Evolution of complexity following a quantum quench in free field theory

Using a recent proposal of circuit complexity in quantum field theories introduced by Jefferson and Myers, we compute the time evolution of the complexity following a smooth mass quench characterized by a time scale $\delta t$ in a free scalar field theory. We show that the dynamics has two distinct phases, namely an early regime of approximately linear evolution followed by a saturation phase characterized by oscillations around a mean value. The behavior is similar to previous conjectures for the complexity growth in chaotic and holographic systems, although here we have found that the complexity may grow or decrease depending on whether the quench increases or decreases the mass, and also that the time scale for saturation of the complexity is of order $\delta t$ (not parametrically larger).Comment: V2: added references, new plots, and improved discussion of results on Section 5, V3: Few minor corrections. Published versio

Characterization of heterogeneity and spatial distribution of phases in complex solid dispersions by thermal analysis by structural characterization and X-ray micro computed tomography

Purpose: This study investigated the effect of drug-excipient miscibility on the heterogeneity and spatial distribution of phase separation in pharmaceutical solid dispersions at a micron-scale using two novel and complementary characterization techniques, thermal analysis by structural characterization (TASC) and X-ray micro-computed tomography (XCT) in conjunction with conventional characterization methods. Method: Complex dispersions containing felodipine, TPGS, PEG and PEO were prepared using hot melt extrusion-injection moulding. The phase separation behavior of the samples was characterized using TASC and XCT in conjunction with conventional thermal, microscopic and spectroscopic techniques. The in vitro drug release study was performed to demonstrate the impact of phase separation on dissolution of the dispersions. Results: The conventional characterization results indicated the phase separating nature of the carrier materials in the patches and the presence of crystalline drug in the patches with the highest drug loading (30% w/w). TASC and XCT where used to provide insight into the spatial configuration of the separate phases. TASC enabled assessment of the increased heterogeneity of the dispersions with increasing the drug loading. XCT allowed the visualization of the accumulation of phase separated (crystalline) drug clusters at the interface of air pockets in the patches with highest drug loading which led to poor dissolution performance. Semi-quantitative assessment of the phase separated drug clusters in the patches were attempted using XCT. Conclusion: TASC and XμCT can provide unique information regarding the phase separation behavior of solid dispersions which can be closely associated with important product quality indicators such as heterogeneity and microstructure

The Mixmaster Spacetime, Geroch's Transformation and Constants of Motion

We show that for $U(1)$-symmetric spacetimes on $S^3 \times R$ a constant of motion associated with the well known Geroch transformation, a functional $K[h_{ij},\pi^{ij}]$, quadratic in gravitational momenta, is strictly positive in an open subset of the set of all $U(1)$-symmetric initial data, and therefore not weakly zero. The Mixmaster initial data appear to be on the boundary of that set. We calculate the constant of motion perturbatively for the Mixmaster spacetime and find it to be proportional to the minisuperspace Hamiltonian to the first order in the Misner anisotropy variables, i.e. weakly zero. Assuming that $K$ is exactly zero for the Mixmaster spacetime, we show that Geroch's transformation, when applied to the Mixmaster spacetime, gives a new \mbox{$U(1)$-symmetric} solution of the vacuum Einstein equations, globally defined on \mbox{$S^2 \times S^1 \times R$},which is non-homogeneous and presumably exhibits Mixmaster-like complicated dynamical behavior.Comment: 25 pages, preprint YCTP-20-93, Revte

High-temperature constitutive modeling

Thermomechanical service conditions for high-temperature levels, thermal transients, and mechanical loads severe enough to cause measurable inelastic deformation are studied. Structural analysis in support of the design of high-temperature components depends strongly on accurate mathematical representations of the nonlinear, hereditary, inelastic behavior of structural alloys at high temperature, particularly in the relatively small strain range. Progress is discussed in the following areas: multiaxial experimentation to provide a basis for high-temperature multiaxial constitutive relationships; nonisothermal testing and theoretical development toward a complete thermomechanically path dependent formulation of viscoplasticity; and development of viscoplastic constitutive model accounting for initial anisotropy

Carbon Chemistry in Dense Molecular Clouds: Theory and Observational Constraints

For the most part, gas phase models of the chemistry of dense molecular clouds predict the abundances of simple species rather well. However, for larger molecules and even for small systems rich in carbon these models often fail spectacularly. We present a brief review of the basic assumptions and results of large scale modeling of the carbon chemistry in dense molecular clouds. Particular attention will be paid to the influence of the gas phase C/O ratio in molecular clouds, and the likely role grains play in maintaining this ratio as clouds evolve from initially diffuse objects to denser cores with associated stellar and planetary formation. Recent spectral line surveys at centimeter and millimeter wavelengths along with selected observations in the submillimeter have now produced an accurate "inventory" of the gas phase carbon budget in several different types of molecular clouds, though gaps in our knowledge clearly remain. The constraints these observations place on theoretical models of interstellar chemistry can be used to gain insights into why the models fail, and show also which neglected processes must be included in more complete analyses. Looking toward the future, larger molecules are especially difficult to study both experimentally and theoretically in such dense, cold regions, and some new methods are therefore outlined which may ultimately push the detectability of small carbon chains and rings to much heavier species

