The microwave spectrum of IF5 in excited vibrational states: Accidental degeneracy and avoided crossing of the kl = 3 and kl = −1 levels in the state v9(E) = 1

Measurements of the microwave spectrum of the C_4v molecule IF₅ in the excited vibrational states v₉(E) = 1 and v₅(B₁) = 1 are reported for the transitions J12 ← 11 and J13 ← 12 (65–72 GHz). The considerable spectral perturbations produced by an accidental degeneracy and avoided crossing of the ψ^? (kl = 3) and ψ^? (kl = ?1) levels of the v₉(E) = 1 state have been measured and analyzed. A spectroscopic determination of the axial rotation constant C₉ is reported and its implications for the molecular structure of IF₅ discussed.     

Description of uniform many-particle systems in density operator function space

Assuming the ground state wavefunction, ψ₀, of a boson fluid is known, and writing the excited state wavefunctions in the form Fψ₀, a linear eigenvalue equation of the form $\text{H}\text{F = EF}$ is obtained, where E₀ + $\text{E}$ is the excited state energy, E₀ is the ground state energy, and H is a non-hermitian operator which depends in a simple way upon U ≡ ln ψ₀² instead of the potential energy function. An extremum principle is derived in terms of an auxiliary hermitian Hamiltonian operator, H′. The many-body boson plane-wave basis, ?_n(k₁ … k_n) is used to express U in terms of its Fourier components (ordered conveniently in terms of the number of nonzero arguments), making it possible to calculate matrix elements of ovcirc|H and H′ in that basis. A perturbation theory similar to Brillouin-Wigner perturbation theory is developed for the non-hermitian eigenvalue problem. Nonorthogonal perturbation theory is developed for the correlated basis ?_nψ₀. The requirement that these two perturbation theories be consistent produces useful relationships between the components of U and the static structure functions of ψ₀. These relationships are shown to reduce to previous results in the extreme case of low density and weak interactions.     

Threshold singularities of theS-matrix and convergence of Haag-Ruelle approximations

We establish a one-to-one correspondence between the continuity properties of theS-matrix at the 2-particle threshold and the rate of convergence of the Haag-Ruelle approximations ψ(t) for asymptotic 2-particle states ψ with smooth wavefunctions. It turns out that the norm distance ∥ψ?ψ(t)∥ approaches 0 liktt ^?5/4 if theS-matrix has the normal threshold singularities and liket ^?3/4 in the exceptional case where the threshold has “absorbed” a bound state. These connections are valid both in relativistic quantum field theory and in non-relativistic models with short range interaction.     

Self-consistent surface calculation of electron-hole drops in gallium phosphide

Self-consistent Kohn-Sham method is used to investigate the surface structure of electron-hole drops (EHD) in GaP. If the conduction bands are located on the X-point and have a degeneracy of 3, the surface tension is found to be 85 × 10^?4 erg cm^?2. In the presence of a “camel's-back” structure and a conduction band degeneracy of 6, the surface tension is calculated to be 130 × 10^?4 erg cm^?2. The surface charge on the EHD is found to be negative irrespective of whether the conduction band degeneracy is 3 or 6.     

Exclusive J/ψ production from e + e − annihilation in SCET

We study the possibility of using soft-collinear effective theory (SCET) and non-relativistic QCD (NRQCD) to investigate the exclusive J/ψ production from e ⁺ e ^? annihilation. By performing a two-step matching at scale μ _H and μ _c respectively, we determine the SCET Wilson coefficient and run to the scale Λ～1 GeV to sum large logarithms. We apply our model to the two-body final state. In order to fit our SCET model, we estimate the upper limit on the mass of the exclusive particle. Together with the symmetry consideration, we conclude that our model is applicable to J/ψ production accompanied with an f ₂ meson or a ground state glueball. Finally, we use our results to calculate the cross section for the e ⁺ e ^?→J/ψ+f ₂(1270) process.     

Phenyl substituted Mg porphyrazines: The effect of annulation of a chalcogen-containing heterocycle on the spectral-luminescent properties

We have performed complex experimental and theoretical investigations of the spectral-luminescent properties and electronic structure of new phthalocyanine analogs, Mg octaphenylporphyrazine and its derivatives with an annulated thiadiazole or selenadiazole ring instead of two phenyl groups. Fluorescence characteristics have been determined at 293 and 77 K: emission, excitation, and fluorescence polarization spectra; fluorescence quantum yield ?? _F , and lifetime ?? _F . Annulation of a five-membered chalcogen-containing heterocycle leads to splitting of the long-wavelength absorption band Q(0-0) and to the bathochromic shift of its longest wavelength component Q _x (0-0), which increase upon passage from S to Se. At the same time, the fluorescence quantum yield ?? _F and lifetime ?? _F decrease, which is related to the intramolecular heavy-atom effect. The geometric structure of the ground state of the Mg porphyrazine molecules has been determined based on the density functional theory (DFT), and excited electronic states have been calculated with modified parametrization of the INDO/S method, INDO/Sm. Semiquantitatively, the calculated level positions of the lowest Q states and spectral shifts of Mg octaphenylporphyrazine and S-derivative agree with experimental data. For the range of the Soret band, calculated transition energies and their intensity distributions substantially depend on the dihedral angle ?? between a phenyl ring and porphyrazine macrocycle. We show that, based on calculations at the angle ?? = 60°, bands in the observed absorption spectra can be assigned with an accuracy of ??2000 cm^?1.     

