Parafermionic theory with the symmetry Z5

A parafermionic conformal theory with the symmetry Z₅ is constructed, based on the second solution of Fateev–Zamolodchikov for the corresponding parafermionic chiral algebra.The primary operators of the theory, which are the singlet, doublet 1, doublet 2, and disorder operators, are found to be accommodated by the weight lattice of the classical Lie algebra B₂. The finite Kac tables for unitary theories are defined and the formula for the conformal dimensions of primary operators is given.     

The Definition of Physical Observable in Singular Systems

The explicit expression of evolution of the phase space function in time is derived. The physical observables are shown, in general, not always to have weakly vanishing Poisson brackets with all the first-class constraints according to Bergmann's physical requirement and then the corrected definition of the physical observable is given. The relations between this definition with the extended Dirac's conjecture and the gauge conditions are discussed.     

Observable Correlations in Two-Qubit States

The total correlations in a bipartite quantum state are well quantified by the quantum mutual information, the amount of which is not necessarily fully extractable by local measurements. The observable correlations are the maximal correlations that can be extracted via local measurements, and have an intuitive interpretation as a measure of classical correlations. We evaluate the observable correlations for generic two-qubit states and obtain analytical expressions in some particular cases. The intricate and subtle relationships among the total, quantum and classical correlations are illustrated in terms of observable correlations. In the course, we also disprove an intuitive conjecture of Lindblad which states that the classical correlations account for at least half of the total correlations, or equivalently, correlations are more classical than quantum.     

Observable entities in quantum-optics networks

We consider the quantum analogue of the classical Jones calculus for passive linear optical systems. Those points of the theory where quantum features have to be manifestly included are discussed. The use of different quasidistribution functions and their restrictions to the observable variables only is presented. The consistency of the theory and its usefulness are discussed.Dedicated to H. Walther on the occasion of his 60th birthday     

Paths for $${\mathcal{Z}}_k$$ Parafermionic Models

We present a simple bijection between restricted Bressoud lattice paths and paths in regime II of the Andrews–Baxter–Forrester restricted solid–on–solid model. Both types of paths describe states in parafermionic irreducible modules. The bijection implies a direct correspondence between a RSOS path and a parafermionic state in a quasi-particle basis.      

Observable radiation zeroes in HERA interactions

Radiation zeroes were discovered over 10 years ago and heralded as a direct probe of gauge couplings and fractional quark charges. Observations of such zeroes have eluded proton-antiproton collider experiments so far. We here point out that radiation zeroes appear in electron-quark collisions and conclude that they should be observable at HERA in the subprocesseqeq. Choosing suitable cuts, we expect 660 (430) events/year in the electron (positron) channel of the neutral current single jet plus direct photon events at HERA, i.e. we expect 12 (4) events/bin/year in the electron (positron) channel over a large fraction of the range of cos (10 of the 30 bins we use).     

Parafermionic polynomials,Selberg integrals and three-point correlation function in parafermionic Liouville field theory

In this paper we consider parafermionic Liouville field theory. We study integral representations of three-point correlation functions and develop a method allowing us to compute them exactly. In particular, we evaluate the generalization of Selberg integral obtained by insertion of parafermionic polynomial. Our result is justified by different approach based on dual representation of parafermionic Liouville field theory described by three-exponential model.     

Observable Relations in Relativistic Cosmology. II

Recent observations show that the assumption that the universe is isotropic and homogeneous, which forms part of current theories of the expanding universe, is probably not satisfied by the actual universe. This paper is an attempt to discover the type of relation which must hold between observable quantities if the theory of general relativity is applicable but if the assumption of isotropy and homogeneity is not made. It is first shown that Hubble's law, or something of a very similar character, must hold to a first approximation, independently of the distribution of matter. In order to relate the apparent recession of the nebulae to the distribution of matter, we must proceed to higher approximations in its relation to distance. With a certain relativistic representation of the universe in our neighbourhood, it is shown how the second approximation in the dependence of the apparent recession on distance can in fact be related to the mean density in our neighbourhood, whether or not the distribution is homogeneous or isotropic. The problem of expressing this relation in terms of quantities which are observable by astronomical methods is discussed, but is not completely solved.     