Predictability: a way to characterize Complexity

Different aspects of the predictability problem in dynamical systems are reviewed. The deep relation among Lyapunov exponents, Kolmogorov-Sinai entropy, Shannon entropy and algorithmic complexity is discussed. In particular, we emphasize how a characterization of the unpredictability of a system gives a measure of its complexity. Adopting this point of view, we review some developments in the characterization of the predictability of systems showing different kind of complexity: from low-dimensional systems to high-dimensional ones with spatio-temporal chaos and to fully developed turbulence. A special attention is devoted to finite-time and finite-resolution effects on predictability, which can be accounted with suitable generalization of the standard indicators. The problems involved in systems with intrinsic randomness is discussed, with emphasis on the important problems of distinguishing chaos from noise and of modeling the system. The characterization of irregular behavior in systems with discrete phase space is also considered.Comment: 142 Latex pgs. 41 included eps figures, submitted to Physics Reports. Related information at this http://axtnt2.phys.uniroma1.i

Evolution of Complexity in Out-of-Equilibrium Systems by Time-Resolved or Space-Resolved Synchrotron Radiation Techniques

Out-of-equilibrium phenomena are attracting high interest in physics, materials science, chemistry and life sciences. In this state, the study of structural fluctuations at different length scales in time and space are necessary to achieve significant advances in the understanding of structure-functionality relationship. The visualization of patterns arising from spatiotemporal fluctuations is nowadays possible thanks to new advances in X-ray instrumentation development that combine high resolution both in space and in time. We present novel experimental approaches using high brilliance synchrotron radiation sources, fast detectors and focusing optics, joint with advanced data analysis based on automated statistical, mathematical and imaging processing tools. This approach has been used to investigate structural fluctuations in out-of-equilibrium systems in the novel field of inhomogeneous quantum complex matter at the crossing point of technology, physics and biology. In particular, we discuss how nanoscale complexity controls the emergence of high temperature superconductivity (HTS), myelin functionality and formation of hybrid organic-inorganic nanostructures. The emergent complex geometries, opening novel venues to quantum technology and to development of quantum physics of living systems, are discussedComment: 18 pages, 7 figure

Interdisciplinary research on the nature and properties of ceramic materials

Several investigations concerning the properties and processing of brittle ceramic materials as related to design considerations are briefly described. Surface characterization techniques, fractography, high purity materials, creep properties, impact and thermal shock resistance, and reaction bonding are discussed

Chemistry in Dense Molecular Clouds: Theory and Observational Constraints

For the most part, gas phase models of the chemistry of dense molecular clouds predict the abundances of simple species rather well. However, for larger molecules and even for small systems rich in carbon these models often fail spectacularly. We present a brief review of the basic assumptions and results of large scale modeling of the chemistry in dense molecular clouds. Particular attention will be paid to the influence of the gas phase ratios of the major elements in molecular clouds, and the likely role grains play in maintaining these ratios as clouds evolve from initially diffuse objects to denser cores with associated stellar and planetary formation. Recent spectral line surveys at centimeter and millimeter wavelengths along with selected observations in the submillimeter have now produced an accurate "inventory" of the gas phase elemental budgets in different types of molecular clouds, though gaps in our knowledge clearly remain. The constraints these observations place on theoretical models of interstellar chemistry can be used to gain insights into why the models fail, and show also which neglected processes must be included in more complete analyses. Looking toward the future, truly protostellar regions are only now becoming available for both experimental and theoretical study, and some of the expected modifications of molecular cloud chemistry in these sources are therefore outlined

Detection of a branched alkyl molecule in the interstellar medium: iso-propyl cyanide

The largest non-cyclic molecules detected in the interstellar medium (ISM) are organic with a straight-chain carbon backbone. We report an interstellar detection of a branched alkyl molecule, iso-propyl cyanide (i-C3H7CN), with an abundance 0.4 times that of its straight-chain structural isomer. This detection suggests that branched carbon-chain molecules may be generally abundant in the ISM. Our astrochemical model indicates that both isomers are produced within or upon dust grain ice mantles through the addition of molecular radicals, albeit via differing reaction pathways. The production of iso-propyl cyanide appears to require the addition of a functional group to a non-terminal carbon in the chain. Its detection therefore bodes well for the presence in the ISM of amino acids, for which such side-chain structure is a key characteristic.Comment: This is the author's version of the work. It is posted here by permission of the AAAS for non-commercial use. The definitive version was published in Science 345, 1584 (2014), doi:10.1126/science.125667