Structure of Shocks in Burgers Turbulence with Lévy Noise Initial Data

We study the structure of the shocks for the inviscid Burgers equation in dimension 1 when the initial velocity is given by Lévy noise, or equivalently when the initial potential is a two-sided Lévy process ψ ₀. When ψ ₀ is abrupt in the sense of Vigon or has bounded variation with lim?sup_|h|↓0 h ^?2 ψ ₀(h)=∞, we prove that the set of points with zero velocity is regenerative, and that in the latter case this set is equal to the set of Lagrangian regular points, which is non-empty. When ψ ₀ is abrupt we show that the shock structure is discrete. When ψ ₀ is eroded we show that there are no rarefaction intervals.     

A new potential for quarkonium

We suggest a new potential for bound states of a heavy quark-antiquark pair. This potential has a logarithmic piece interpolating between a confining linear part at large distances and an asymptotically free Coulombic part at short distances. We show that the logarithmic piece of our potential considerably influences the $\text{ψ}\text{J}$-family spectrum, and dominates the ?-family. An excellent fit to the $\text{psi;}\text{J}$ data below the DD? threshold and the correct ?′?? mass splitting is obtained in a natural way. We suggest a possible test for this new potential through the leptonic widths of the ?-family.     

Local transformations of superpositions of entangled states

Suppose that we have two entangled states |?₁〉, |ψ₁〉 that cannot be converted to any of other two states |?₂〉, |ψ₂〉 by local operations and classical communication. We analyze the possibility of locally transforming a superposition of |?₁〉 and |ψ₁〉 into a superposition of |?₂〉 and |ψ₂〉. By using the Nielsen's theorem we find the necessary and sufficient conditions for this conversion to be performed.     

Zweig's rule violation,SU(3) character of the decay of the new particles,and pole dominance picture

The decays ψ′ → ψππ and ψ → ω? are studied in the framework of Zweig Rule violation via SU(4) pole dominance. The SU(3) character of the decay of the ψ is discussed in the same model. Using results of the purely hadronic decays, the cascade transition rates ψ′ → ?_c + γ and ?_carψ + γ are calculated and compared to recent experimental data.     

Partially disordered antiferromagnetic state in two-dimensional triangular-lattice antiferromagnet

The partially disordered antiferromagnetic (PDA) state, as an exotic phase peculiar to the antiferromagnet with Ising spin in triangular lattice, is investigated by using Monte Carlo simulations of Wang-Landau algorithm and Glauber algorithm. It is revealed that PDA state, as the ground state of the triangular antiferromagnetic system, presents the complicated spin configuration due to geometrical frustration. The formation of multi-domain structure within the framework of honeycomb antiferromagnet results in the high degeneracy of PDA state. And this degeneracy of ground state can be lifted by a small magnetic field. Consequently the system shows the ferrimagnetic state, and the magnetization plateau of 1/3 saturate value (Ms) is observed in many experiments. Moreover, due to the multi-domain structure of PDA state and those spins on domain walls, the metastable steps may manifest themselves superposed on the 1/3Ms plateau in some special cases.     

The electronic states of carbon monofluoride: Rydberg states

Hartree-Fock and multiconfiguration Hartree-Fock calculations are reported on some low-lying Rydberg states of CF and the ground state of CF⁺. For the CF⁺ ground state, ¹Σ⁺, the calculations give a bond length of 1.55 Å, a fundamental frequency of 1821 cm^?1, and a dissociation energy of 6.9 eV. Many interactions between the valence and Rydberg state manifolds are revealed. Also a strong mixing of the 3dσ and 4sσ components due to an accidental degeneracy is described.     

A one dimensional microscopical model for the study of the coherence in the stopping power problem. Part 3

We consider the quantum mechanical problem of a particle being scattered inelastically by a chain ofN infinitely heavy, equidistantly spaced two-level atoms. In a previous paper (Süßmann, G., Szilas, P.: Z. Phys. B — Condensed Matter42, 253 (1981)) the time dependent problem of a Gaussian wave packet impinging on the target atoms has been studied and an explicit asymptotic expression for the reduced density matrix ρ _R of the particle has been given. We now introduce the coarse grained density matrix \(\bar \rho _R\) . The incoherenceI?1-Tr( \(\bar \rho _R^2\) ), i.e. the deviation of the state of the particle from a pure state, being small on certain conditions, we find a single particle wave function ψ with \(\psi (x',t)\psi ^* (x'',t) \approx \left\langle {x'\left| {\bar \rho _R (t)} \right|x''} \right\rangle\) and a nonlinear Hermitean HamiltonianH _ψ=p ²/2m+W _ψ such thati?ψ(x, t)=H _ψψ(x, t) describes the time evolution. Finally we also considerW _ψ within the framework of the phenomenological theory of nonlinear frictional operators.     

