50nm ultra thin body silicon on insulator MOSFET are simulated. Results indicate that this method can be used to simulate the 2D QM effects in semiconductor devices including tunnelling effect.

State-to-state dynamics of reactions H+DH'(v=0,j=0)→HH'(v',j')+D/HD(v',j')+H'with time-dependent quantum wave packet method

State-to-state time-dependent quantum dynamics calculations have been carried out to study H+DH'→HH'+D/HD+H'reactions on BKMP2 surface.The total integral cross sections of both reactions are in good agreement with earlier theoretical and experimental results,moreover the rotational state-resolved reaction cross sections of H+DH'→HH‘+D at collision energy Ec=0.5 eV are closer to the experimental values than the ones calculated by Chao et al[J.Chem.Phys.1178341(2002)],which proves the higher precision of the quantum calculation in this work.In addition,the state-to-state dynamics of H+DH'→HD'+H reaction channel have been discussed in detail,and the differences of the micro-mechanism of the two reaction channels have been revealed and analyzed clearly.

Preparation of Hadamard Gate for Open Quantum Systems by the Lyapunov Control Method

In this paper, the control laws based on the Lyapunov stability theorem are designed for a two-level open quantum system to prepare the Hadamard gate, which is an important basic gate for the quantum computers. First, the density matrix interested in quantum system is transferred to vector formation.Then, in order to obtain a controller with higher accuracy and faster convergence rate, a Lyapunov function based on the matrix logarithm function is designed. After that, a procedure for the controller design is derived based on the Lyapunov stability theorem. Finally, the numerical simulation experiments for an amplitude damping Markovian open quantum system are performed to prepare the desired quantum gate. The simulation results show that the preparation of Hadamard gate based on the proposed control laws can achieve the fidelity up to 0.9985 for the different coupling strengths.

A method to calculate effective Hamiltonians in quantum information

Effective Hamiltonian method is widely used in quantum information. We introduce a method to calculate effective Hamiltonians and give two examples in quantum information to demonstrate the method. We also give a relation between the effective Hamiltonian in the Shr?dinger picture and the corresponding effective Hamiltonian in the interaction picture.Finally, we present a relation between our effective Hamiltonian method and the James–Jerke method which is currently used by many authors to calculate effective Hamiltonians in quantum information science.

Security Simulation of Continuous-Variable Quantum Key Distribution over Air-to-Water Channel Using Monte Carlo Method

Considering the ocean water＇s optical attenuation and the roughness of the sea surface, we analyze the security of continuous-variable （CV） quantum key distribution （QKD） based Mr-to-water channel. The effects of the absorp- tion and scattering on the transmittance of underwater quantum channel and the maximum secure transmission distance are studied. Considering the roughness of the sea surface, we simulate the performance bounds of CV QKD with different wind speeds using the Monte Carlo method. The results show that even if the secret key rate gradually reduces as the wind speed increases, the maximum transmission distance will not be affected obviously. Compared to the works regarding short-distance underwater optical communication, our research represents a significant step towards establishing secure communication between air platform and submarine vehicle.

Evaluation of Quantum Chemical Methods and Basis Sets Applied in the Molecular Modeling of Artemisinin

In this paper, we evaluate semiempirical methods (AM1, PM3, and ZINDO), HF and DFT (B3LYP) in different basis sets to determine which method best describes the sign and magnitude of the geometrical parameters of artemisinin in the region of the endoperoxide ring compared to crystallographic data. We also classify these methods using statistical analysis. The results of PCA were based on three main components, explaining 98.0539% of the total variance, for the geometrical parameters C3O13, O1O2C3, O13C12C12a, and O2C3O13C12. The DFT method (B3LYP) corresponded well with the experimental data in the hierarchical cluster analysis (HCA). The experimental and theoretical angles were analyzed by simple linear regression, and statistical parameters (correlation coefficients, significance, and predictability) were evaluated to determine the accuracy of the calculations. The statistical analysis exhibited a good correlation and high predictive power for the DFT (B3LYP) method in the 6-31G** basis set.

