Spin-flavor oscillations of Dirac neutrinos described by relativistic quantum mechanics

Spin-flavor oscillations of Dirac neutrinos in matter and a magnetic field are studied using the method of relativistic quantum mechanics. Using the exact solution of the wave equation for a massive neutrino, taking into account external fields, the effective Hamiltonian governing neutrino spin-flavor oscillations is derived. Then the The consistency of our approach with the commonly used quantum mechanical method is demonstrated. The obtained correction to the usual effective Hamiltonian results in the appearance of the new resonance in neutrino oscillations. Applications to spin-flavor neutrino oscillations in an expanding envelope of a supernova are discussed. In particular, transitions between right-polarized electron neutrinos and additional sterile neutrinos are studied for realistic background matter and magnetic field distributions. The influence of other factors such as the longitudinal magnetic field, the matter polarization, and the non-standard contributions to the neutrino effective potential, is also analyzed.     

Discrete representation of the spectral shift function and the multichannel <Emphasis Type="Italic">S</Emphasis>-matrix

A new method for solving the multichannel quantum scattering problem in a wide energy range based on the single diagonalization of the Hamiltonian matrix of the system in a finite-dimensional basis is briefly described. It has been shown that the interaction-matrix-induced shifts of the eigenvalues of the free Hamiltonian matrix in the continuous spectrum are directly related to the partial phase shifts. The two-channel scattering problem with shifted channel thresholds is considered for illustration.     

Quantum resonances of the kicked rotor and the SU(q) group

The quantum kicked rotor map is embedded into a continuous unitary transformation generated by a time-independent quasi Hamiltonian. In some vicinity of a quantum resonance of order q, we relate the problem to the regular motion along a circle in a (q(2)-1) component inhomogeneous "magnetic" field of a quantum particle with q intrinsic degrees of freedom described by the SU(q) group. This motion is in parallel with the classical phase oscillations near a nonlinear resonance.     

Four-band Hamiltonian for fast calculations in intermediate-band solar cells

The 8-dimensional Luttinger–Kohn–Pikus–Bir Hamiltonian matrix may be made up of four 4-dimensional blocks. A 4-band Hamiltonian is presented, obtained from making the non-diagonal blocks zero. The parameters of the new Hamiltonian are adjusted to fit the calculated effective masses and strained QD bandgap with the measured ones. The 4-dimensional Hamiltonian thus obtained agrees well with measured quantum efficiency of a quantum dot intermediate band solar cell and the full absorption spectrum can be calculated in about two hours using Mathematica© and a notebook. This is a hundred times faster than with the commonly-used 8-band Hamiltonian and is considered suitable for helping design engineers in the development of nanostructured solar cells.     

Off-resonant two-photon-assisted electron transfer between quantum dots

Electron transfer between bound states of remote quantum dots driven by an off-resonant electromagnetic pulse is analyzed. In the case of nearly equal energies of the states, a two-photon transfer mechanism related to the high-frequency off-resonant Stark effect is proposed. An equivalent transformation is used to derive an effective Hamiltonian that provides a basis for correct treatment of continuum (conduction-band) states. It is shown that optimal conditions for electron transfer correspond to quasi-resonant excitation of states near the lower edge of the continuum. The characteristics of the process are evaluated.     

Topological transitions in size-quantized heterostructures

An exact solution is obtained to the problem of the spectrum of holes, described by the Luttinger Hamiltonian, in a quantum well of finite depth under arbitrary uniaxial stresses in the well and the barrier. Conditions for the topological transitions accompanied by the variation in the connectivity of the isoenergetic surface are found. It is shown that, for certain values of model parameters, the effective mass of holes in the ground-state subband of size quantization becomes negative.     

A quasi-energy operator in the Jaynes-Cummings model in a polychromatic classical field

A perturbation theory is developed for constructing the quasi-energy operator Q of the Tavis-Cummings Hamiltonian, which includes the interaction of atoms with a classical quasi-monochromatic field. The operator Q of the first order in the interaction δ of an atom with a resonator mode has a form of the generalized Tavis-Cummings Hamiltonian (in the interaction representation) to which the oppositely rotating terms with a changed interaction constant are added. Such a Hamiltonian has a singularity in the dimensionless amplitude σ of a classical field. In the vicinity of this singularity, the Hamiltonian spectrum tends to a continuous one, while the degree of squeezing of field quadratures (in its eigenstates) increases infinitely. In the case of one atom and the biharmonic perturbation, the operator Q is obtained up to the third order of the perturbation theory. The spectral problem for Q is studied. The features of the dependence of the quasi-energy spectrum on σ are explained by the presence of an efficient barrier between the regions of the “coordinate” space. It is found that the above-mentioned singularity corresponds to the beginning of the parametric resonance zone. Analytic expressions for the top and bottom of this zone in the δσ plane are presented.     

