Factorisation of analytic representations in the unit disk and number-phase statistics of a quantum harmonic oscillator

The inner-outer part factorisation of analytic representations in the unit disk is used for an effective characterisation of the number-phase statistical properties of a quantum harmonic oscillator. It is shown that the factorisation is intimately connected to the number-phase Weyl semigroup and its properties. In the Barut-Girardello analytic representation the factorisation is implemented as a convolution. Several examples are given which demonstrate the physical significance of the factorisation and its role for quantum statistics. In particular, we study the effect of phase-space interference on the factorisation properties of a superposition state.Comment: to appear in J. Phys. A, LaTeX, 13 pages, no figures. More information on http://www.technion.ac.il/~brif/science.htm

Arms Racing, Military Build-Ups and Dispute Intensity: Evidence from the Greek-Turkish Rivalry, 1985-2020

Arms races are linked in the public conscience to potential violence. Following gas discoveries in eastern Mediterranean, Greece and Turkey nearly came to blows in August 2020 and both states have enacted military expansion plans, further risking escalation. We present a novel approach to study the effect of military build-ups on dispute intensity, using monthly data on Turkish incursions into Greek-claimed airspace. Because airspace claims feature strongly in the dispute, these contestations represent an appropriate measure of the intensity with which Turkey pursues the conflict. Theoretically, we suggest that bilateral factors drive this intensity. We argue that increased Greek military capabilities deter incursions whereas increased Turkish military capabilities fuel them. Results from time-series models support the second expectation. Consequently, the study provides a novel methodological approach to studying interstate conflict intensity and shines new light on escalation dynamics in the Greek-Turkish dispute

Creating quanta with "annihilation" operator

An asymmetric nature of the boson `destruction' operator $\hat{a}$ and its `creation' partner $\hat{a}^{\dagger}$ is made apparent by applying them to a quantum state $|\psi>$ different from the Fock state $|n>$. We show that it is possible to {\em increase} (by many times or by any quantity) the mean number of quanta in the new `photon-subtracted' state $\hat{a}|\psi >$. Moreover, for certain `hyper-Poissonian' states $|\psi>$ the mean number of quanta in the (normalized) state $\hat{a}|\psi>$ can be much greater than in the `photon-added' state $\hat{a}^{\dagger}|\psi >$. The explanation of this `paradox' is given and some examples elucidating the meaning of Mandel's $q$-parameter and the exponential phase operators are considered.Comment: 10 pages, LaTex, an extended version with several references added and the text divided into sections; to appear in J. Phys.

A consistent quantum model for continuous photodetection processes

We are modifying some aspects of the continuous photodetection theory, proposed by Srinivas and Davies [Optica Acta 28, 981 (1981)], which describes the non-unitary evolution of a quantum field state subjected to a continuous photocount measurement. In order to remedy inconsistencies that appear in their approach, we redefine the `annihilation' and `creation' operators that enter in the photocount superoperators. We show that this new approach not only still satisfies all the requirements for a consistent photocount theory according to Srinivas and Davies precepts, but also avoids some weird result appearing when previous definitions are used.Comment: 12 pages, 4 figure

Exact solutions of the semi-infinite Toda lattice with applications to the inverse spectral problem

Several inverse spectral problems are solved by a method which is based on exact solutions of the semi-infinite Toda lattice. In fact, starting with a well-known and appropriate probability measure μ, the solution αn(t), bn(t) of the Toda lattice is exactly determined and by taking t=0, the solution αn(0), bn(0) of the inverse spectral problem is obtained. The solutions of the Toda lattice which are found in this way are finite for every t>0 and can also be obtained from the solutions of a simple differential equation. Many other exact solutions obtained from this differential equation show that there exist initial conditions αn(0)>0 and bn(0)∈ℝ such that the semi-infinite Toda lattice is not integrable in the sense that the functions αn(t) and bn(t) are not finite for every t>0