The analytical transfer matrix method for quantum reflection

In this paper, the analytical transfer matrix method （ATMM） is applied to study the properties of quantum reflection in three systems： a sech2 barrier, a ramp potential and an inverse harmonic oscillator. Our results agree with those obtained by Landau and Lifshitz [Landau L D and Lifshitz E M 1977 Quantum Mechanics （Non-relativistic Theory） （New York： Pergamon）], which proves that ATMM is a simple and effective method for quantum reflection.

An Entropy Measurement Method of Quantum Information System under Uncertain Environment

Under uncertain environment, it is very difficult to measure the entropy of quantum information system, because there is no effective method to model the randomness. First, different from the traditional classic uncertainty, a quantum uncertain model is proposed to simulate a quantum information system under uncertain environment, and to simplify the entropy measurement of quantum information system. Second, different from the classic random seed under uncertain environment which is often called as pseudo-random number, here the quantum random is employed to provide us a true random model for the entropy of quantum information system. Third, the complex interaction and entangling activity of uncertain factors of quantum information is modeled as quantum binary instead of classic binary, which can help us to evaluate the entropy of uncertain environment, to analyze the entropy divergence in quantum information system. This work presents a non-classic risk factor measurement for quantum information system and a helpful entropy measurement.

The Quantum Scattering Study for Ion-pair Formation Reaction Na+I_2→Na^+I_2^- with the LCAC-SW method

The selected-state probabilities of collinear ion-pair formation process Na+I2→Na++I2-on Aten-Laming-Los two-State potential energy surface have been calculated by using LCAC-SW method. The results show that reaction probabilities are oscillatory with collision energy; the threshold energy of this ioniZation reaction is 2.8 ev, which is in modest agreement with experimental result.

Calculation of the Approximate Energy of Ground and Excited Stationary States in Quantum Mechanics Using Delta Method

In this paper, pursuing a new advised method called Delta method which is basically similar to variational method, we find the ground and excited states, according to a typical quantum Hamiltonian. Moreover, applying this method, the upper bound values for the eigenenergies of the so-called ground and excited states are estimated. We will show that this new method, is as beneficial as the traditional variational method which is common in deriving eigenenergies of some of the quantum Hamiltonians. This method helps physics students to broaden their knowledge about the possible mathematical ways;they can use to obtain eigenenergies of some quantum Hamiltonians. The advantage of Delta method to variational method is in its simplicity and reduction of the calculation procedures.

An analytical variational method for the biased quantum Rabi model in the ultra-strong coupling regime

An analytical variational method for the ground state of the biased quantum Rabi model in the ultra-strong coupling regime is presented. This analytical variational method can be obtained by a unitary transformation or alternatively by assuming the form of the ground state wave function. The key of the method is to introduce a variational parameter λ,which can be determined by minimizing the energy functional. Using this method, we calculate the physical observables with high accuracy in comparison with the numerical exact ones. Our method evidently improves over the widely used general rotating-wave approximation（GRWA） in both qualitative and quantitative aspects.

An optimized encoding method for secure key distribution by swapping quantum entanglement and its extension

Song [Song D 2004 Phys. Rev. A69034301] first proposed two key distribution schemes with the symmetry feature.We find that, in the schemes, the private channels which Alice and Bob publicly announce the initial Bell state or the measurement result through are not needed in discovering keys, and Song’s encoding methods do not arrive at the optimization.Here, an optimized encoding method is given so that the efficiencies of Song’s schemes are improved by 7/3 times. Interestingly, this optimized encoding method can be extended to the key distribution scheme composed of generalized Bell states.

Dynamics of Quantum State and Effective Hamiltonian with Vector Differential Form of Motion Method

Effective Hamiltonians in periodically driven systems have received widespread attention for realization of novel quantum phases, non-equilibrium phase transition, and Majorana mode. Recently, the study of effective Hamiltonian using various methods has gained great interest. We consider a vector differential equation of motion to derive the effective Hamiltonian for any periodically driven two-level system, and the dynamics of the spin vector are an evolution under the Bloch sphere. Here, we investigate the properties of this equation and show that a sudden change of the effective Hamiltonian is expected. Furthermore, we present several exact relations, whose expressions are independent of the different starting points. Moreover, we deduce the effective Hamiltonian from the high-frequency limit, which approximately equals the results in previous studies. Our results show that the vector differential equation of motion is not affected by a convergence problem, and thus, can be used to numerically investigate the effective models in any periodic modulating system. Finally, we anticipate that the proposed method can be applied to experimental platforms that require time-periodic modulation, such as ultracold atoms and optical lattices.

