Terms Of SU Research Articles

A Spectroscopic Description of Asymmetric Isotopologues of CO2.

A polyad-conserving algebraic model applied to vibrational excitations of asymmetric isotopologues of CO2 is presented. First, the problem of vibrational excitations is studied by taking into account only the minimum subspace of states to characterize the Fermi interaction. This analysis allows an estimation of the force constants as well as the feasibility of describing the system in a local mode scheme, in terms of SU(2) operators associated with Morse ladder operators for the stretches. This description together with the algebraic U(3) for the bends establishes the dynamical group SU1(2) × U(3) × SU2(2) for a series of isotopologues. Six isotopologues are considered, namely, 16O12C18O, 16O12C17O, 16O13C18O, 16O13C17O, 17O13C18O, and 17O12C18O in their electronic ground states. For isotopologues 16O12C18O, 16O12C17O, 17O12C18O, and 16O13C18O, the vibrational description was carried out using a Hamiltonian involving 14 parameters. For this series of isotopologues with a number of energy terms 90, 57, 42, and 40, the deviations obtained were rms = 0.15, 0.10, 0.06, and 0.07 cm-1, respectively. For 16O13C17O, with 28 experimental energies and involving 13 parameters, the deviation was rms = 0.05 cm-1, while for 17O13C18O, a different strategy was proposed since only 12 experimental energy levels. In all cases, the polyad scheme P212 = 2(ν1 + ν3) + ν2 was considered. In addition, a new criterion of locality/normality degree is proposed, embracing the case of molecules with normal mode behavior, in particular, the isotopologues of CO2.

A study of the local to normal mode transition in pyramidal molecules and their vibrational description in terms of an algebraic model

First a new perspective to study the local to normal mode transition in the series of pyramidal molecules is presented. Then a full study of the vibrational excitations of the series of pyramidal molecules XH3 with X = P, As and Sb is given in the framework of a polyad-conserving Hamiltonian of a set of interacting Morse oscillators. The model is based on an algebraic representation of the Hamiltonian in terms of su(2)-operators. A simple Hamiltonian including both Fermi and Darling–Dennison interactions is considered. For the PH3 molecule a fit involving 64 experimental energies up to polyad 8 (energies up to 9054 cm−1) provided an rms=1.74cm−1 using a Hamiltonian with 14+3(frozen) parameters. For the AsH3, with 35 experimental energies the deviation obtained was rms=2.50cm−1 with 10+4 parameters. Lastly, for the SbH3 molecule, considering 23 experimental energy levels an rms=0.86cm−1 was reached with 9+6 parameters. In all cases the polyad scheme P=2(ν1+ν3)+ν2+ν4 was considered.

Inverse Holstein-Primakoff transformation of bosonic operators —Application to a bilayer model

An inversion of the Holstein-Primakoff transformation is proposed such that creation and annihilation operators for a bosonic field are rewritten as operators of an SU(2) algebra. In association with more common quadratic combinations for fermionic operators, that inverse transformation sets a quantum Hamiltonian fully in terms of SU(2) operators. A subsequent application of the prescription by Lieb, to obtain the classical limit for spin operators, then allows one to write effciently a classical Hamiltonian for the system. This process is illustrated for a bilayer model undergoing an (electron-hole)-to-exciton quantum phase transition.

Supersymmetric dS4 solutions in D = 11 supergravity

The necessary and sufficient conditions for warped product dS4 solutions in D = 11 supergravity to be supersymmetric are determined. The Killing spinor is associated with two possible stabilizer groups, SU(3) and G2. We show that there are no solutions to the Killing Spinor equations in the G2 stabilizer case. For the SU(3) stablilzer case, all of the conditions imposed from supersymmetry on the 4-form flux, and the geometry of the internal manifold, are determined in terms of SU(3) invariant spinor bilinears.

Resistance to skirt-tip with external bevels of suction caissons penetrating clay

Suction caisson is an alternative to the foundation for offshore wind turbines due to easy installation and retrieval for reuse. It is partially installed by self-weight followed by insertion to the final depth by applying suction. During suction penetration, the soil accommodated by skirt wall will move into the caisson inside, leading to soil plug heave that prevents the caisson from penetrating to the desired depth. To mitigate the effect of the soil plug heave, suction caissons are fabricated with external bevels, so as to force the more expelled soil to the outside of the caisson. This paper presents failure mechanisms for calculating the penetration resistance to skirt-tip with various external bevels under two limit conditions. For the smooth base, the failure mechanism consists of two active shear zones below the smooth base and two radial and passive shear zones that are identical to those of a deep foundation. For the rough base, two active shear zones formed below the smooth base are replaced by the radial shear zones. According to the slip-line theory, the penetration resistance of skirt-tip with various external bevels is deduced in terms of su and weighted average of σi and σo (where su is undrained shear strength, σi and σo are equivalent overburdens inside and outside the caisson at the skirt-tip level). Theoretical result shows that the resistance factor Nc of skirt-tip increases with increasing αi and αo and decreasing δ (where αi and αo are adhesion factors, and δ is the angle of external bevel from the horizontal). The difference of resistance factor Nc between rough and smooth bases identically equals 0.57. Finally, numerical simulations borrowed from the literature are used to testify the rationality of the analytical solution presented in this study.

