Angular Momentum Number Research Articles

Staggered Spin-Orbit Order: A New Paradigm of Broken Symmetry Phase of Matter

We propose a novel spin-orbit density wave order, which can arise in a variety of materials classes. In systems where the noninteracting wavefunctions are defined by an exotic quantum number such as total angular momentum, pseudospin, or helical quantum number owing to spin-orbit coupling of various natures, interaction can induce an emergent spin-orbit density wave even when time-reversal symmetry is intact. This density wave order is different from standard time-reversal breaking spin or orbital density wave. We apply this idea to explain the enigmatic “hidden order” phase in heavy fermion URu2Si2 as well as an unknown gapped quasiparticle state observed in two-dimensional electron gases, such as the surface state of BiAg2.

Angular profile of particle emission from a higher-dimensional black hole: analytic results

During the spin-down phase of the life of a higher-dimensional black hole, the emission of particles on the brane exhibits a strong angular variation with respect to the rotation axis of the black hole. It has been suggested that this angular variation is the observable that could disentangle the dependence of the radiation spectra on the number of extra dimensions and angular momentum of the black hole. Working in the low-energy regime, we have employed analytical formulae for the greybody factors, angular eigenvalues and eigenfunctions of fermions and gauge bosons, and studied the characteristics of the corresponding angular profiles of emission spectra in terms of only a few dominant partial modes. We have confirmed that, in the low-energy channel, the emitted gauge bosons become aligned to the rotation axis of the produced black hole while fermions form an angle with the rotation axis whose exact value depends on the angular-momentum of the black hole. In the case of scalar fields, we demonstrated the existence of a "spherically-symmetric zone" that is followed by the concentration of the emission on the equatorial plane, again in total agreement with the exact numerical results.

Interplay of classical and quantal features within the coherent-state model

The classical and quantal features of a quadrupole coherent state and its projections over angular momentum and boson number are quantitatively analyzed in terms of the departure of the Heisenberg uncertainty relations from the classical limit. This study is performed alternatively for two choices of the pairs of conjugate coordinates. The role of deformation as mediator of classical and quantal behaviors is also commented. Although restoring the rotational and gauge symmetries makes the quantal features manifest dominantly for small deformation, these are blurred by increasing the deformation which pushes the system toward a classical limit.

Spectroscopies of Extreme Black Holes

The spectroscopies of extreme black holes are investigated by the intrinsic property of these black holes in this paper. We find that the area spectrum of the extreme Reissner-Nordstrom black hole is dependent on the fine structure constant. While the area spectra share the same expression and are determined by the quantum numbers of angular momentum for the extreme Kerr-Sen Dilaton-Axion and Kaluza-Klein black holes.

Application of Heisenberg’s S Matrix Program to the Angular Scattering of the H + D2(vi = 0, ji = 0) → HD(vf = 3, jf = 0) + D Reaction: Piecewise S Matrix Elements Using Linear, Quadratic, Step-Function, and Top-Hat Parametrizations

A previous paper by Shan and Connor (Phys. Chem. Chem. Phys. 2011, 13, 8392) reported the surprising result that four simple parametrized S matrices can reproduce the forward-angle glory scattering of the H + D(2)(v(i)=0,j(i)=0) → HD(v(f)=3,j(f)=0) + D reaction, whose differential cross section (DCS) had been computed in a state-of-the-art scattering calculation for a state-of-the-art potential energy surface. Here, v and j are vibrational and rotational quantum numbers, respectively, and the translational energy is 1.81 eV. This paper asks the question: Can we replace the analytic functions (of class C(ω)) used by Shan-Connor with simpler mathematical functions and still reproduce the forward-angle glory scattering? We first construct S matrix elements (of class C(0)) using a quadratic phase and a piecewise-continuous pre-exponential factor consisting of three pieces. Two of the pieces are constants, with one taking the value N (a real normalization constant) at small values of the total angular momentum number, J; the other piece has the value 0 at large J. These two pieces are joined at intermediate values of J by either a straight line, giving rise to the linear parametrization (denoted param L), or a quadratic curve, which defines the quadratic parametrization (param Q). We find that both param L and param Q can reproduce the glory scattering for center-of-mass reactive scattering angles, θ(R) ≲ 30°. Second, we use a piecewise-discontinuous pre-exponential factor and a quadratic phase, giving rise to a step-function parametrization (param SF) and a top-hat parametrization (param TH). We find that both param SF and param TH can reproduce the forward-angle scattering, even though these class C(-1) parametrizations are usually considered too simplistic to be useful for calculations of DCSs. We find that an ultrasimplistic param THz, which is param TH with a phase of zero, can also reproduce the glory scattering at forward angles. The S matrix elements for param THz are real and consist of five nonzero equal values, given by S(J) = 0.02266, for the window, J = 21(1)25. Param THz is sufficiently simple that we can derive closed forms for the partial wave scattering amplitude, f(θ(R)), and the near-side (N) and far-side (F) subamplitudes. We show that window representations of f(θ(R)) provide important insights into the range of J values that contribute to the reaction dynamics. Other theoretical techniques used are NF theory for the analysis of DCSs and full and NF local angular momentum theory, in both cases including up to three resummations of f(θ(R)) before making the NF decomposition. Finally, we investigate the accuracy of various semiclassical glory theories for the DCS of param L. By varying one phase parameter for param L, we show that the uniform semiclassical approximation is accurate from θ(R) = 0° to close to θ(R) = 180°. Our approach is an example of a "weak" form of Heisenberg's S matrix program, which does not use a potential energy surface(s); rather it focuses on the properties of the S matrix. Our method is easy to apply to DCSs from experimental measurements or from computer simulations.

