Surface optical phonon—assisted electron Raman scattering in a semiconductor quantum disc

We have carried out a theoretical calculation of the differential cross section for the electron Raman scattering process associated with the surface optical phonon modes in a semiconductor quantum disc.electron states are considered to be confined within a quantum disc with infinite potential barriers.The optical phonon modes we have adopted are the slab phonon modes by taking into consideration the Frohlich interaction between an electron and a phonon.The selection rules for the Raman process are given.Numerical results and a discussion are also presented for various radii and thicknesses of the disc,and different incident radiation energies.     

Coulomb effects in artificial molecules

We study the capacitance spectra of artificial molecules consisting of two and three coupled quantum dots from an extended Hubbard Hamiltonian model that takes into account quantum confinement, intra- and inter-dot Coulomb interaction and tunneling coupling between all single particle states in nearest neighbor dots. We find that, for weak coupling, the interdot Coulomb interaction dominates the formation of a collective molecular state. We also calculate the effects of correlations on the tunneling probability through the evaluation of the spectral weights, and corroborate the importance of selection rules for understanding experimental conductance spectra.     

Intersubband optical transitions in one dimensional quantum wire structures

One dimensional (1D) quantum wire structures are emerging as the new generation of semiconductor nanostructures offering exciting physical properties which have significant potential for novel device applications. These structures have been the subject of intensive investigation recently including extensive theoretical and experimental studies of their interband optical properties. In this work we present the results of our study of the intersubband optical transitions in 1D semiconductor quantum wires. The crescent shaped quantum wire structures used for this research were grown on non-planar GaAs substrates. The intersubband transition energy spectra, the selection rules, and the two dimensional envelope wavefunctions were theoretically investigated by using our new LENS (local envelope states) expansion. We present recent experimental results on modulation doped V-groove quantum wires, including PL, PLE, TEM, CL, and infrared polarization resolved spectroscopy. We have observed a very unusual absorption lineshape at the far-infrared wavelengths that we assigned to phonon assisted Fano resonance in a modulation doped quantum wire structure.     

Effect of interdiffusion on nonlinear intraband light absorption in Gaussian-shaped double quantum rings

The effect of interdiffusion on electronic states and nonlinear light absorption in Gaussian-shaped double quantum rings is studied. The confining potential, electron energy spectrum, wave functions and absorption coefficient are obtained for different values of diffusion parameter. The effect of the variation of Gaussian parameters is considered as well. The selection rules for the intraband transitions in the cases of the light polarization parallel and perpendicular to the quantum rings' axis are obtained. It is shown that the interdiffusion can be used as an effective tool for the purposeful manipulation of the electric and optical properties of the considered structure.     

Selection Rules for Multiple Quantum NMR Excitation in Solids: Derivation from Time-Reversal Symmetry and Comparison with Simulations and C NMR Experiments

New derivations of selection rules for excitation and detection of multiple quantum coherences in coupled spin-1/2 systems are presented. The selection rules apply to experiments in which the effective coupling Hamiltonian used for multiple quantum excitation is both time-reversal invariant and time-reversible by a phase shift of the radiofrequency pulse sequence that generates the effective couplings. The selection rules are shown to be consequences of time-reversal invariance and time-reversibility and otherwise independent of the specific form of the effective coupling Hamiltonian. Numerical simulations of multiple quantum NMR signal amplitudes and experimental multiple quantum excitation spectra are presented for the case of a multiply ¹³C-labeled helical polypeptide. The simulations and experiments confirm the selection rules and demonstrate their impact on multiple quantum ¹³C NMR spectra in this biochemically relevant case.     

Feature Selection for Recommender Systems with Quantum Computing

The promise of quantum computing to open new unexplored possibilities in several scientific fields has been long discussed, but until recently the lack of a functional quantum computer has confined this discussion mostly to theoretical algorithmic papers. It was only in the last few years that small but functional quantum computers have become available to the broader research community. One paradigm in particular, quantum annealing, can be used to sample optimal solutions for a number of NP-hard optimization problems represented with classical operations research tools, providing an easy access to the potential of this emerging technology. One of the tasks that most naturally fits in this mathematical formulation is feature selection. In this paper, we investigate how to design a hybrid feature selection algorithm for recommender systems that leverages the domain knowledge and behavior hidden in the user interactions data. We represent the feature selection as an optimization problem and solve it on a real quantum computer, provided by D-Wave. The results indicate that the proposed approach is effective in selecting a limited set of important features and that quantum computers are becoming powerful enough to enter the wider realm of applied science.     