Observable manifestations of phase transitions in lasers

The well-known analogy between the Landau theory of phase transitions and lasers is discussed. It is shown that the AC-response of the output intensity to the modulation of the passive cavity losses gives an appealing correspondence to the specific heat. Experiments performed with a laser having an intracavity absorber are described to illustrate the first-order analogy.     

Observable consequences of Langmuir turbulence in active galacticnuclei

The author discusses in detail the observable consequences of nonlinear microscopic plasma processes in active galactic nuclei. The combination of several elementary momentum-gain (shock acceleration and stochastic acceleration) and momentum-loss processes (synchrotron radiation, inverse Compton scattering) produces an almost monoenergetic distribution function of relativistic electrons, called the pile-up, which excites Langmuir waves. Turbulent wave-wave and wave-particle interactions lead to nonlinear stabilization of the pile-up. The temporal and spatial evolution of the Langmuir waves and the relativistic electrons determines the shape and time scale of the spectral variations. The model is applied to extragalactic nuclei and to the galactic center as well     

Observable N-N oscillation in high scale seesaw models

We discuss a realistic high scale (nu(B-L) approximately 10(12) GeV) supersymmetric seesaw model based on the gauge group SU(2)L x SU(2)R x SU(4)c where neutron-antineutron oscillation can be in the observable range. This is contrary to the naive dimensional arguments which say that tau(N-N) is proportional to nu(B-L)5 and should therefore be unobservable for seesaw scale nu(B-L) > or = 10(5) GeV. Two reasons for this enhancement are (i) accidental symmetries which keep some of the diquark Higgs masses at the weak scale and (ii) a new supersymmetric contribution from a lower dimensional operator. The net result is that tau(N-N) is proportional to nu(B-L)2 nu(wk)3 rather than nu(B-L)5. The model also can explain the origin of matter via the leptogenesis mechanism and predicts light diquark states which can be produced at LHC.     

Observable measure of bipartite quantum correlations

We introduce a measure Q of bipartite quantum correlations for arbitrary two-qubit states, expressed as a state-independent function of the density matrix elements. The amount of quantum correlations can be quantified experimentally by measuring the expectation value of a small set of observables on up to four copies of the state, without the need for a full tomography. We extend the measure to 2×d systems, providing its explicit form in terms of observables and applying it to the relevant class of multiqubit states employed in the deterministic quantum computation with one quantum bit model. The number of required measurements to determine Q in our scheme does not increase with d. Our results provide an experimentally friendly framework to estimate quantitatively the degree of general quantum correlations in composite systems.     

Observable estimation of bipartite mixed-state entanglement

An analytic lower bound is presented for bipartite mixed-state entanglement which is obtained from convex roof construction of a variational definition of pure-state negativity. It is shown that this lower bound can be directly measured by one single projection operator or a few local observables in experiments without the requirement of simultaneous multiple copies of states. In particular, we show that the lower bound can serve as an exact entanglement measure for isotropic states.     

Observable Properties of q-Deformed Physical Systems

Letters in Mathematical Physics -     

Observable frequency shifts via spin-rotation coupling

The phase perturbation arising from spin-rotation coupling is developed as a natural extension of the celebrated Sagnac effect. Experimental evidence in support of this phase shift, however, has yet to be realized due to the exceptional sensitivity required. We draw attention to the relevance of a series of experiments establishing that circularly polarized light, upon passing through a rotating half-wave plate, is changed in frequency by twice the rotation rate. These experiments may be interpreted as demonstrating the role of spin-rotation coupling in inducing this frequency shift, thus providing direct empirical verification of the coupling of the photon helicity to rotation. A neutron interferometry experiment is proposed which would be sensitive to an analogous frequency shift for fermions. In this arrangement, polarized neutrons enter an interferometer containing two spin flippers, one of which is rotating while the other is held stationary. An observable beating in the transmitted neutron beam intensity is predicted.