Magnetopolaritons in ZnTe

From an invariant expansion, we construct the exciton Hamiltonian for the Γ₆×Γ₈ excitons in theT _d -type material ZnTe represented by an 8×8 matrix including the influences of a finite wave vector and an external magnetic field. We diagonalize the Hamiltonian matrix to obtain the exciton states. Then the excitons are coupled to the electromagnetic radiation field thus giving the polariton states. The theoretical dispersion curves are fitted to the results of two-photon Raman scattering and reflection experiments in magnetic fields up to 22 T. From this fit we deduce precise values for the eigenergies, exciton masses,g-factors, and diamagnetic shifts.     

Theory of the electronic structure of Ga1-yInyNxAs1−x and related alloys

Abstract

We present a quantitative k.P Hamiltonian which describes analytically the composition dependence of the energy gap, interband momentum matrix element, band edge effective masses and conduction band dispersion of GaN_XAs_1?x alloys for low N concentrations (x < ～ 0.05). The model has been confirmed using an sp³s? tight-binding Hamiltonian whose results agree well both with experiment and with previous pseudopotential calculations. The model should be of wide use to guide the future development of this material system and its applications.     

KaonB parameter with static cavity QCD corrections

The kaonB parameter is computed in a framework in which static cavity QCD loop corrections to the weak interactions of hadrons are included by extending the Fock state wavefunction to includeO(g) bremsstrahlung and vacuum fluctuation states. Since the QCD corrections are inherent in the calculation of the matrix elements of the bare effective weak ΔS=2 Hamiltonian between hadronic states the scale matching problem of the standard short distance analysis is alleviated. The modified static cavity model used is characterised by four parameters; the effective quarkgluon coupling constant, the confinement pressure, the zero-point energy and a parameter governing the centre-of-mass corrections. These parameters are fitted to the π and ? masses and the charge radii of π andK. Results are given for the ultra-relativistic (m _u=m _d=0) sector and for a region (m _u=m _d≈140 MeV) where the ΔI=1/2 rule is uniquely reproduced. For the parameter set which describes the ΔI=1/2 rule we findB _K=0.58 at a basis size ofN _B=6.     

Theory of the Zeeman effect in doublet states of a near-symmetric rotor: Application to the A2 ← B1 transition of ClO2

Matrix elements of the Hamiltonian for doublet states of rotating molecules in a Zeeman field are calculated in the uncoupled (J, S) representation. The energy matrix assumes a simple form for near-symmetric rotors, when the magnetic interactions are diagonal in K.     

Heavy quark 1/m Q expansion of meson weak decay form factors in the relativistic quark model

The method of systematical expansion in the inverse powers of the heavy quark masses of the weak current matrix elements between heavy meson states is developed in the framework of the relativistic quark model based on the quasipotential approach in quantum field theory. The comparison of the first and second order terms of this expansion with the structure predicted by the heavy quark effective theory imposes strong constraints on the form of the long-range confining potential of quark-antiquark interaction. It is found that the confinig $q\bar q$ potential is effectively vector, while scalar potential is anticonfining and helps to reproduce the correct nonrelativistic limit. At large distances quarks have nonperturbative anomalous chromomagnetic moments. The obtained values of the potential parameters are in accord with the ones found in our previous consideration of meson masses and decay rates. We calculate the Isgur-Wise function. The first and the second order form factors within 1/m _Q expansion.     

A new class of adiabatic cyclic states and geometric phases for non-Hermitian Hamiltonians

For a T-periodic non-Hermitian Hamiltonian H(t), we construct a class of adiabatic cyclic states of period T which are not eigenstates of the initial Hamiltonian H(0). We show that the corresponding adiabatic geometric phase angles are real and discuss their relationship with the conventional complex adiabatic geometric phase angles. We present a detailed calculation of the new adiabatic cyclic states and their geometric phases for a non-Hermitian analog of the spin 1/2 particle in a precessing magnetic field.     

Vibration-rotation energies of harmonic and combination levels in tetrahedral XY4 molecules: Theory and extrapolation method

This paper presents a general method for studying overtones and combination bands of tetrahedral XY₄ molecules. Making full use of group theory, the matrix representation of the Hamiltonian restricted to any set of vibrational sublevels is easily derived from a basis of rovibrational matrices. Explicit expressions for the reduced matrix elements are developed for all the operators of any order occurring in states for which Σ_sv_s ≤ 2, including any interaction type. The parameters introduced are directly the Hamiltonian expansion coefficients and consequently have the same physical significance in any vibrational state. The treatment of overtones and combination bands for which the corresponding fundamentals are analyzed is considered in detail. In this case, the parameters of the ground and fundamental states remain fixed and only a few new parameters occurring specifically in the studied state need to be determined. In this way, the convergence of least-squares fits is greatly improved. The example of methane is used to illustrate the efficiency of this method suitable for the direct determination of potential constants.     