Energy level of an electron in a saddle-potential quantum dot under a uniform magnetic field obtained by the invariant eigenoperator method

We show that the recently proposed invariant eigenoperator method can be successfully applied to solving the energy levels of an electron in a saddle-potential quantum dot under a uniform magnetic field. The Landau diamagnetism decreases with the value wy2 - wx2 due to the existence of the saddle potential.

Numerical Verification of Transition’s Energies of Excitons in Quantum Well of ZnO with the Finite Difference Method

This paper shows that the experimental results of quantum well energy transitions can be found numerically. The cases of several ZnO-ZnMgO wells are considered and their excitonic transition energies were calculated using the finite difference method. In that way, the one-dimensional Schrödinger equation has been solved by using the BLAS and LAPACK libraries. The numerical results are in good agreement with the experimental ones.

Simulations of the Electron Spectrum of Quantum Wires in <i>n</i>-Si of Arbitrarily Doping Profile by Thomas-Fermi Method

Electron spectrum in doped n-Si quantum wires is calculated by the Thomas-Fermi (TF) method under finite temperatures. The many-body exchange corrections are taken into account. The doping profile is arbitrary. At the first stage, the electron potential energy is calculated from a simple two-dimensional equation. The effective iteration scheme is proposed there that is valid for multidimensional problems. Then the energy levels and wave functions of this quantum well are simulated from the Schr&#246;dinger equations. The expansion by the full set of eigenfunctions of the linear harmonic oscillator is used. The quantum mechanical perturbation theory can be utilized to compute the energy levels. Generally, the perturbation theory for degenerate energy levels should be used.

Quantum-Mechanical Information Content of Multiples Hartree-Fock Solutions. The Multi-Reference Hartree-Fock Configuration Interaction Method

The Hartree-Fock equation is non-linear and has, in principle, multiple solutions. The ωth HF extreme and its associated virtual spin-orbitals furnish an orthogonal base Bω of the full configuration interaction space. Although all Bω bases generate the same CI space, the corresponding configurations of each Bω base have distinct quantum-mechanical information contents. In previous works, we have introduced a multi-reference configuration interaction method, based on the multiple extremes of the Hartree-Fock problem. This method was applied to calculate the permanent electrical dipole and quadrupole moments of some small molecules using minimal and double, triple and polarized double-zeta bases. In all cases were possible, using a reduced number of configurations, to obtain dipole and quadrupole moments in close agreement with the experimental values and energies without compromising the energy of the state function. These results show the positive effect of the use of the multi-reference Hartree-Fock bases that allowed a better extraction of quantum mechanical information from the several Bω bases. But to extend these ideas for larger systems and atomic bases, it is necessary to develop criteria to build the multireference Hartree-Fock bases. In this project, we are beginning a study of the non-uniform distribution of quantum-mechanical information content of the Bω bases, searching identify the factors that allowed obtain the good results cited

Quantum Dynamics Study on D＋OD＋ Reaction： Competition between Exchange and Abstraction Channels

Quantum dynamics for the D＋OD＋ reaction at the collision energy range of 0.0-1.0 eV was studied on an accurate ab initio potential energy surface. Both of the endothermic abstraction （D＋OD＋-→O＋＋D2） and thermoneutral exchange （D＋OD＋--＊D＋OD＋） channels were investigated from the same set of time-dependent quantum wave packets method under cen- trifugal sudden approximation. The reaction probability dependence with collision energy, the integral cross sections, and the thermal rate constant of the both channels are calculated. It is found that there is a convex structure in the reaction path of the exchange reaction. The calculated time evolution of the wave packet distribution at J=0 clearly indicates that the convex structure significantly influences the dynamics of the exchange and abstraction channels of title reaction.