Infrared Behavior of High-Temperature QCD

The damping rate \gamma_t(p) of on-shell transverse gluons with ultrasoft momentum p is calculated in the context of next-to-leading-order hard-thermal-loop-summed perturbation of high-temperature QCD. It is obtained in an expansion to second order in p. The first coefficient is recovered but that of order p^2 is found divergent in the infrared. Divergences from light-like momenta do also occur but are circumvented. Our result and method are critically discussed, particularly regarding a Ward identity obtained in the literature. When enforcing the equality between \gamma_t(0) and \gamma_l(0), a rough estimate of the magnetic mass is obtained. Carrying a similar calculation in the context of scalar quantum electrodynamics shows that the early ultrasoft-momentum expansion we make has little to do with the infrared sensitivity of the result.Comment: REVTEX4, 55 page

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.

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

Dynamic shear suppression in quantum phase space

© 2019 American Physical Society. All rights reserved.Classical phase space flow is inviscid. Here we show that in quantum phase space Wigner's probability current J can be effectively viscous. This results in shear suppression in quantum phase space dynamics which enforces Zurek's limit for the minimum size scale of spotty structures that develop dynamically. Quantum shear suppression is given by gradients of the quantum terms of J's vorticity. Used as a new measure of quantum dynamics applied to several evolving closed conservative 1D bound state systems, we find that shear suppression explains the saturation at Zurek's scale limit and additionally singles out special quantum states.Peer reviewe

Origin and higher-level diversification of acariform mites – evidence from nuclear ribosomal genes, extensive taxon sampling, and secondary structure alignment

Abstract Background Acariformes is the most species-rich and morphologically diverse radiation of chelicerate arthropods, known from the oldest terrestrial ecosystems. It is also a key lineage in understanding the evolution of this group, with the most vexing question whether mites, or Acari (Parasitiformes and Acariformes) is monophyletic. Previous molecular studies recovered Acari either as monophyletic or non-monophyletic, albeit with a limited taxon sampling. Similarly, relationships between basal acariform groups (include little-known, deep-soil 'endeostigmatan' mites) and major lineages of Acariformes (Sarcoptiformes, Prostigmata) are virtually unknown. We infer phylogeny of chelicerate arthropods, using a large and representative dataset, comprising all main in- and outgroups (228 taxa). Basal diversity of Acariformes is particularly well sampled. With this dataset, we conduct a series of phylogenetically explicit tests of chelicerate and acariform relationships and present a phylogenetic framework for internal relationships of acariform mites. Results Our molecular data strongly support a diphyletic Acari, with Acariformes as the sister group to Solifugae (PP =1.0; BP = 100), the so called Poecilophysidea. Among Acariformes, some representatives of the basal group Endeostigmata (mainly deep-soil mites) were recovered as sister-groups to the remaining Acariformes (i. e., Trombidiformes + and most of Sarcoptiformes). Desmonomatan oribatid mites (soil and litter mites) were recovered as the monophyletic sister group of Astigmata (e. g., stored product mites, house dust mites, mange mites, feather and fur mites). Trombidiformes (Sphaerolichida + Prostigmata) is strongly supported (PP =1.0; BP = 98–100). Labidostommatina was inferred as the basal lineage of Prostigmata. Eleutherengona (e. g., spider mites) and Parasitengona (e. g., chiggers, fresh water mites) were recovered as monophyletic. By contrast, Eupodina (e. g., snout mites and relatives) was not. Marine mites (Halacaridae) were traditionally regarded as the sister-group to Bdelloidea (Eupodina), but our analyses show their close relationships to Parasitengona. Conclusions Non-trivial relationships recovered by our analyses with high support (i.e., basal arrangement of endeostigmatid lineages, the position of marine mites, polyphyly of Eupodina) had been  proposed by previous underappreciated morphological studies. Thus, we update currently the accepted taxonomic classification to reflect these results: the superfamily Halacaroidea Murray, 1877 is moved from the infraorder Eupodina Krantz, 1978 to Anystina van der Hammen, 1972; and the subfamily Erythracarinae Oudemans, 1936 (formerly in Anystidae Oudemans, 1902) is elevated to family rank, Erythracaridae stat. ressur., leaving Anystidae only with the nominal subfamily. Our study also shows that a clade comprising early derivative Endeostigmata (Alycidae, Nanorchestidae, Nematalycidae, and maybe Alicorhagiidae) should be treated as a taxon with the same rank as Sarcoptiformes and Trombidiformes, and the scope of the superfamily Bdelloidea should  be changed. Before turning those findings into nomenclatural changes, however, we consider that our study calls for (i) finding shared apomorphies of the early derivative Endeostigmata clade and the clade including the remaining Acariformes; (ii) a well-supported hypothesis  for Alicorhagiidae placement; (iii) sampling the families Proterorhagiidae, Proteonematalycidae and Grandjeanicidae not yet included in molecular analyses; (iv) undertake a denser sampling of clades traditionally placed in Eupodina, Anystina (Trombidiformes) and Palaeosomata (Sarcoptiformes), since consensus networks and Internode certainty (IC) and IC All (ICA) indices indicate high levels of conflict in these tree regions. Our study shows that regions of ambiguous alignment may provide useful phylogenetic signal when secondary structure information is used to guide the alignment procedure and provides an R implementation to the Bayesian Relative Rates test.http://deepblue.lib.umich.edu/bitstream/2027.42/113097/1/12862_2015_Article_458.pd

