The role of temperature dependent string-inspired CPT violating backgrounds in leptogenesis and the chiral magnetic effect.

In a temperature dependent CPT-Violating (CPTV) axial time-like background (induced by the Kalb-Ramond tensor field of string theory) we discuss leptogenesis by solving the Boltzmann equation.The current work non-trivially modifies the framework of a previous phenomenological approach by the authors where the CPTV axial background was considered to be a constant (with no microscopic justification). The constant background approximation though is shown to capture the main phenomenological features of leptogenesis. On comparing our analysis to the related chiral magnetic effect for axial current condensates, we conclude that the Kalb-Ramond field does not play the role of the chiral chemical potential needed for that effect.

Leptogenesis from heavy right-handed neutrinos in CPT violating backgrounds.

We discuss leptogenesis in a model with heavy right-handed Majorana neutrinos propagating in a constant but otherwise generic CPT-violating axial time-like background (motivated by string theory). At temperatures much higher than the temperature of the electroweak phase transition, we solve approximately, but analytically (using Padé approximants), the corresponding Boltzmann equations, which describe the generation of lepton asymmetry from the tree-level decays of heavy neutrinos into Standard Model leptons. At such temperatures these leptons are effectively massless. The current work completes in a rigorous way a preliminary treatment of the same system, by some of the present authors. In this earlier work, lepton asymmetry was crudely estimated considering the decay of a right-handed neutrino at rest. Our present analysis includes thermal momentum modes for the heavy neutrino and this leads to a total lepton asymmetry which is bigger by a factor of two as compared to the previous estimate. Nevertheless, our current and preliminary results for the freezeout are found to be in agreement (within a ∼ 12.5 % uncertainty). Our analysis depends on a novel use of Padé approximants to solve the Boltzmann equations and may be more widely useful in cosmology.

Two-Dimensional Pulse Propagation without Anomalous Dispersion.

Anomalous dispersion is a surprising phenomenon associated with wave propagation in an even number of space dimensions. In particular, wave pulses propagating in two-dimensional space change shape and develop a tail even in the absence of a dispersive medium. We show mathematically that this dispersion can be eliminated by considering a modified wave equation with two geometric spatial dimensions and, unconventionally, two timelike dimensions. Experimentally, such a wave equation describes pulse propagation in an optical or acoustic medium with hyperbolic dispersion, leading to a fundamental understanding and new approaches to ultrashort pulse shaping in nanostructured metamaterials.

On the possibility of tree-level leptogenesis from Kalb-Ramond torsion background.

In this work we consider a phenomenological model for leptogenesis in the context of a Standard Model Extension with an axial-like background coupling to fermions that violates both Lorentz and CPT symmetries. The latter is motivated by a background geometry of the early Universe involving a particular kind of torsion, arising from the Kalb-Ramond antisymmetric tensor field which appears in the gravitational multiplet of string theory, although we do not restrict ourselves to this framework. It is shown that leptogenesis can occur even at tree level and with only one generation of right-handed heavy Majorana neutrinos, due to [Formula: see text] and CPT violation introduced by the background geometry. Important issues for the model, including (a) its compatibility with a conventional-like cosmology and (b) current-era phenomenology (characterised by very stringent bounds on the allowed amount of torsion) are pointed out, and potential ways of resolving them, within the framework of string-theory models, are discussed.

Infinite class of PT-symmetric theories from one timelike Liouville Lagrangian.

Logarithmic timelike Liouville quantum field theory has a generalized PT invariance, where T is the time-reversal operator and P stands for an S-duality reflection of the Liouville field ϕ. In Euclidean space, the Lagrangian of such a theory L=1/2(∇ϕ)^{2}-igϕexp(iaϕ) is analyzed using the techniques of PT-symmetric quantum theory. It is shown that L defines an infinite number of unitarily inequivalent sectors of the theory labeled by the integer n. In one-dimensional space (quantum mechanics), the energy spectrum is calculated in the semiclassical limit and the mth energy level in the nth sector is given by E_{m,n}∼(m+1/2)^{2}a^{2}/(16n^{2}).

Optimal coupling of entangled photons into single-mode optical fibers.

We present a consistent multimode theory that describes the coupling of single photons generated by collinear Type-I parametric downconversion into single-mode optical fibers. We have calculated an analytic expression for the fiber diameter which maximizes the pair photon count rate. For a given focal length and wavelength, a lower limit of the fiber diameter for satisfactory coupling is obtained.

Theory of photon statistics and squeezing in quantum interference of a sub-threshold parametric oscillator.

A multimode theory describing quantum interference of a subthreshold optical parametric oscillator (OPO) with a coherent local oscillator (LO) in a homodyne detection scheme is presented. Analytic expressions for the count rates in terms of the correlation time and relative phase difference between the LO and OPO have been derived. The spectrum of squeezing is also derived and the threshold for squeezing obtained in terms of the crystal nonlinearity and LO and OPO beam intensities.

Photon correlations of a sub-threshold optical parametric oscillator.

A microscopic multimode theory of collinear type-I spontaneous parametric downconversion in a cavity is presented. Single-mode and multimode correlation functions have been derived using fully quantized atom and electromagnetic field variables. From a first principles calculation the FWHM of the single-mode correlation function and the cavity enhancement factor have been obtained in terms of mirror reflectivities and the first-order crystal dispersion coefficient. The values obtained are in good agreement with recent experimental results [Phys. Rev. A 62 , 033804 (2000)].