Effects of non-Kolmogorov Zernike tilt corrected turbulence on entangled orbital angular momentum states

Based on the paraxial approximation of Laguerre–Gaussian beam propagation in communication system, the Rytov approximation for solving the stochastic Helmholtz equation, the square approximation of the structure function, non-Kolmogorov spectrum model of index-of-refraction fluctuation in slant path, the Zernike polynomial expansion of atmospheric turbulence-aberration and the assumption of the signal photon propagation in slant Zernike tilt corrected turbulence-channel, we analyze the effect of the non-Kolmogorov residue aberrations on entangled orbital angular momentum states generated by the continuous wave pump parametric down conversion and noncollinear phase matching of signal and idler photons. The joint detection probability models of orbital angular momentum state entangled photons as a function of the propagation distance, the zenith angle θ of the communication channel, the fractal constant of the non-Kolmogorov power spectrum of atmospheric turbulence, the orbital angular momentum number of signal mode and idler mode and the structure parameter at the ground are developed, in the weak atmospheric turbulence influences region. Our results shown that the turbulent tilt aberration, corrected by adaptive optics will improve the joint detection probability of orbital angular momentum state entangled photons.

Solar turbulent magnetic fields: Non-LTE modeling of the Hanle effect in the C2molecule

Context. Scattering polarization measurements contain a wealth of information that needs a thorough interpretation. This often requires accounting for the non-local origin of photons with different frequencies and at different limb positions. Currently, modeling scattering polarization in several molecular C2 lines simultaneously is only successful for lines with similar quantum numbers. More sophisticated models are needed to understand the dependence on quantum numbers and to reliably derive the strength of the turbulent magnetic fields using the differential Hanle effect. Aims. We have developed a non-LTE analyzing technique for the C2 lines to determine the strength of turbulent magnetic fields and have applied it to observations obtained during our synoptic program at the Istituto Ricerche SOlari Locarno (IRSOL). Methods. The influence of magnetic fields on scattering polarization can be interpreted differentially, i.e., by comparing several spectral lines within one spectral region. Through the application of the differential Hanle effect and non-LTE 1D radiative transfer, we are able to infer a magnetic field strength from the photospheric C2 lines around 5141 A. Compared to previous models we include the effect of collisions and investigate their dependence on the total angular momentum number J . Results. We carry out a detailed parameter study to investigate the influence of model parameters on the resulting scattering polarization. A good fit can now be obtained for spectral lines from different C2 triplets. For the 78 measurements obtained during the solar minimum in 2007–2009 we infer a mean magnetic field strength of 7.41 G with a standard deviation of 0.76 G.

Influence of self-induced transparency on adiabatons in the lambda EIT scheme with degeneracy of levels

We present the results of numerical simulation of the adiabaton emergence process in the lambda scheme of degenerate energy levels with the quantum number of the total angular momentum,J = 0, 2, 1. In the case of linear polarisation of the input highfrequency field and circular polarisation of the input low-frequency field, the energy of the high-frequency component of the adiabatonis shown to focus in two or more pulses: in one of the pulses the field is circularly polarised in a direction opposite to that of the low-frequency input field, whereas in other pulses it is circularly polarised in the same direction as that of the field. This effect is caused by the specific character of electromagnetically induced transparency in the lambda scheme under study and by the trends introduced by self-induced transparency in it.