Entropy of Quantum States

Given the algebra of observables of a quantum system subject to selection rules, a state can be represented by different density matrices. As a result, different von Neumann entropies can be associated with the same state. Motivated by a minimality property of the von Neumann entropy of a density matrix with respect to its possible decompositions into pure states, we give a purely algebraic definition of entropy for states of an algebra of observables, thus solving the above ambiguity. The entropy so-defined satisfies all the desirable thermodynamic properties and reduces to the von Neumann entropy in the quantum mechanical case. Moreover, it can be shown to be equal to the von Neumann entropy of the unique representative density matrix belonging to the operator algebra of a multiplicity-free Hilbert-space representation.     

Interband transitions in a spherical quantum layer in the presence of an electric field: Spherical rotator model

The interband transitions in a spherical GaAs quantum layer in the presence of an arbitrarily directed electric field are studied theoretically within the framework of the rigid spherical rotator model. The problem is solved under the assumption that the external field is a perturbation. Within the framework of the dipole approximation an expression for the interband absorption coefficient is obtained, and the absorption threshold frequency is determined. The corresponding selection rules are derived. A comparison with the case of quantum transitions in a spherical quantum layer in the presence of a radial electric field is performed.     

Dynamic Analysis for Bose-Einstein Condensation in Quantum Cavity

For the two-level atoms system interacting with single-mode active field in a quantum cavity, the dynamics of the Bose-Einstein Condensation (BEC) is analyzed using an ordinary method suggested by authors to solve the system of Schrödinger representation in the Heisenberg representation. The wave function of the atoms is given. The stability factor determining the BEC and the selection rules of the quantum transition are solved.     

Major features of frequency sweeping of emission from heterojunction quantum lasers

We have used numerical modeling to establish the major features of the variation (sweeping) of the “ instantaneous” laser frequency of heterojunction quantum lasers as a function of the pump current modulation frequency and tuning of the lasing frequency within the gain band. The active medium is described within a two-band model with identical distribution of levels for the electron and hole subbands, assuming transitions with no selection rule between the ground-state subbands. Sweeping of the laser frequency occurs due to variation of the refractive index of the active medium, as a result of the variation in the concentration of nonequilibrium charge carriers. Laser frequency sweeping does not occur for low current modulation frequencies, corresponding to realization of the quasisteady-state lasing regime. In the other limiting case of relatively high current modulation frequencies, the modulation depth of the laser output also tends toward zero. The magnitude of the sweep is greatest in the intermediate current modulation frequency region. For a specified current modulation frequency, the dynamic shift of the laser mode depends on the position of the lasing frequency within the gain band. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 74, No. 2, pp. 223–229, March–April, 2007.     

One phonon-assisted electron Raman scattering in a wurtzite cylindrical quantum well wire

We report the electron resonant Raman scattering (ERRS) process related to the longitudinal optical (LO), interface optical (IO) and quasi-confined (QC) phonons in a cylindrical GaN-AlN quantum well wire (QWW). We present the differential cross-section (DCS) and study the selection rules. Results reveal that the emitted photon frequency decreases with increasing the radius because of the size-selective Raman scattering effect and the built-in electric field. The contribution to the DCS mainly stems from the GaN-type LO (LO1), QC and IO phonons when the wire is thin, but the LO1 and QC phonons are dominant for the thick wire.     

精确的量子化条件和不变量

提出并证明了一维量子系统和三维球对称量子系统的一个精确的量子化条件.在此精确量子化条件中, 除了通常的Nπ项外, 还有一积分项, 称为修正项. 发现该修正项正是在超对称量子力学中所谓的有形状不变势的量子系统的一个不变量，它不依赖于波函数的节点数.对这些系统, 可用基态能级和波函数确定此不变量的值, 从而由精确的量子化条件容易算出全部束缚态的能级. 计算得到能级的正确性又反过来验证了在有形状不变势的量子系统中此修正项确实是不变量.计算的有形状不变势的量子系统, 包括一维的有限方势阱、Morse势及其变形、R 关键词： 量子化条件 超对称量子力学 形状不变势 不变量     

Interband transitions in a narrow-band spherical InSb quantum layer in the presence of an electric field

The interband transitions in a narrow-band InSb quantum spherical layer are studied theoretically within the framework of the spherical rotator model. The electron and light-hole dispersions are described using the two-band Kane approximation, while for heavy holes the standard dispersion is considered. The absorption coefficients for transitions between conduction and lighthole, heavy-hole bands are calculated. The selection rules and threshold absorption frequencies are determined. It is shown that in the presence of a weak electric field the selection rules and threshold absorption frequencies for dipole transitions are modified.     

