Translation-Invariant Excitons in a Phonon Field

Large-radius excitons in polar crystals are considered. It is shown that translation invariant description of excitons interacting with a phonon field leads to a nonzero contribution of phonons into the exciton ground state energy only in the case of weak or intermediate electron-phonon coupling. A conclusion is made that self-trapped excitons cannot exist in the limit of strong coupling. Peculiarities of the absorption and emission spectra of translation invariant excitons in a phonon field are discussed. Conditions when the hydrogen-like exciton model remains valid in the case of electron-phonon interaction are found.

On the Normal Form of the Kirchhoff Equation

Consider the Kirchhoff equation $$\begin{aligned} \partial _{tt} u - \Delta u \Big ( 1 + \int _{\mathbb {T}^d} |\nabla u|^2 \Big ) = 0 \end{aligned}$$ ∂ tt u - Δ u ( 1 + ∫ T d | ∇ u | 2 ) = 0 on the d-dimensional torus $$\mathbb {T}^d$$ T d . In a previous paper we proved that, after a first step of quasilinear normal form, the resonant cubic terms show an integrable behavior, namely they give no contribution to the energy estimates. This leads to the question whether the same structure also emerges at the next steps of normal form. In this paper, we perform the second step and give a negative answer to the previous question: the quintic resonant terms give a nonzero contribution to the energy estimates. This is not only a formal calculation, as we prove that the normal form transformation is bounded between Sobolev spaces.

VECTOR AND AXIAL-VECTOR CORRELATORS AND THE FOUR-QUARK CONDENSATE

In this paper we calculate the difference between vector and axial-vector correlators with two different vertices: the bare vertex and the Ball–Chiu vertex (BC vertex) ansatz. Through the difference we compare the results drawn from the chiral sum rules. The leading nonzero contribution of the difference of the correlators in the ultraviolet identifies the four-quark condensate, which is the leading nonperturbative phenomenon in QCD. Also the pion decay constant can be drawn. For the quark propagator, we employ two different models. One is calculated in the framework of the rainbow-ladder approximation scheme in the Dyson–Schwinger approach. The other is the analytic fit employed in Ref. 1. Results show that the dressing effects of the vector and axial-vector vertices are very important.

On Finite-Temperature and Finite-Density Radiative Corrections to the Neutrino Effective Potential in the Early Universe

Finite-temperature and finite-density radiative corrections to the neutrino effective potential in the otherwise CP-symmetric early Universe are considered in the real-time approach of thermal field theory. A consistent perturbation theory endowed with the hard thermal loop resummation techniques developed by Braaten and Pisarski is applied. Special attention is focused on the question whether such corrections can generate any nonzero contribution to the CP-symmetric part of the neutrino potential, if the contact approximation for the W-propagator is used.

Anharmonic Librations and the Temperature Dependence of NQR Frequencies

The temperature dependence of NQR frequencies of nuclei in molecules undergoing quasi-har-monic rotational oscillations is calculated. Following the model proposed by Bayer, the instanta-neous orientation of the electric field gradient principal axes is assumed to change from its average orientation as a result of rotational oscillations, while the EFG magnitude remains constant. The eigenstates and energy eigenvalues of a rotator in a potential of the form V(θ)= V2θ2 - K4θ4 are calculated by standard perturbation methods, followed by the evaluation of statistical averages of square angular amplitudes. For molecular crystals with more than one molecule in a unit cell the angular displacements are expressed in terms of normal coordinates, and the same procedure is followed. The final expression for the change in the NQR frequency consists of two terms, the first one being related to the harmonic part of the potential and the second one to the quartic term. At the absolute zero it yields a nonzero contribution to ⟨θ2⟩, and for high temperatures it reproduces the nonlinear character of νQ(T) observed experimentally. The model has been tested with measure-ments on solid Cl2 performed by Nakamura and Chihara, combined with libration mode frequencies measured in Raman spectroscopy by Cahill and Leroi and analysed according to our anharmonic libration picture. The fitting of our equation to experimental data supports Cahill and Leroi's hypothesis about the existence of an undetected libration mode in Cl2 Raman spectra of frequency near 60 cm- 1

WORLD-SHEET INSTANTONS IN THE 2D BLACK HOLE

Nonperturbative effects in the gauged SL (2, R)/ U (1) WZW model, which has the black hold target space geometry, are considered. It is shown that the model has world-sheet instantons which give a nonzero contribution to the partition function. The question of the breakdown of the conformal invariance by instantons is studied. The answer depends on whether the topological term is introduced into the model or not.