SU(3) truncated Wigner approximation for strongly interacting Bose gases

We develop and utilize the SU(3) truncated Wigner approximation (TWA) in order to analyze far-from-equilibrium quantum dynamics of strongly interacting Bose gases in an optical lattice. Specifically, we explicitly represent the corresponding Bose-Hubbard model at an arbitrary filling factor with restricted local Hilbert spaces in terms of SU(3) matrices. Moreover, we introduce a discrete Wigner sampling technique for the SU(3) TWA and examine its performance as well as that of the SU(3) TWA with the Gaussian approximation for the continuous Wigner function. We directly compare outputs of these two approaches with exact computations regarding dynamics of the Bose-Hubbard model at unit filling with a small size and that of a fully connected spin-1 model with a large size. We show that both approaches can quantitatively capture quantum dynamics on a timescale of $\ensuremath{\hbar}/(Jz)$, where $J$ and $z$ denote the hopping energy and the coordination number. We apply the two kinds of SU(3) TWA to dynamical spreading of a two-point correlation function of the Bose-Hubbard model on a square lattice with a large system size, which has been measured in recent experiments. Noticeable deviations between the theories and experiments indicate that proper inclusion of effects of the spatial inhomogeneity, which is not straightforward in our formulation of the SU(3) TWA, may be necessary.

Weak decays of doubly heavy baryons: four-body nonleptonic decay channels

The LHCb Collaboration announced the observation of doubly charmed baryon through $$\Xi _{c c}^{++} \rightarrow \Lambda _{c}^{+} K^{-} \pi ^{+} \pi ^{+}$$ in 2017. Since then, a series of studies of doubly heavy baryons have been presented. $$\Xi _{cc}^{++}$$ was discovered through nonleptonic four-body decay mode, and experimental data have indicated that the decay modes of $$\Xi _{c c}^{++}$$ are not saturated by two- and three-body intermediate states. In this work, we analyze the four-body weak decays of doubly heavy baryons $$\Xi _{cc}^{++}, \Xi _{cc}^+$$ , and $$\Omega _{cc}^+$$ . Decay amplitudes for various channels are parameterized in terms of SU(3) irreducible amplitudes. We point out that branching fractions for Cabibbo-allowed processes $$\Xi _{cc}^{+}\rightarrow \Lambda _c^+\pi ^+ \pi ^0 K^-$$ , $$\Omega _{cc}^{+}\rightarrow \Lambda _c^+\pi ^+ {\overline{K}}^0 K^-$$ would be helpful to search for $$\Xi _{cc}^+$$ and $$\Omega _{cc}^+$$ in future measurements at experimental facilities like LHC, Belle II, and CEPC.

Euclidean LQG dynamics: an electric shift in perspective

Loop quantum gravity (LQG) is a non-perturbative attempt at quantization of a classical phase space description of gravity in terms of SU(2) connections and electric fields. As emphasized recently Ashtekar and Varadarajan (2020 arXiv:2012.12094 [gr-qc]), on this phase space, classical gravitational evolution in time can be understood in terms of certain gauge covariant generalizations of Lie derivatives with respect to a spatial SU(2) Lie algebra valued vector field called the electric shift. We present a derivation of a quantum dynamics for Euclidean LQG which is informed by this understanding. In addition to the physically motivated nature of the action of the Euclidean Hamiltonian constraint so derived, the derivation implies that the spin labels of regulating holonomies are determined by corresponding labels of the spin network state being acted upon thus eliminating the ‘spin j-ambiguity’ pointed out by Perez. By virtue of Thiemann’s seminal work, the Euclidean quantum dynamics plays a crucial role in the construction of the Lorentzian quantum dynamics so that our considerations also have application to Lorentzian LQG.

Quantum SU(2|1) supersymmetric \u2102N Smorodinsky-Winternitz system

We study quantum properties of SU(2|1) supersymmetric (deformed mathcal{N} = 4, d = 1 supersymmetric) extension of the superintegrable Smorodinsky-Winternitz system on a complex Euclidian space ℂN. The full set of wave functions is constructed and the energy spectrum is calculated. It is shown that SU(2|1) supersymmetry implies the bosonic and fermionic states to belong to separate energy levels, thus exhibiting the “even-odd” splitting of the spectra. The superextended hidden symmetry operators are also defined and their action on SU(2|1) multiplets of the wave functions is given. An equivalent description of the same system in terms of superconformal SU(2|1, 1) quantum mechanics is considered and a new representation of the hidden symmetry generators in terms of the SU(2|1, 1) ones is found.

