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Symmetry in Quantum Optics Models

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ISBN: 9783039218585 / 9783039218592 Year: Pages: 92 DOI: 10.3390/books978-3-03921-859-2 Language: eng
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Physics (General)
Added to DOAB on : 2019-12-09 16:39:37
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Prototypical quantum optics models, such as the Jaynes–Cummings, Rabi, Tavis–Cummings, and Dicke models, are commonly analyzed with diverse techniques, including analytical exact solutions, mean-field theory, exact diagonalization, and so on. Analysis of these systems strongly depends on their symmetries, ranging, e.g., from a U(1) group in the Jaynes–Cummings model to a Z2 symmetry in the full-fledged quantum Rabi model. In recent years, novel regimes of light–matter interactions, namely, the ultrastrong and deep-strong coupling regimes, have been attracting an increasing amount of interest. The quantum Rabi and Dicke models in these exotic regimes present new features, such as collapses and revivals of the population, bounces of photon-number wave packets, as well as the breakdown of the rotating-wave approximation. Symmetries also play an important role in these regimes and will additionally change depending on whether the few- or many-qubit systems considered have associated inhomogeneous or equal couplings to the bosonic mode. Moreover, there is a growing interest in proposing and carrying out quantum simulations of these models in quantum platforms such as trapped ions, superconducting circuits, and quantum photonics. In this Special Issue Reprint, we have gathered a series of articles related to symmetry in quantum optics models, including the quantum Rabi model and its symmetries, Floquet topological quantum states in optically driven semiconductors, the spin–boson model as a simulator of non-Markovian multiphoton Jaynes–Cummings models, parity-assisted generation of nonclassical states of light in circuit quantum electrodynamics, and quasiprobability distribution functions from fractional Fourier transforms.

Fractional Order Systems

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ISBN: 9783039216086 / 9783039216093 Year: Pages: 114 DOI: 10.3390/books978-3-03921-609-3 Language: eng
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2019-12-09 11:49:16
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This book is focused on fractional order systems. Historically, fractional calculus has been recognized since the inception of regular calculus, with the first written reference dated in September 1695 in a letter from Leibniz to L’Hospital. Nowadays, fractional calculus has a wide area of applications in areas such as physics, chemistry, bioengineering, chaos theory, control systems engineering, and many others. In all those applications, we deal with fractional order systems in general. Moreover, fractional calculus plays an important role even in complex systems and therefore allows us to develop better descriptions of real-world phenomena. On that basis, fractional order systems are ubiquitous, as the whole real world around us is fractional. Due to this reason, it is urgent to consider almost all systems as fractional order systems.

Joseph Fourier 250th Birthday. Modern Fourier Analysis and Fourier Heat Equation in Information Sciences for the XXIst century

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ISBN: 9783038977469 Year: Pages: 260 DOI: 10.3390/books978-3-03897-747-6 Language: eng
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Physics (General)
Added to DOAB on : 2019-04-05 11:17:10
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For the 250th birthday of Joseph Fourier, born in 1768 in Auxerre, France, this MDPI Special Issue will explore modern topics related to Fourier Analysis and Heat Equation. Modern developments of Fourier analysis during the 20th century have explored generalizations of Fourier and Fourier–Plancherel formula for non-commutative harmonic analysis, applied to locally-compact, non-Abelian groups. In parallel, the theory of coherent states and wavelets has been generalized over Lie groups. One should add the developments, over the last 30 years, of the applications of harmonic analysis to the description of the fascinating world of aperiodic structures in condensed matter physics. The notions of model sets, introduced by Y. Meyer, and of almost periodic functions, have revealed themselves to be extremely fruitful in this domain of natural sciences. The name of Joseph Fourier is also inseparable from the study of the mathematics of heat. Modern research on heat equations explores the extension of the classical diffusion equation on Riemannian, sub-Riemannian manifolds, and Lie groups. In parallel, in geometric mechanics, Jean-Marie Souriau interpreted the temperature vector of Planck as a space-time vector, obtaining, in this way, a phenomenological model of continuous media, which presents some interesting properties. One last comment concerns the fundamental contributions of Fourier analysis to quantum physics: Quantum mechanics and quantum field theory. The content of this Special Issue will highlight papers exploring non-commutative Fourier harmonic analysis, spectral properties of aperiodic order, the hypoelliptic heat equation, and the relativistic heat equation in the context of Information Theory and Geometric Science of Information.