MV3: A new word based stream cipher using rapid mixing and revolving buffers

MV3 is a new word based stream cipher for encrypting long streams of data. A direct adaptation of a byte based cipher such as RC4 into a 32- or 64-bit word version will obviously need vast amounts of memory. This scaling issue necessitates a look for new components and principles, as well as mathematical analysis to justify their use. Our approach, like RC4's, is based on rapidly mixing random walks on directed graphs (that is, walks which reach a random state quickly, from any starting point). We begin with some well understood walks, and then introduce nonlinearity in their steps in order to improve security and show long term statistical correlations are negligible. To minimize the short term correlations, as well as to deter attacks using equations involving successive outputs, we provide a method for sequencing the outputs derived from the walk using three revolving buffers. The cipher is fast -- it runs at a speed of less than 5 cycles per byte on a Pentium IV processor. A word based cipher needs to output more bits per step, which exposes more correlations for attacks. Moreover we seek simplicity of construction and transparent analysis. To meet these requirements, we use a larger state and claim security corresponding to only a fraction of it. Our design is for an adequately secure word-based cipher; our very preliminary estimate puts the security close to exhaustive search for keys of size < 256 bits.Comment: 27 pages, shortened version will appear in "Topics in Cryptology - CT-RSA 2007

Unpolarized states and hidden polarization

We capitalize on a multipolar expansion of the polarisation density matrix, in which multipoles appear as successive moments of the Stokes variables. When all the multipoles up to a given order $K$ vanish, we can properly say that the state is $K$th-order unpolarized, as it lacks of polarization information to that order. First-order unpolarized states coincide with the corresponding classical ones, whereas unpolarized to any order tally with the quantum notion of fully invariant states. In between these two extreme cases, there is a rich variety of situations that are explored here. The existence of \textit{hidden} polarisation emerges in a natural way in this context.Comment: 7 pages, 3 eps-color figures. Submitted to PRA. Comments welcome

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

A complementarity-based approach to phase in finite-dimensional quantum systems

We develop a comprehensive theory of phase for finite-dimensional quantum systems. The only physical requirement we impose is that phase is complementary to amplitude. To implement this complementarity we use the notion of mutually unbiased bases, which exist for dimensions that are powers of a prime. For a d-dimensional system (qudit) we explicitly construct d+1 classes of maximally commuting operators, each one consisting of d-1 operators. One of this class consists of diagonal operators that represent amplitudes (or inversions). By the finite Fourier transform, it is mapped onto ladder operators that can be appropriately interpreted as phase variables. We discuss the examples of qubits and qutrits, and show how these results generalize previous approaches.Comment: 6 pages, no figure

Quantum polarization tomography of bright squeezed light

We reconstruct the polarization sector of a bright polarization squeezed beam starting from a complete set of Stokes measurements. Given the symmetry that underlies the polarization structure of quantum fields, we use the unique SU(2) Wigner distribution to represent states. In the limit of localized and bright states, the Wigner function can be approximated by an inverse three-dimensional Radon transform. We compare this direct reconstruction with the results of a maximum likelihood estimation, finding an excellent agreement.Comment: 15 pages, 5 figures. Contribution to New Journal of Physics, Focus Issue on Quantum Tomography. Comments welcom