Non-classical properties for SU(1, 1) pair coherent states

A new type of pair quantum states is introduced. Which can be considered as pair Barut-Girardello coherent states. It is an eigenstate of the operators and . We construct these eigenstates and generation scheme is proposed in terms of two mode state described in terms of su(1, 1) Lie algebra , We employ the second-order correlation function to discuss some non-classical properties,and violations of Cauchy-Schwarz inequalities. The phenomenon of squeezing is examined , squeezing is clear and Q-functions support that. Finally the phase distribution in the framework of an appropriate Pegg and Barnett formalism is considered and discussed.

Potential algebra approach to quantum mechanics with generalized uncertainty principle

In this note, we study the potential algebra for several models arising out of quantum mechanics with generalized uncertainty principle. We first show that the eigenvalue equation corresponding to the momentum-space HamiltonianH=−(1+βp2)ddp(1+βp2)ddp+g(g−1)β2p2−gβ, which is associated with some one-dimensional models with minimal length uncertainty, can be solved by the unitary representations of the Lie algebra su(2) if g∈{12,1,32,2,⋯}. We then apply this result to spectral problems for the non-relativistic harmonic oscillator as well as the relativistic Dirac oscillator in the presence of a minimal length and show that these problems can be solved solely in terms of su(2).

Weak decays of stable doubly heavy tetraquark states

In the light of the recent discovery of the $\Xi^{++}_{cc}$ by LHCb collaboration, we study the stable doubly heavy tetraquarks. These states are compact exotic hadrons which can be approximated as the diquark-anti-diquark correlations. In the flavor SU(3) symmetry, they form an SU(3) triplet or anti-sextet. The spectra of the stable doubly heavy tetraquark states are predicted by Sakharov-Zeldovich formula. We find that the $T^+_{cc\bar{u}\bar{d}}({\bf 3})$ is about 16MeV below the $DD^*$ threshold, while $T^{-}_{bb\bar{u}\bar{d}}({\bf 3})$ is about 73MeV below the $BB^*$ threshold. We then study the semileptonic and nonleptonic weak decays of the stable doubly heavy tetraquark states. The decay amplitudes are parametrized in terms of SU(3)-irreducible amplitudes. Ratios between decay widths of different channels are also derived. At the end, we collect the Cabibbo allowed two-body and three-body decay channels, which are most promising to search for the stable doubly heavy tetraquark states at LHCb and Belle II experiments.

Tribaryon configurations and the inevitable three nucleon repulsions at short distance

We decompose the tribaryon configuration in terms of SU(3) flavor and spin state and analyse their color-spin-flavor wave function following Pauli principle. By comparing the color-color and color-spin interactions of compact tribaryon configuration against the lowest three nucleon threshold within a constituent quark model, we show that the three nucleon forces have to be repulsive at short distance for all possible quantum numbers and all values of the SU(3) symmetry breaking parameter. Our work identifies the origin of the repulsive nuclear three body forces including the hyperons at short distance that are called for from phenomenological considerations starting from nuclear matter to the maximum mass of a neutron star.

Deformed mathcal{N}=8 mechanics of (8, 8, 0) multiplets

We construct new models of “curved” SU(4|1) supersymmetric mechanics based on two versions of the off-shell multiplet (8, 8, 0) which are “mirror” to each other. The worldline realizations of the supergroup SU(4|1) are treated as a deformation of flat mathcal{N}=8 , d = 1 supersymmetry. Using SU(4|1) chiral superfields, we derive invariant actions for the first-type (8, 8, 0) multiplet, which parametrizes special Kähler manifolds. Since we are not aware of a manifestly SU(4|1) covariant superfield formalism for the second-type (8, 8, 0) multiplet, we perform a general construction of SU(4|1) invariant actions for both multiplet types in terms of SU(2|1) superfields. An important class of such actions enjoys superconformal OSp(8|2) invariance. We also build off-shell actions for the SU(4|1) multiplets (6, 8, 2) and (7, 8, 1) through appropriate substitutions for the component fields in the (8, 8, 0) actions. The (6, 8, 2) actions are shown to respect superconformal SU(4|1, 1) invariance.