The Geometry of the Semiclassical Wave Front Set for Schrödinger Eigenfunctions on the Torus

This paper deals with the phase space analysis for a family of Schrödinger eigenfunctions ψ _? on the flat torus ?? ⁿ = (?/2π?) ⁿ by the semiclassical Wave Front Set. We study those ψ _? such that WF_?(ψ _?) is contained in the graph of the gradient of some viscosity solutions of the Hamilton-Jacobi equation. It turns out that the semiclassical Wave Front Set of such Schrödinger eigenfunctions is stable under viscous perturbations of Mean Field Game kind. These results provide a further viewpoint, and in a wider setting, of the link between the smooth invariant tori of Liouville integrable Hamiltonian systems and the semiclassical localization of Schrödinger eigenfunctions on the torus.     

In search of the ηc

We argue that the X(2.88) detected in π^?p → γγ + n at 40 GeV/c cannot be the η_c. We discuss the possibility that a qq?cc? state is produced there, probably the same state discovered in radiative decay of the J/ψ. Only at much higher energies is the η_c expected to dominate over qq?cc? in the π^?p interaction. We also discuss coherent photoproduction and find that four quark state production would dominate over η_c.     

Non-degenerated Ground States and Low-degenerated Excited States in the Antiferromagnetic Ising Model on Triangulations

We study the unexpected asymptotic behavior of the degeneracy of the first few energy levels in the antiferromagnetic Ising model on triangulations of closed Riemann surfaces. There are strong mathematical and physical reasons to expect that the number of ground states (i.e., degeneracy) of the antiferromagnetic Ising model on the triangulations of a fixed closed Riemann surface is exponential in the number of vertices. In the set of plane triangulations, the degeneracy equals the number of perfect matchings of the geometric duals, and thus it is exponential by a recent result of Chudnovsky and Seymour. From the physics point of view, antiferromagnetic triangulations are geometrically frustrated systems, and in such systems exponential degeneracy is predicted. We present results that contradict these predictions. We prove that for each closed Riemann surface S of positive genus, there are sequences of triangulations of S with exactly one ground state. One possible explanation of this phenomenon is that exponential degeneracy would be found in the excited states with energy close to the ground state energy. However, as our second result, we show the existence of a sequence of triangulations ${(\mathcal{T}_n)}$ of a closed Riemann surface of genus 10 with exactly one ground state such that the degeneracy of each of the 1^st, 2^nd, 3^rd and 4^th excited energy levels belongs to O(n), O(n ²), O(n ³) and O(n ⁴), respectively.     

An abstract derivation of the inequality related to heisenberg's uncertainty principle

It is shown that Heisenberg's uncertainty principle can be derived from algebraic properties of observables, without involving Hilbert space formalism of quantum mechanics. Namely, if m(A,? ) denotes the statisctical second moment of an observable A measured in the state ? and we define $\text{m([A,B]),?)=}\text{1}\text{2}\text{(m(A+B,?)?m(A,?) ?(B,?))}$, then the property of oddness with respect to observables m([A,?B],?) =?m([A,B),?) implies an abstract from of Heisenberg's inequality. If, in addition, there is a canonical pair of observables A,B such that m([A,B],[?,?ψ]) =?m([A,B],[?,ψ]), then the classical uncertainty principle of Heisenberg follows. These results allow us to formulate and derive Heisenberg's principle in the framework of axiomatic quantum mechanics from an equational assumption about the profitability function of the system.     

Radiative decays of the Jψ and evidence for a new heavy resonance

The three photon final state produced in e⁺e^? collisions has been measured at the mass of the $\text{J}\text{ψ}$ resonance using the nonmagnetic part of the double arm spectrometer DASP. The decays $\text{J}\text{ψ}\text{→ ηγ, η'γ}$ and π^oγ were observed and their branching ratios are given. A four standard deviation signal was observed in the γγ mass spectrum at a mass of (2.83 ± 0.03) GeV. An upper limit is given for the direct decay $\text{J}\text{ψ}\text{→ 3γ}$.     

The theoretical basis and phenomenology of the OZI rule

No reliable theoretical recipe exists for predicting strengths of OZI-forbidden transitions proceeding via two OZI-allowed transitions like φ→K⁺K^?→?π, π^?p→K⁺K^?n→φφn or π^?p→ηn→φφn. Nonet symmetry, exchange degeneracy and duality suppress such transitions by cancellations between different diagrams. Unpredictable OZI violations are introduced by breaking of these symmetries. Phenomenological analyses of charmonium decays and meson photoproduction establish an emperical topological criterion for classifying some processes as less forbidden and suggest that π^?p→φφn should not be suppressed by a factor of more than three in amplitude. Its observation is not conclusive evidence for new exotic particles.