Resonant Relaxation in Electroweak Baryogenesis

We compute the leading, chiral charge-changing relaxation term in the quantum transport equations that govern electroweak baryogenesis using the closed time path formulation of non-equilibrium quantum field theory. We show that the relaxation transport coefficients may be resonantly enhanced under appropriate conditions on electroweak model parameters and that such enhancements can mitigate the impact of similar enhancements in the CP-violating source terms. We also develop a power counting in the time and energy scales entering electroweak baryogenesis and include effects through second order in ratios $\epsilon$ of the small and large scales. We illustrate the implications of the resonantly enhanced ${\cal O}(\epsilon^2)$ terms using the Minimal Supersymmetric Standard Model, focusing on the interplay between the requirements of baryogenesis and constraints obtained from collider studies, precision electroweak data, and electric dipole moment searches.Comment: 30 pages plus appendices, 7 figure

Geometrical approach to mutually unbiased bases

We propose a unifying phase-space approach to the construction of mutually unbiased bases for a two-qubit system. It is based on an explicit classification of the geometrical structures compatible with the notion of unbiasedness. These consist of bundles of discrete curves intersecting only at the origin and satisfying certain additional properties. We also consider the feasible transformations between different kinds of curves and show that they correspond to local rotations around the Bloch-sphere principal axes. We suggest how to generalize the method to systems in dimensions that are powers of a prime.Comment: 10 pages. Some typos in the journal version have been correcte

Multiexcitons confined within a sub-excitonic volume: Spectroscopic and dynamical signatures of neutral and charged biexcitons in ultrasmall semiconductor nanocrystals

The use of ultrafast gating techniques allows us to resolve both spectrally and temporally the emission from short-lived neutral and negatively charged biexcitons in ultrasmall (sub-10 nm) CdSe nanocrystals (nanocrystal quantum dots). Because of forced overlap of electronic wave functions and reduced dielectric screening, these states are characterized by giant interaction energies of tens (neutral biexcitons) to hundreds (charged biexcitons) of meV. Both types of biexcitons show extremely short lifetimes (from sub-100 picoseconds to sub-picosecond time scales) that rapidly shorten with decreasing nanocrystal size. These ultrafast relaxation dynamics are explained in terms of highly efficient nonradiative Auger recombination.Comment: 5 pages, 4 figures, to be published in Phys. Rev.

One-particle and collective electron spectra in hot and dense QED and their gauge dependence

The one-particle electron spectrum is found for hot and dense QED and its properties are investigated in comparison with the collective spectrum. It is shown that the one-particle spectrum (in any case its zero momentum limit) is gauge invariant, but the collective spectrum, being qualitatively different, is always gauge dependent. The exception is the case $m,\mu=0$ for which the collective spectrum long wavelength limit demonstrates the gauge invariance as well.Comment: 9 pages, latex, no figure

Pauli graphs when the Hilbert space dimension contains a square: why the Dedekind psi function ?

We study the commutation relations within the Pauli groups built on all decompositions of a given Hilbert space dimension $q$, containing a square, into its factors. Illustrative low dimensional examples are the quartit ($q=4$) and two-qubit ($q=2^2$) systems, the octit ($q=8$), qubit/quartit ($q=2\times 4$) and three-qubit ($q=2^3$) systems, and so on. In the single qudit case, e.g. $q=4,8,12,...$, one defines a bijection between the $\sigma (q)$ maximal commuting sets [with $\sigma[q)$ the sum of divisors of $q$] of Pauli observables and the maximal submodules of the modular ring $\mathbb{Z}_q^2$, that arrange into the projective line $P_1(\mathbb{Z}_q)$ and a independent set of size $\sigma (q)-\psi(q)$ [with $\psi(q)$ the Dedekind psi function]. In the multiple qudit case, e.g. $q=2^2, 2^3, 3^2,...$, the Pauli graphs rely on symplectic polar spaces such as the generalized quadrangles GQ(2,2) (if $q=2^2$) and GQ(3,3) (if $q=3^2$). More precisely, in dimension $p^n$ ($p$ a prime) of the Hilbert space, the observables of the Pauli group (modulo the center) are seen as the elements of the $2n$-dimensional vector space over the field $\mathbb{F}_p$. In this space, one makes use of the commutator to define a symplectic polar space $W_{2n-1}(p)$ of cardinality $\sigma(p^{2n-1})$, that encodes the maximal commuting sets of the Pauli group by its totally isotropic subspaces. Building blocks of $W_{2n-1}(p)$ are punctured polar spaces (i.e. a observable and all maximum cliques passing to it are removed) of size given by the Dedekind psi function $\psi(p^{2n-1})$. For multiple qudit mixtures (e.g. qubit/quartit, qubit/octit and so on), one finds multiple copies of polar spaces, ponctured polar spaces, hypercube geometries and other intricate structures. Such structures play a role in the science of quantum information.Comment: 18 pages, version submiited to J. Phys. A: Math. Theo

Entanglement discontinuity

We identify a class of two-mode squeezed states which are parametrized by an angular variable ${0\le\theta<2\pi}$ and a squeezing parameter $r$. We show that, for a large squeezing value, these states are either (almost) maximally entangled or product states depending on the value of $\theta$. This peculiar behavior of entanglement is unique for infinite dimensional Hilbert space and has consequences for the entangling power of unitary operators in such systems. Finally, we show that, at the limit ${r\to\infty}$ these states demonstrate a discontinuity attribute of entanglement.Comment: 5 pages, 3 figure

Effective attraction between oscillating electrons in a plasmoid via acoustic waves exchange

We consider the effective interaction between electrons due to the exchange of virtual acoustic waves in a low temperature plasma. Electrons are supposed to participate in rapid radial oscillations forming a spherically symmetric plasma structure. We show that under certain conditions this effective interaction can result in the attraction between oscillating electrons and can be important for the dynamics of a plasmoid. Some possible applications of the obtained results to the theory of natural long-lived plasma structures are also discussed.Comment: 14 pages in LaTeX2e, two columns, 3 eps figures; minimal changes, some typos are corrected; version published on-line in Proc. R. Soc.

Photothermal Absorption Spectroscopy of Individual Semiconductor Nanocrystals

Photothermal heterodyne detection is used to record the first room-temperature absorption spectra of single CdSe/ZnS semiconductor nanocrystals. These spectra are recorded in the high cw excitation regime, and the observed bands are assigned to transitions involving biexciton and trion states. Comparison with the single nanocrystals photoluminescence spectra leads to the measurement of spectral Stokes shifts free from ensemble averaging

Mathematical Simulation of the Gas-Particles Reaction Flows in Incineration of Metal-Containing Waste

A ''quasi-equilibrium'' approach for thermodynamic calculation of chemical composition and properties of metal-containing fuel combustion products has been developed and used as a part of the mathematical model of heterogeneous reacting flow which carry burning and/or evaporating particles. By using of this approach, the applicable mathematical model has been devised, which allows defining the change in chemical composition and thermal characteristics of combustion products along the incineration chamber. As an example, the simulation results of the reacting flow of magnesium-sodium nitrate-organic mixture are presented. The simulation results on the gas phase temperature in the flow of combustion products are in good agreement with those obtained experimentally. The proposed method of ''quasi-equilibrium'' thermodynamic calculation and mathematical model provide a real possibility for performing of numerical experiments on the basis of mathematical simulation of nonequilibrium flows of combustion products. Numerical experiments help correctly to estimate the work characteristics in the process of treatment devices design saving time and costs