Local field corrections in trigonal Se

The inverse dielectric tensor ?^-1₀₀(q) in the static limit isevaluated in crystalline Se along two symmetry directions, by using a proper model Hamiltonian describing the covalent bond and modified sp³ orbitals as basis states. By comparing the results in diagonal approximation with these obtained including the off diagonal elements (ODE) of the dielectric matrix (DM) it is found that the local field corrections are very large and essential to reproduce the experimental dielectric tensor.     

On the magnetocaloric effect in Gd(Zn1−xCdx)

In this work, we calculate the magnetocaloric effect in the compounds Gd(Zn_1−xCd_x). We use a model Hamiltonian of interacting spins in which the indirect exchange interaction parameter between localized spins was calculated as a function of Cd concentration. The calculated isothermal entropy changes and the adiabatic temperature changes upon magnetic field variations are in good agreement with the available experimental data.     

Baryogenesis via Sterile neutrino oscillation and neutrino parameters

We investigate baryogenesis in the νMSM which is the Minimal Standard Model (MSM) extended by three right-handed neutrinos with Majorana masses being smaller than the weak scale. In this model three sterile neutrinos, which are almost right-handed states, play important roles in cosmology. The baryon asymmetry of the universe (BAU) is generated via mechanism through flavor oscillation between two sterile neutrinos N₂ and N₃ which are degenerate in masses. We consider the case when BAU is solely originated from the CP violating phases in the mixing matrix of active neutrinos, i.e., the Dirac phase δ and the Majorana phase η, and study how BAU depends on these CP violating phases.     

Simultaneous analysis of the ν1, ν4, 2ν2, ν2 + ν5, and 2ν5 infrared bands of 12CH3F

The Fourier-transform spectrum of CH₃F from 2800 to 3100 cm^?1, obtained by Guelachvili in Orsay at a resolution of about 0.003 cm^?1, was analyzed. The effective Hamiltonian used contained all symmetry allowed interactions up to second order in the Amat-Nielsen classification, together with selected third-order terms, amongst the set of nine vibrational basis functions represented by the states ν₁(A₁), ν₄(E), 2ν₂(A₁), ν₂ + ν₅(E), 2ν₅⁰(A₁), and 2ν₅^±2(E). A number of strong Fermi and Coriolis resonances are involved. The vibrational Hamiltonian matrix was not factorized beyond the requirements of symmetry. A total of 59 molecular parameters were refined in a simultaneous least-squares analysis to over 1500 upper-state energy levels for J ≤ 20 with a standard deviation of 0.013 cm^?1. Although the standard deviation remains an order of magnitude greater than the precision of the measurements, this work breaks new ground in the simultaneous analysis of interacting symmetric top vibrational levels, in terms of the number of interacting vibrational states and the number of parameters in the Hamiltonian.     

Supermultiplicity and the relativistic Coulomb problem with arbitrary spin

The Hamiltonian for n relativistic electrons without interaction but in a Coulomb potential is well known. If in this Hamiltonian we take r _′ ^u =r′, P _′ ^u =P′ with u=1,2,..., n, we obtain a one-body problem in a Coulomb field, but the appearance of n of the α _u , u=1,..., n, each of which corresponds to spin $\tfrac{1}{2}$ , indicates that we may have spins up to (n/2). We analyze this last problem first by denoting the 4×4 matrices α, β as direct products of 2×2 matrices which correspond to the ordinary spin, and a new concept, also related to the SU(2) group, which we call sign spin. In this new notation our problem depends on the sixteen generators of a U(4) group reduced along the chain Û(2)??(2) sub-groups associated with the ordinary and sign spins. We now make a change of variables in our Hamiltonian so a term ε related to the frequency ω of an oscillator, which will be our variational parameter, appears in it, and later construct the full states of the problem with a harmonic oscillator of frequency 1 and ordinary and sign spin parts. Finally we obtain the matrix representation of our Hamiltonian with respect to the states mentioned and discuss the energy spectra of the problem where the partition {h} representing the irrep of U(4) and j the total angular momentum, take the values {h}=[1], j= $\tfrac{1}{2}$ ; {h}=[11], j=0; {h}=[2], j=0.     

Reggeon field theory for α(0) > 1

We obtain the asymptotic behaviour of the scattering amplitude when the pomeron has intercept α(0) larger than one. The reggeon field theory is studied by introducing a lattice in impact parameter space. Use is made of a previous result showing asymptotically the dynamics is controlled at each lattice site (α′ = 0 case) by a two-level structure. This leads to a non-Hermitean Hamiltonian expressed in terms of spin operators in which the intersite interaction terms is proportional to the pomeron slope α′. The spectrum of such a system shows a degenerate ground state for α(0) > α_c >~ 1 and a continuum with vanishing excitation gap at α(0) = α_c. The vacuum does not change structure at the critical value. The critically is shown by an order parameter which is given by the matrix element of a field operator between the vacuum and its degenerate companion. The nature of this critical phenomenon is better understood by continuously transforming the Hamiltonian into that of an Ising model with a transverse field which shows a well-known second-order phase transition. By defining the S-matrix so as to preserve the formal perturbation expansion, we find that for α(0) > α_c, the zero gap state contributes a non-trivial asymptotic constant. The final asymptotic picture is that of a gray disc expanding like log s, so that the total cross section behaves as (log s)². For α(0) < α_C, the vacuum is non-degenerate and correspondingly the total cross section drops to zero as an inverse power of s.     