Anomalous paramagnetism in graphene on hexagonal boron nitride substrates

We report the static magnetization measurements of a few graphene layers on hexagonal boron nitride substrates (gra/h-BN) prepared by chemical vapor deposition. No ferromagnetic signal is detected for the gra/h-BN structures at temperatures between 5 and 300 K. At high temperatures ($Tg100$ K), the gra/h-BN structures are diamagnetic with mass magnetic susceptibilities independent of temperature and close to, or slightly larger than, that of h-BN substrates. At low temperatures ($Tl20$ K), the gra/h-BN structures exhibit paramagnetic responses, which depend sensitively on the growth time of the graphene layers. The origin of this paramagnetism is attributed to the localized spins of the point defects in the graphene layers. The angular momentum number of these spins is $J=1/2$ and is derived by fitting the magnetization data after subtraction of the diamagnetic background of the h-BN substrates to the standard Brillouin functions. A saturated mass magnetization of about 0.13 to 0.25 emu/g at $T=5$ K is estimated for our gra/h-BN samples. At temperatures between 20 and 50 K, the measured magnetic susceptibilities of the gra/h-BN samples deviate significantly from that of a Curie-type paramagnetic material. A local maximum is found in the temperature dependence of the magnetic susceptibilities of our gra/h-BN samples. Several possible explanations, including the Ruderman-Kittle-Kasuya-Yosida interactions among local magnetic moments and the itinerant electrons in the graphene/h-BN interfaces in our gra/h-BN samples, are discussed and compared to the experimental results.

Collective motion in complex nuclei

We present the implementation in the (β,γ) plane of the generator coordinate method with full triaxial angular momentum and particle number projected wave functions using the Gogny force. We apply the method to the study of 24Mg, the calculated energies of excited states as well as the transition probabilities are compared to the available experimental data showing a good overall agreement. In addition we also show preliminary results for the γ-soft nucleus 126Xe.

Cavity Ringdown Spectroscopy of PH2 Radical in 465–555 nm

Absorption spectra of jet-cooled PH2 radicals were recorded in the wavelength range of 465–555 nm using cavity ringdown spectroscopy. The PH2 radicals were produced in a supersonic jet by pulsed direct current discharge of a mixture of PH3 and SF6 in argon. Seven vibronic bands with fine rotational structures have been observed and assigned as 000, 2n0, and 2n1 (n = 1–3) bands of the Ã2A1−X̃2B1 electronic transition. Rotational assignments and rotational term values for each band were re-identified, and the molecular parameters including rotational constants, centrifugal distortion constants, and spin-rotation interaction constants were also improved with reasonably high precision. In addition, large perturbations observed in each quantum number of total angular momentum of the a axis level of the excited vibronic states were briefly discussed.

Winding-number dependence of Bose-Einstein condensates in a ring-shaped lattice

We study the winding-number dependence of the stationary states of a Bose-Einstein condensate in a ring-shaped lattice. The system is obtained by confining atoms in a toroidal trap with equally spaced radial barriers. We calculate the energy and angular momentum as functions of the winding number and the barrier height for two quite distinct particle numbers. In both cases we observe two clearly differentiated regimes. For low barriers, metastable vortex states are obtained up to a maximum winding number that depends on the particle number and barrier height. In this regime, the angular momentum and energy show, respectively, almost linear and quadratic dependences on the winding number. For large barrier heights, on the other hand, stationary states are obtained up to a maximum winding number that depends only on the number of lattice sites, whereas energy and angular momentum are shown to be sinusoidal functions of the winding number.

Covariant density functional theory with spectroscopic properties and a microscopic theory of quantum phase transitions in nuclei

Covariant Density functional theory is used as a basis for a microscopic description of spectroscopic properties of quantum phase transitions in nuclei. Since it is well known that the mean field approximation breaks down in transitional nuclei, where configuration mixing and fluctuations connected with broken symmetries play an important role, a theory is developed which uses the Relativistic Generator Coordinate Method to perform configuration mixing calculations of angular momentum and particle number projected wave functions. As applications with show 3D-calculations of the spectrum of low-lying collective states in the nucleus 24Mg. This method can also be used to study the behavior of characteristic physical quantities as a function of the physical control parameter, the number of nucleons, in the region of quantum phase transitions.