Absorption interferometer of two-sided cavity

We propose a scheme in which an arbitrary incidence can be made perfectly reflected/transmitted with a phase modulator. We analyze the variation of intracavity field as well as output field with closed-loop phase φ1 of the control fields and relative phase φ2 of the probe beams. With two phases, medium absorption and light interference can be controlled so that photon escape from the cavity can be manipulated, thus an intensity switching based on phase modulation can be realized. And the condition for perfect transmitter or reflector is obtained. Then based on the transmission/reflection analysis,the total absorption of this system can be investigated. Therefore our scheme can be used as an absorption interferometer to explore the optical absorption in some complicated system. The state delay of the output light intensity, which is dependent on φ1 or φ2, can be applied in the realization of quantum phase gate and subtle wave filter. And based on this scheme, we implement the state transfer between perfect transmitter/reflector and non-perfect coherent photon absorber via relative-phase modulation.     

An Improved Analysis of Masses and Decay Constants of Heavy Flavour Mesons within Variational Approach

We employ the variational method to study the properties such as masses, decay constants, oscillation frequency and branching ratios of leptonic decays of heavy flavour mesons with linear cum coulomb Cornell potential.Gaussian function, Coulomb wave function and Airy function are taken as the trial wave-function of variational method in this study. Our analysis suggests that Gaussian trial wave-function provides results which are in close proximity with the experimental results. We also make a comparison with the results from QCD Sum rules and lattice QCD, as well as with recent PDG data.     

Quantum rules: an Effect can have more than one Operation

We review the formalism of Effects and Operations in order to demonstrate that this formalism is equivalent to the standard rules of quantum mechanics. D'Espagnat has studied an example where he finds a discrepancy between an analysis based on the standard quantum rule for calculating probabilities and an analysis that uses a particular Operation taken from the work of Barchielli and his collaborators. We use the formalism of Effects and Operations to explore and explain this discrepancy.     

Binding energy and photoionization cross-section of a hydrogen-like donor impurity in a quantum well-wire in a magnetic field

The effect of a uniform longitudinal magnetic field on the binding energy and photoionization cross-section of a hydrogen-like donor impurity is studied for a semiconductor quantum well-wire approximated by a cylindrical well of finite depth. The selection rules and analytical expressions for the photoionization cross-section are obtained depending on the magnetic field induction, impurity position, and light wave polarization.     

One‐phonon resonant electron Raman scattering in a cylindrical GaAs/AlAs quantum dot

We have presented a theoretical calculation of the differential cross section for the electron Raman scattering process associated with the interface optical phonon modes in cylindrical GaAs quantum dots (QDs) with a AlAs matrix. We consider the Fröhlich electron–phonon interaction in the framework of the dielectric continuum approach. The selection rules for the processes are studied. Singularities are found to be sensitively size‐dependent, and, by varying the size of the QDs, it is possible to control the frequency shift in the Raman spectra. A discussion of the phonon behavior for QDs with different size is presented. Copyright © 2013 John Wiley & Sons, Ltd.     

On the quantization of general relativity in anholonomic variables

In discussing Bohr-Sommerfeld-like quantum rules for gravity, it is argued that Einstein's Riemannian theory of general relativity rather leads to a quantum field-mechanics than to a quantum-field theory of gravity. We construct the canonically conjugate coordinates and momenta of this gravito-dynamics in the framework of the Einstein-Cartan teleparallelism.     

Well width‐dependent electron Raman scattering in ZnS/CdSe cylindrical quantum dot quantum well

Electron Raman scattering (ERS) is investigated in ZnS/CdSe cylindrical quantum dot quantum well (QDQW). The differential cross section (DCS) is calculated as a function of the scattering frequency and the sizes of QDQW. Single parabolic conduction and valence bands are assumed. Different scattering configurations are discussed and the selection rules for the processes are also studied. Singularities in the spectrum are found and interpreted. The ERS studied here can be used to provide direct information about the electron band structure of these systems. Copyright © 2008 John Wiley & Sons, Ltd.