With the aid of the creation operators introduced in our previous works, we show how to construct a basis of the space of quasi-local operators for the homogeneous XXZ chain.

Eigenstates of the linear combinations a 2 + βa †2 and ab + βa † b † of two boson creation and annihilation operators are presented. The algebraic procedure given here is based on the work of Shanta et al. 1994] for constructing eigenstates of generalized annihilation operators.

Positron annihilation spectroscopy is nowadays well recognised as a powerful tool of microstructure investigations of condensed matter. An overview of the method aimed for users from other fields is given and supplemented with several examples of applications.

The new closed form solutions of the (2+1)-dimensional Zabolotskaya–Khokhlov equation are constructed by using the similarity transformations method via Lie group theory. The Zabolotskaya–Khokhlov equation has been reduced into a new partial differential equation with smaller number of independent variables. Further using the similarity transformations method the new partial differential equati...

We consider a stationary, spherically outflowing wind consisting of electron-positron pairs and photons. We do not assume thermal equilibrium, and include the two-body processes that occur in such a wind: Møller and Bhaba scattering of pairs, Compton scattering, two-photon pair annihilation, and two-photon pair production, together with their radiative three-body variants: bremsstrahlung, doubl...

A probabilistic interpretation is constructed for the symmetry group G of the finite differencedifferential equation ∂tη(x, t) = η(x, t) − η(x+ 1, t) using the Doob transform for Markov (jump) processes. While the first three generators of G correspond to the identity and to space and time shifts, we show that in this interpretation the fourth generator of G is associated to time dilations and ...

so that the creation operator is separated from the annihilation one. Later, we will also need the concept of normal order ; so let us define the normal ordering symbol N() to place whatever operators in normal order, for example N ( a(p)a(k)†a(q) ) ≡ a(k)†a(p)a(q) . (4) The meaning of the “time–ordering” symbol T is well known: it instructs us to place the operators that follow in order with t...

A fully developed Bose-Einstein condensate, containing macroscopically large number of bosons can under certain conditions be considered as a generalized vacuum state. Applying the annihilation operator to the condensate hole states can be defined. Infinite ladders of such hole states can be considered as generalized coherent states of the creation operator. Dedicated to the memory of Professor...

The spectrum of gravitational waves that have been produced in innation is modiied during cosmological transitions. Large drops in the number of relativistic particles, like in the QCD transition or at the e + e ?-annihilation, lead to steps in the energy spectrum of gravitational waves.