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...

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...

We systematically investigate the exciton dynamics in monolayered, bilayered, and trilayered WS2 two-dimensional (2D) crystals by time-resolved photoluminescence (TRPL) spectroscopy. The exciton lifetime when free of exciton annihilation was determined to be 806 ± 37 ps, 401 ± 25 ps, and 332 ± 19 ps for WS2 monolayer, bilayer, and trilayer, respectively. By measuring the fluorescence quantum yi...

High-energy photons from pair annihilation of dark matter particles contribute to the cosmic gamma-ray background (CGB) observed in a wide energy range. The precise shape of the energy spectrum of CGB depends on the nature of dark matter particles. In order to discriminate between the signals from dark matter annihilation and other astrophysical sources, however, the information from the energy...

High-energy photons from pair annihilation of dark matter particles contribute to the cosmic gamma-ray background (CGB) observed in a wide energy range. Since dark matter particles are weakly interacting, annihilation can happen only in high density regions such as dark matter halos. The precise shape of the energy spectrum of CGB depends on the nature of dark matter particles — their mass and ...