An accurate Fortran code for computing hydrogenic continuum wave functions at a wide range of parameters

Abstract The accurate computations of hydrogenic continuum wave functions are very important in many branches of physics such as electron-atom collisions, cold atom physics, and atomic ionization in strong laser fields, etc. Although there already exist various algorithms and codes, most of them are only reliable in a certain ranges of parameters. In some practical applications, accurate continuum wave functions need to be calculated at extremely low energies, large radial distances and/or large angular momentum number. Here we provide such a code, which can generate accurate hydrogenic continuum wave functions and corresponding Coulomb phase shifts at a wide range of parameters. Without any essential restrict to angular momentum number, the present code is able to give reliable results at the electron energy range [ 10 − 3 , 10 3 ] eV for radial distances of [ 10 − 2 , 10 4 ] a.u. We also find the present code is very efficient, which should find numerous applications in many fields such as strong field physics. Program summary Program title: HContinuumGautchi Catalogue identifier: AEHD_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEHD_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 1233 No. of bytes in distributed program, including test data, etc.: 7405 Distribution format: tar.gz Programming language: Fortran90 in fixed format Computer: AMD Processors Operating system: Linux RAM: 20 MBytes Classification: 2.7, 4.5 Nature of problem: The accurate computation of atomic continuum wave functions is very important in many research fields such as strong field physics and cold atom physics. Although there have already existed various algorithms and codes, most of them can only be applicable and reliable in a certain range of parameters. We present here an accurate FORTRAN program for calculating the hydrogenic continuum wave functions in a very wide range of parameters, which suffices the needs of most practical applications. The Coulomb phases are also calculated. For any given momentum, radial point, and the largest angular momentum number, the code calculates all the angular components at once. The algorithm we adopt has been given in details by Gautchi [1,2], who suggested a stable minimal solution of general three term recurrence relations. Solution method: Minimum solution of three-term recurrence relations developed by W. Gautchi [1,2]. Running time: A few seconds to a few minutes, depending how many different wave functions one needs to calculate.

Triaxial angular momentum projection and configuration mixing calculations with the Gogny force

We present the first implementation in the $(\ensuremath{\beta},\ensuremath{\gamma})$ plane of the generator coordinate method with full triaxial angular momentum and particle number projected wave functions using the Gogny force. Technical details about the performance of the method and the convergence of the results in both the symmetry restoration and the configuration mixing parts are discussed in detail. We apply the method to the study of $^{24}\mathrm{Mg}$; the calculated energies of excited states as well as the transition probabilities are compared to the available experimental data, showing a good overall agreement. In addition, we present the RVAMPIR approach, which provides a good description of the ground and $\ensuremath{\gamma}$ bands in the absence of strong mixing.

Dirac Quasinormal Modes of Reissner–Nödstrom Black Hole Surrounded by Quintessence

Using the third-order WKB approximation, we evaluate the quasinormal frequencies of massless Dirac field perturbation around a Reissner-Nördstrom black hole surrounded by a static and spherically symmetric quintessence. We study the variation of quasinormal frequencies with the quintessential state parameter ∊, the total angular momentum number |k|, the charge Q, and the overtone number n changes, respectively. Moreover, from the results we obtained, we find that the massless Dirac field damps more slowly due to the presence of quintessence.

Coulomb excitation of multiphonon levels of the giant dipole resonance

A closed expression is obtained for the cross-section for Coulomb excitation of levels of the giant dipole resonance of given angular momentum and phonon number. Applications are made to the Goldhaber-Teller and Steinwedel-Jensen descriptions of the resonance at relativistic bombarding energies.

Approximate analytical solutions of the Klein–Gordon equation with the Pöschl–Teller potential including the centrifugal term

By employing a new improved approximation scheme to deal with the centrifugal term, we solve approximately the Klein–Gordon equation with scalar and vector Pöschl–Teller potentials for the arbitrary orbital angular momentum number l. The bound state energy equation and the unnormalized radial wave functions have been approximately obtained by using the basic concept of the supersymmetric shape invariance formalism and the function analysis method. We also discuss in detail the identity of the energy spectra for the Pöschl–Teller potential in the Klein–Gordon equation and the Dirac equation under the limits of the spin symmetry and pseudospin spin symmetry.

Optimal waveform estimation for classical and quantum systems via time-symmetric smoothing. II. Applications to atomic magnetometry and Hardy’s paradox

The time-symmetric quantum smoothing theory [Tsang, Phys. Rev. Lett. 102, 250403 (2009); Phys. Rev. A 80, 033840 (2009)] is extended to account for discrete jumps in the classical random process to be estimated, discrete variables in the quantum system, such as spin, angular momentum, and photon number, and Poisson measurements, such as photon counting. The extended theory is used to model atomic magnetometers and study Hardy's paradox in phase space.

Theoretical calculation of the low-energy scattering cross sections for He-Li2 system

In this paper, the Fuchs potential model and the Close-coupling method are used to calculate the low-energy cross sections for a He-Li2 scattering system. The dependences of total cross section on energies, differential section on angles, and partial wave cross section on quantum number of total angular momentum are discussed . The quantum effect on energy obtained.