Four-pomeron vertex

The four-pomeron vertex is studied in the perturbative QCD. Its dominating terms of the leading (zeroth and first) orders in the coupling constant and subdominant in the number of colors are constructed. The vertex consists of two terms, one with a derivative in rapidity $$\partial _y$$ ∂ y and the other with the BFKL interaction between pomerons. The corresponding part of the action and equations of motion are found. The iterative solution of the latter is possible only for rapidities smaller than 2 and quite large coupling constant $$\alpha _s$$ α s , of the order or greater than unity, when the quadruple pomeron interaction is relatively small. Also iteration of the part with $$\partial _y$$ ∂ y is unstable in the infrared region and compels to introduce an infrared cut. The variational approach with simple trying functions allows to find the minimum of the action at $$\alpha _s$$ α s of the order 0.2 and rapidities up to 25. Numerical estimates for O–O collisions show that actually the influence of the quadruple pomeron interaction turns out to be rather small.

Optical properties of two-dimensional two-electron quantum dot in parabolic confinement

The Hamiltonian and wavefunctions of two-dimensional two-electron quantum dots (2D2eQD) in parabolic confinement are determined. The ground and excited state energies are calculated solving the Schrödinger equation analytically and numerically. To determine the energy eigen-value of the system variational method is employed due to the large coupling constant λ ≈ 1.1 \lambda \approx 1.1 . The trial wavefunctions are developed for both ground and excited states. The ground state wave function is a para state and the excited state wavefunctions belong to both para and ortho states based on the symmetry and antisymmetry of spatial wavefunctions. Using the obtained energy eigen-values at the two states, the first- and third-order nonlinear absorption coefficient and refractive index are analytically obtained with the help of density matrix formalism and iterative procedure.

Multiphoton annihilation of monopolium

We show that due to the large coupling constant of the monopole–photon interaction the annihilation of monopole–antimonopole and monopolium into many photons must be considered experimentally. For monopole–antimonopole annihilation and lightly bound monopolium, even in the less favorable scenario, multiphoton events (four and more photons in the final state) are dominant, while for strongly bound monopolium, although two photon events are important, four- and six-photon events are also sizable.

ON CONVERGENCE TO EQUILIBRIUM IN STRONGLY COUPLED BOGOLIUBOV'S OSCILLATOR MODEL

We examine classical Bogoliubov's model of a particle coupled to a heat bath which consists of infinitely many stochastic oscillators. Bogoliubov's result1 suggests that, in the stochastic limit, the model exhibits convergence to thermodynamical equilibrium. It has recently been shown that the system does attain the equilibrium if the coupling constant is small enough.12 We show that in the case of the large coupling constant, the distribution function ρS (q, p, t) → 0 pointwise as t → ∞. This implies that if there is convergence to equilibrium, then the limit measure has no finite momenta. Besides, the probability to find the particle in any finite domain of phase space tends to zero. This is also true for domains in the coordinate space and in the momentum space.

A NEW SYNCHRONIZATION PRINCIPLE AND APPLICATION TO CHUA'S CIRCUITS

In the paper we propose a new synchronization principle. To guarantee synchronization between coupled chaotic oscillators, proper coupling constants are selected by the Liapunov stability theory and Hurwitz Theorem. As an example and application, we prove the conjecture [Wu & Chua, 1994] that synchronization between two chaotic Chua's circuits can be achieved by using the second state as feedback variable for sufficiently large coupling constant.