垂直耦合自组织InAs双量子点中激子能的计算

在有效质量近似条件下研究了垂直耦合的自组织InAs/GaAs量子点的激子态.在绝热近似条件下，采用传递矩阵方法计算了电子和空穴的能谱.通过哈密顿量矩阵的对角化，对电子和空穴间的库仑相互作用进行了精确处理.讨论了两量子点间的垂直距离对激子基态能的影响.从基态波函数概率分布的角度，讨论了激子的束缚能.计算了重空穴和轻空穴激子的基态能随外部垂直磁场变化的函数关系.计算了量子点大小（量子点半径）对激子能的影响. 关键词： 量子点 激子 对角化     

Energy spectrum and coupling intensity between three helical chains in α-helical protein molecules

A new Hamiltonian of α-helical protein molecules is presented according to the mechanism of interaction between their components. We obtain the Raman spectrum of the protein molecules on the basis of the Hamiltonian and quantum transition theory. The coupling intensity between the main chain and side chains of the molecules is obtained by comparing with the laser-Raman spectrum experimentally measured.     

Renormalization of the energy spectrum of quantum dots under vibrational resonance conditions: Persistent hole burning spectroscopy

A theory of photophysical burning of spectral holes in an inhomogeneously broadened light absorption profile of spherical quantum dots under vibrational resonance conditions is developed. The energy spectrum and the eigenfunctions of polaron-like excitations that arise in a quantum dot when the energy of an optical phonon is close to the energy gap between some pair of levels of the quantum dot electron subsystem are found by the method of canonical transformations. Expressions describing the difference light absorption spectra of quantum dots in the regimes of strong and weak confinement are obtained within a simple kinetic model.     

From quantum mechanics to classical statistical physics: Generalized Rokhsar-Kivelson Hamiltonians and the “Stochastic Matrix Form” decomposition

Quantum Hamiltonians that are fine-tuned to their so-called Rokhsar-Kivelson (RK) points, first presented in the context of quantum dimer models, are defined by their representations in preferred bases in which their ground state wave functions are intimately related to the partition functions of combinatorial problems of classical statistical physics. We show that all the known examples of quantum Hamiltonians, when fine-tuned to their RK points, belong to a larger class of real, symmetric, and irreducible matrices that admit what we dub a Stochastic Matrix Form (SMF) decomposition. Matrices that are SMF decomposable are shown to be in one-to-one correspondence with stochastic classical systems described by a Master equation of the matrix type, hence their name. It then follows that the equilibrium partition function of the stochastic classical system partly controls the zero-temperature quantum phase diagram, while the relaxation rates of the stochastic classical system coincide with the excitation spectrum of the quantum problem. Given a generic quantum Hamiltonian construed as an abstract operator defined on some Hilbert space, we prove that there exists a continuous manifold of bases in which the representation of the quantum Hamiltonian is SMF decomposable, i.e., there is a (continuous) manifold of distinct stochastic classical systems related to the same quantum problem. Finally, we illustrate with three examples of Hamiltonians fine-tuned to their RK points, the triangular quantum dimer model, the quantum eight-vertex model, and the quantum three-coloring model on the honeycomb lattice, how they can be understood within our framework, and how this allows for immediate generalizations, e.g., by adding non-trivial interactions to these models.     

Selected aspects of the quantum dynamics and electronic structure of atoms in magnetic microtraps

We analyze the quantum properties of atoms in a magnetic quadrupole field. The quantum dynamics of ground state atoms in this field configuration is studied firstly. We formulate the Hamiltonian and perform a symmetry analysis. Due to the particular shape of the quadrupole field in general there exist no stable states. We provide resonance energies, lifetimes and calculate the density of states and investigate under what conditions quasi-bound states occur that possess long lifetimes. An effective scalar Schrödinger equation describing such states is derived. As a next step we explore the influence of a high gradient quadrupole field on the electronic structure of excited atoms. An effective one-body approach together with the fixed nucleus approximation is employed in order to derive the electronic Hamiltonian. We present the energy spectrum and discuss peculiar features such as non-trivial spin densities and magnetic field induced electric dipole moments.     

Dynamics of classically chaotic quantum systems in Wigner representation

The dynamics of a quantum rotator kicked by a periodic succession of δ-pulses is analysed in the Wigner representation. If the quantum resonance condition does not hold the quasi-energy wave functions are shown not to belong to a certain class of functions of the continuous spectrum. Exact quantum mappings for the rotator model are obtained and the influence of the discreteness of the phase space on the time behavior of the quantum correlation functions is analysed.     

On the Lorentz group SO(3, 1), geometrical supersymmetric action for particles, and square root operators

In this work the problem of the square-root quantum operators is analyzed from the theoretical group point of view. To this end, we considered the relativistic geometrical action of a particle in the superspace in order to quantize it and to obtain the spectrum of physical states with the Hamiltonian remaining in the natural square-root form. The generators of group SO(3, 1) are introduced and the quantization of this model is performed completely. The obtained spectrum of physical states and the Fock construction for the physical states from the Hamiltonian operator in square-root form was proposed, explicitly constructed, and compared with the spectrum and Fock construction obtained from the Hamiltonian in the standard form (i.e., quadratic in momenta). We show that the only states that the square-root Hamiltonian can operate with correspond to the representations with the lowest weights λ = 1/4 and 3/4 with four possible (nontrivial) fractional representations for the group decomposition of the spin structure. The text was submitted by the author in English.     