Convergence properties of the Brillouin-Wigner type of perturbation expansion

We study the Brillouin-Wigner perturbation expansion of the model-space effective Hamiltonian corresponding to the full Hamiltonian H(x) = H₀ + xH₁, H₀ and H₁ being respectively the unperturbed and the interaction Hamiltonian and x being a strength parameter. The radius of convergence for the perturbation expansion is related to the poles of the energy-dependent effective interaction, and the location of these poles in the complex x-plane is discussed. The situation with poles lying off the real x-axis is examined. In terms of the spectrum of the unperturbed Hamiltonian H₀, some necessary conditions for convergence are derived, and the effects of intruder states are discussed. It is shown that the BW expansion of the ground-state energy can always be made convergent by a shift of the unperturbed energy spectrum.     

Scattering from correlated systems

A difficulty usually encountered in formulating the problem of scattering of identical particles from correlated systems is that the customary choice of an unperturbed Hamiltonian as the target Hamiltonian plus the kinetic energy of the projectile is not symmetric under particle exchange. This choice of unperturbed Hamiltonian leads to wavefunctions which, if they are antisymmetrized, are not orthonormal. In this paper an orthonormal, antisymmetrized set of basis states is constructed. These states are then used to construct a symmetric unperturbed Hamiltonian, so that a formal scattering equation with appropriate boundary conditions can be written. An expression for a T matrix describing nucleon-nucleus scattering can then be obtained. The formalism leads to a two-potential form for the T matrix, the first term of which describes the effect of the orthogonality of the scattering state and the negative energy states.     

Effect of hydrostatic pressure on the hole effective mass in a strained InGaAs/GaAs quantum well

A systematic analysis of the hydrostatic pressure effects on the effective masses of holes in strained single In_xGa_1−xAs/GaAs quantum-well (Qw) is performed. The strain effect on the shift of the subband energies and the effective masses is also investigated. A 14-band k.p Hamiltonian matrix is used in the calculations and solved by iteration with the Bir–Pikus Hamiltonian. Numerical results have been presented over a pressure range from 0 to 16 kbar. Our results show that especially for the calculation of the light-hole mass, it is necessary to use the 14-band and not the 8-band k.p model. This is supported by the fact that the 8-band k.p model predicts an increasing mass with pressure which does not reproduce the experimental results. Finally our calculations clearly confirm the available experimental results given in the literature.     

Inflation and conformal invariance: the perspective from radial quantization

According to the dS/CFT correspondence, correlators of fields generated during a primordial de Sitter phase are constrained by three‐dimensional conformal invariance. Using the properties of radially quantized conformal field theories and the operator‐state correspondence, we glean information on some points. The Higuchi bound on the masses of spin‐s states in de Sitter is a direct consequence of reflection positivity in radially quantized CFT₃ and the fact that scaling dimensions of operators are energies of states. The partial massless states appearing in de Sitter correspond from the boundary CFT₃ perspective to boundary states with highest weight for the conformal group. Finally, we discuss the inflationary consistency relations and the role of asymptotic symmetries which transform asymptotic vacua to new physically inequivalent vacua by generating long perturbation modes. We show that on the CFT₃ side, asymptotic symmetries have a nice quantum mechanics interpretation. For instance, acting with the asymptotic dilation symmetry corresponds to evolving states forward (or backward) in “time” and the charge generating the asymptotic symmetry transformation is the Hamiltonian itself.     

Unified calculations of the optical and electron paramagnetic resonance spectral data for Ce ion in Y3Ga5O12 crystal

Seven crystal field energy levels (obtained from the optical spectra) and three g factors g_x, g_y and g_z (obtained from electron paramagnetic resonance (EPR) spectra) for Ce³⁺ ion in Y₃Ga₅O₁₂ crystal are calculated together by diagonalizing a complete energy matrix. The Hamiltonian of this energy matrix includes all the interactions for 4f¹ ion Ce³⁺ in rhombic crystal field and under an external magnetic field, and so the optical and EPR data can be studied in a unified way. The calculated crystal field energy levels are in better agreement with the experimental values than the calculated values in the previous paper, and the g factors (which have not been calculated previously) are explained reasonably. The results are discussed.     

Cyclotron masses in n-GaAs/Ga 1−xAl xAs heterojunctions

Electron cyclotron resonance is studied in single layer GaAs/Ga _1−xAl _xAs heterostructures. The cyclotron mass is measured over a wide range of the two-dimensional electron density N _s and the magnetic field strength B to enable detailed comparison with self-consistent theoretical results that take into account the effects of band nonparabolicity. The calculations are performed using an effective 2 × 2 subband Hamiltonian, which is derived from a five-level k·p-model by fourth order perturbation theory and includes remote band contributions. Close agreement between experimental and theoretical cyclotron masses is achieved and the importance of band nonparabolicity in these systems is demonstrated.