Sol-Gel Chemistry Applied to Materials Science

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ISBN: 9783039213535 / 9783039213542 Year: Pages: 216 DOI: 10.3390/books978-3-03921-354-2 Language: eng
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Chemistry (General)
Added to DOAB on : 2019-12-09 11:49:15
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Sol–gel technology is a contemporary advancement in science that requires taking a multidisciplinary approach with regard to its various applications. This book highlights some applications of the sol–gel technology, including protective coatings, catalysts, piezoelectric devices, wave guides, lenses, high-strength ceramics, superconductors, synthesis of nanoparticles, and insulating materials. In particular, for biotechnological applications, biomolecules or the incorporation of bioactive substances into the sol–gel matrix has been extensively studied and has been a challenge for many researchers. Some sol–gel materials are widely applied in light-emitting diodes, solar cells, sensing, catalysis, integration in photovoltaic devices, and more recently in biosensing, bioimaging, or medical diagnosis; others can be considered excellent drug delivery systems. The goal of an ideal drug delivery system is the prompt delivery of a therapeutic amount of the drug to the proper site in the body, where the desired drug concentration can be maintained. The interactions between drugs and the sol–gel system can affect the release rate. In conclusion, the sol–gel synthesis method offers mixing at the molecular level and is able to improve the chemical homogeneity of the resulting composite. This opens new doors not only regarding

Keywords

sol-gel method --- Fourier transform infrared spectroscopy (FTIR) analysis --- bioactivity --- biocompatibility --- sol–gel method --- organic-inorganic hybrids --- chlorogenic acid --- cytotoxicity --- biocompatibility --- silsesquioxanes --- thiol-ene click reaction --- in situ water production --- hydrophobic coatings --- cotton fabric --- paper --- NMR --- wettability --- sol-gel --- hollow sphere --- 1D structure --- sol-gel --- thin-disk laser --- Yb-doped glasses --- aluminosilicate glasses --- photoluminescence --- ultrasonic spray deposition --- tungsten oxide --- lithium lanthanum titanium oxide --- conformal coating --- Li-ion batteries --- sol-gel technique --- biomaterials --- cell proliferation --- cell cycle --- one transistor and one resistor (1T1R) --- organic thin-film transistor (OTFT) --- resistive random access memory (RRAM) --- sol-gel --- lithium-ion battery --- LiMnxFe(1?x)PO4 --- carbon coating --- pseudo-diffusion coefficient --- potential step voltammetry --- electrochemical impedance spectroscopy --- sol-gel --- oxyfluoride glass-ceramics --- nanocrystal --- optical properties --- sol-gel method --- SiO2–based hybrids --- poly(?-caprolactone) --- TG-DSC --- TG-FTIR --- X-ray diffraction analysis --- computer-aided design (CAD) --- mechanical analysis --- finite element analysis (FEA) --- composites --- organic–inorganic hybrid materials --- biomedical applications --- metal oxides --- multi-layer --- surface plasmon resonance --- optical sensors --- computer-aided design (CAD) --- mechanical analysis --- finite element analysis (FEA) --- composites --- hybrid materials --- biomedical applications

Integral Transforms and Operational Calculus

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ISBN: 9783039216185 / 9783039216192 Year: Pages: 510 DOI: 10.3390/books978-3-03921-619-2 Language: eng
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Technology (General) --- General and Civil Engineering
Added to DOAB on : 2019-12-09 11:49:16
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Researches and investigations involving the theory and applications of integral transforms and operational calculus are remarkably wide-spread in many diverse areas of the mathematical, physical, chemical, engineering and statistical sciences.