Effects of vibrational intercentre interaction in a trigonal two-centre system with twofold electronic degeneracy at each centre

The effect of intercentre interaction (via vibrations and electron-electron coupling) on the magnetic and magnetic resonance characteristics of a pair of Jahn-Teller centres is investigated. In the limiting case of strong vibronic coupling when the splitting of degenerate electronic terms is sufficiently large the exchange Hamiltonian for the pair has the Heisenberg form. The energy spectrum of spin states of the pair system is obtained and the temperature dependence of the effective magnetic moment is investigated. It is shown that under some conditions this temperature dependence has an anomalous nonmonotonic character. The g factors of the two-centre Jahn-Teller system are obtained and the changes of the EPR spectrum with the exchange and vibrational coupling constants is analysed. With inclusion of only the exchange interaction, the pair spectrum possesses an additional isotropic resonance placed in the middle of the known broadened EPR spectrum of single centres with the Jahn-Teller effect for an orbital E term. The vibrational interaction between the centres results in a radical transformation of the spectrum, which in this case contains only an isotropic resonance line.     

基于电子顺磁共振的ZnTPP激发态及其TEMPO各向异性的研究

为了研究卟啉类敏化剂的光致激发态能量转移和电子转移问题,本文基于紫外可见光谱仪和电子顺磁共振波谱仪,构建了以锌卟啉为研究对象的"锌卟啉-稳态自由基-二甲苯"实验体系.锌卟啉的紫外可见光谱显示,在可见光谱的B带和Q带出现明显的特征峰,是锌卟啉分子中电子由基态能级跃迁至激发态能级产生的.低温条件下受紫外可见光辐照的实验体系的电子顺磁共振波谱,检测到了稳态自由基四甲基哌啶氧化物的增强吸收电子顺磁共振波谱.根据分子激发态相关理论、光化学物理反应理论和化学诱导电子自旋极化理论对实验结果进行了分析,结果表明,四甲基哌啶氧化物稳态自由基电子顺磁共振波谱的增强吸收对应于锌卟啉光致激发态的能量转移和电子转移;四甲基哌啶氧化物在低温(143 K)下的电子顺磁共振波谱表现出的各向异性特征现象来源于氮氧自由基电子与氮核的各向异性超精细相互作用.     

芳香分子的发光

芳香分子具有属于整个分子的π电子,它决定了芳香分子一般都具有很强的荧光。研究芳香分子的π电子光谱是量子化学的专门课题。常见的理论方法有;Hückel分子轨道理论,Platt环自由电子轨道模型和PPP近似。芳香分子的发光特性决定于分子的结构,例如,分子的刚性、平面性、取代基及其空间特性等等。芳香分子处于蒸汽和单晶状态或溶解在溶剂和固溶体(例如塑料)中,必然发生分子之间的相互作用和能量传递。分子之间的能量传递有多种方式,例如辐射传递、扩散控制过程、激子扩散、共振传递、交换传递和激光的形成与分解等等。     

Electron energy state spin-splitting in 3D cylindrical semiconductor quantum dots

In this article we study the impact of the spin-orbit interaction on the electron quantum confinement for narrow gap semiconductor quantum dots. The model formulation includes: (1) the effective one-band Hamiltonian approximation; (2) the position- and energy-dependent quasi-particle effective mass approximation; (3) the finite hard wall confinement potential; and (4) the spin-dependent Ben Daniel-Duke boundary conditions. The Hartree-Fock approximation is also utilized for evaluating the characteristics of a two-electron quantum dot system. In our calculation, we describe the spin-orbit interaction which comes from both the spin-dependent boundary conditions and the Rashba term (for two-electron quantum dot system). It can significantly modify the electron energy spectrum for InAs semiconductor quantum dots built in the GaAs matrix. The energy state spin-splitting is strongly dependent on the dot size and reaches an experimentally measurable magnitude for relatively small dots. In addition, we have found the Coulomb interaction and the spin-splitting are suppressed in quantum dots with small height. Received 15 May 2001 / Received in final form 14 May 2002 Published online 13 August 2002     

Primordial power spectrum from the Dapor–Liegener model of loop quantum cosmology

We compute the predictions for the power spectrum of scalar perturbations from a recent new proposal for the effective Hamiltonian of loop quantum cosmology. The model provides an attractive picture of the early cosmos, in which our classical Friedmann–Lemaître–Robertson–Walker universe emerges from a quantum phase where the spacetime curvature remains constant and of Planckian size. We compare the predictions for the cosmic microwave background with previous results obtained within loop quantum cosmology, and discuss the differences and similarities. The analysis provides an example of the way differences between quantization schemes can be translated to physical observables.     

Adiabatic theorem and generalized geometrical phase in the case of continuous spectra

By defining "a virtual gap" for the continuous spectrum through the notion of eigendifferential (Weyl's packet) and using the differential projector operator, we present a rigorous demonstration and discussion of the quantum adiabatic theorem for systems having a nondegenerate continuous spectrum. An explicit formula for a generalized geometrical phase is derived in terms of the eigenstates of the Hamiltonian. Examples are given for illustration.