2-vertex Lorentzian spin foam amplitudes for dipole transitions

We compute transition amplitudes between two spin networks with dipole graphs, using the Lorentzian EPRL model with up to two (non-simplicial) vertices. We find power-law decreasing amplitudes in the large spin limit, decreasing faster as the complexity of the foam increases. There are no oscillations nor asymptotic Regge actions at the order considered, nonetheless the amplitudes still induce non-trivial correlations. Spin correlations between the two dipoles appear only when one internal face is present in the foam. We compute them within a mini-superspace description, finding positive correlations, decreasing in value with the Immirzi parameter. The paper also provides an explicit guide to computing Lorentzian amplitudes using the factorisation property of SL(2,C) Clebsch-Gordan coefficients in terms of SU(2) ones. We discuss some of the difficulties of non-simplicial foams, and provide a specific criterion to partially limit the proliferation of diagrams. We systematically compare the results with the simplified EPRLs model, much faster to evaluate, to learn evidence on when it provides reliable approximations of the full amplitudes. Finally, we comment on implications of our results for the physics of non-simplicial spin foams and their resummation.

Families from supergroups and predictions for leptonic CP violation

As was shown in 1984 by Caneschi, Farrar, and Schwimmer, decomposing representations of the supergroup SU(M |N ), can give interesting anomaly-free sets of fermion representations of SU(M ) × SU(N ) × U(1). It is shown here that such groups can be used to construct realistic grand unified models with non-abelian gauged family symmetries. A particularly simple three-family example based on SU(5) × SU(2) × U(1) is studied. The forms of the mass matrices, including that of the right-handed neutrinos, are determined in terms of SU(2) Clebsch coefficients; and the model is able to fit the lepton sector and predict the Dirac CP-violating phase of the neutrinos. Models of this type would have a rich phenomenology if part of the family symmetry is broken near the electroweak scale.

Thiemann complexifier in classical and quantum FLRW cosmology

In the context of Loop Quantum Gravity (LQG), we study the fate of Thiemann complexifier in homogeneous and isotropic FRW cosmology. The complexifier is the dilatation operator acting on the canonical phase space for gravity and generates the canonical transformations shifting the Barbero-Immirzi parameter. We focus on the closed algebra consisting in the complexifier, the 3d volume and the Hamiltonian constraint, which we call the CVH algebra. In standard cosmology, for gravity coupled to a scalar field, the CVH algebra is identified as a su(1,1) Lie algebra, with the Hamiltonian as a null generator, the complexifier as a boost and the su(1,1) Casimir given by the matter density. The loop gravity cosmology approach introduces a regularization length scale $\lambda$ and regularizes the gravitational Hamiltonian in terms of SU(2) holonomies. We show that this regularization is compatible with the CVH algebra, if we suitably regularize the complexifier and inverse volume factor. The regularized complexifier generates a generalized version of the Barbero's canonical transformation which reduces to the classical one when $\lambda \rightarrow 0$. This structure allows for the exact integration of the actions of the Hamiltonian constraints and the complexifier. This straightforwardly extends to the quantum level: the cosmological evolution is described in terms of SU(1,1) coherent states and the regularized complexifier generates unitary transformations. The Barbero-Immirzi parameter is to be distinguished from the regularization scale $\lambda$, it can be rescaled unitarily and the Immirzi ambiguity ultimately disappears from the physical predictions of the theory. Finally, we show that the complexifier becomes the effective Hamiltonian when deparametrizing the dynamics using the scalar field as a clock, thus underlining the deep relation between cosmological evolution and scale

Time-Dependent Interaction Between a Two-Level Atom and N Two-Level Atoms in Terms of su(2) Lie Algebra

We transform the nonlinear interaction between a two-level atom and two-mode fields in a frequencyconverter-type device into an inactivation governed by su(2) Lie algebra operators with phase and coupling depending on time. Under an integrability condition that relates them, we obtain a solution to the wave function. We investigate the effects of the functional dependence of the coupling and the initial state of the two-level atom on atomic inversion, entanglement, atomic variable, and entropy squeezing, as well as the autocorrelation function. The different changes for each of these phenomena are noted and displayed.

Multiconfigurational quantum propagation with trajectory-guided generalized coherent states.

A generalized version of the coupled coherent states method for coherent states of arbitrary Lie groups is developed. In contrast to the original formulation, which is restricted to frozen-Gaussian basis sets, the extended method is suitable for propagating quantum states of systems featuring diversified physical properties, such as spin degrees of freedom or particle indistinguishability. The approach is illustrated with simple models for interacting bosons trapped in double- and triple-well potentials, most adequately described in terms of SU(2) and SU(3) bosonic coherent states, respectively.

Interaction between two [formula omitted] quantum systems and a two-level atom

We consider a two-level atom interacting with two coupled quantum systems that can be represented in terms of su(1,1) Lie algebra. The wave function that is obtained using the evolution operator for the atom is initially in a superposition state and the coupled su(1,1) systems in a pair coherent Barut–Girardello coherent state. We then discuss atomic inversion, where more periods of revivals are observed and compared with a single su(1,1) quantum system. For entanglement and squeezing phenomena, the atomic angles coherence and phase as well as the detuning are effective parameters. The second-order correlation function displays Bunching and anti-Bunching behavior.