Keywords

highly oscillatory --- convolution quadrature rule --- volterra integral equation --- Bessel kernel --- convergence --- higher order Schwarzian derivatives --- Janowski star-like function --- Janowski convex function --- bound on derivatives --- tangent numbers --- tangent polynomials --- Carlitz-type q-tangent numbers --- Carlitz-type q-tangent polynomials --- (p,q)-analogue of tangent numbers and polynomials --- (p,q)-analogue of tangent zeta function --- symmetric identities --- zeros --- Lommel functions --- univalent functions --- starlike functions --- convex functions --- inclusion relationships --- analytic function --- Hankel determinant --- exponential function --- upper bound --- nonlinear boundary value problems --- fractional-order differential equations --- Riemann-Stieltjes functional integral --- Liouville-Caputo fractional derivative --- infinite-point boundary conditions --- advanced and deviated arguments --- existence of at least one solution --- Fredholm integral equation --- Schauder fixed point theorem --- Hölder condition --- generalized Kuramoto–Sivashinsky equation --- modified Kudryashov method --- exact solutions --- Maple graphs --- analytic function --- Hadamard product (convolution) --- partial sum --- Srivastava–Tomovski generalization of Mittag–Leffler function --- subordination --- differential equation --- differential inclusion --- Liouville–Caputo-type fractional derivative --- fractional integral --- existence --- fixed point --- Bernoulli spiral --- Grandi curves --- Chebyshev polynomials --- pseudo-Chebyshev polynomials --- orthogonality property --- symmetric --- encryption --- password --- hash --- cryptography --- PBKDF --- q–Bleimann–Butzer–Hahn operators --- (p,q)-integers --- (p,q)-Bernstein operators --- (p,q)-Bleimann–Butzer–Hahn operators --- modulus of continuity --- rate of approximation --- K-functional --- Hurwitz-Lerch zeta function --- generalized functions --- analytic number theory --- ?-generalized Hurwitz-Lerch zeta functions --- derivative properties --- series representation --- basic hypergeometric functions --- generating functions --- q-polynomials --- analytic functions --- Mittag–Leffler functions --- starlike functions --- convex functions --- Hardy space --- vibrating string equation --- initial conditions --- spectral decomposition --- regular solution --- the uniqueness of the solution --- the existence of a solution --- analytic --- ?-convex function --- starlike function --- strongly-starlike function --- subordination --- q -Sheffer–Appell polynomials --- generating relations --- determinant definition --- recurrence relation --- q -Hermite–Bernoulli polynomials --- q -Hermite–Euler polynomials --- q -Hermite–Genocchi polynomials --- Volterra integral equations --- highly oscillatory Bessel kernel --- Hermite interpolation --- direct Hermite collocation method --- piecewise Hermite collocation method --- differential operator --- q-hypergeometric functions --- meromorphic function --- Mittag–Leffler function --- Hadamard product --- differential subordination --- starlike functions --- Bell numbers --- radius estimate --- (p, q)-integers --- Dunkl analogue --- generating functions --- generalization of exponential function --- Szász operator --- modulus of continuity --- function spaces and their duals --- distributions --- tempered distributions --- Schwartz testing function space --- generalized functions --- distribution space --- wavelet transform of generalized functions --- Fourier transform --- analytic function --- subordination --- Dziok–Srivastava operator --- nonlinear boundary value problem --- nonlocal --- multi-point --- multi-strip --- existence --- Ulam stability --- functions of bounded boundary and bounded radius rotations --- subordination --- functions with positive real part --- uniformly starlike and convex functions --- analytic functions --- univalent functions --- starlike and q-starlike functions --- q-derivative (or q-difference) operator --- sufficient conditions --- distortion theorems --- Janowski functions --- analytic number theory --- ?-generalized Hurwitz–Lerch zeta functions --- derivative properties --- recurrence relations --- integral representations --- Mellin transform --- natural transform --- Adomian decomposition method --- Caputo fractional derivative --- generalized mittag-leffler function --- analytic functions --- Hadamard product --- starlike functions --- q-derivative (or q-difference) operator --- Hankel determinant --- q-starlike functions --- fuzzy volterra integro-differential equations --- fuzzy general linear method --- fuzzy differential equations --- generalized Hukuhara differentiability --- spectrum symmetry --- DCT --- MFCC --- audio features --- anuran calls --- analytic functions --- convex functions --- starlike functions --- strongly convex functions --- strongly starlike functions --- uniformly convex functions --- Struve functions --- truncated-exponential polynomials --- monomiality principle --- generating functions --- Apostol-type polynomials and Apostol-type numbers --- Bernoulli, Euler and Genocchi polynomials --- Bernoulli, Euler, and Genocchi numbers --- operational methods --- summation formulas --- symmetric identities --- Euler numbers and polynomials --- q-Euler numbers and polynomials --- Hurwitz-Euler eta function --- multiple Hurwitz-Euler eta function --- higher order q-Euler numbers and polynomials --- (p, q)-Euler numbers and polynomials of higher order --- symmetric identities --- symmetry of the zero

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2019 (5)