<i>Modern Quantum Mechanics</i>

Sakurai, Jun; Tuan, S. F.; Newton, Roger G.

doi:10.1063/1.2815083

Cited by 105 publications

(101 citation statements)

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“…The propagator given in Eq. (2.24) is closely related to the quantum propagator constructed using the Feynman path integrals 22 . The end-integrated propagators are calculated as,…”

Section: Theoretical Frameworkmentioning

confidence: 99%

Modeling Hydrogen Bonding in Diblock Copolymer/Homopolymer Blends

Dehghan

Shi

2013

Macromolecules

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The phase behavior of AB diblock copolymers mixed with C homopolymers (AB/C), in which A and C are capable of forming hydrogen-bonds, is examined using selfconsistent field theory. The study focuses on the modeling of hydrogen-bonding in polymers. Specifically, we examine two models for the formation of hydrogen-bonds between polymer chains. The first commonly used model assumes a large attractive interaction parameter between the A/C monomers. This model reproduces correct phase transition sequences as compared with experiments, but it fails to correctly describe the change of lamellar spacing induced by the addition of the C homopolymers.The second model is based on the fact that hydrogen-bonding leads to A/C complexation. We show that the interpolymer complexation model predicts correctly the order-order phase transition sequences and the decrease of lamellar spacing for strong hydrogen-bonding. Our analysis demonstrates that hydrogen-bonding of polymers should be modeled by interpolymer complexation.iii

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“…The propagator given in Eq. (2.24) is closely related to the quantum propagator constructed using the Feynman path integrals 22 . The end-integrated propagators are calculated as,…”

Section: Theoretical Frameworkmentioning

confidence: 99%

Modeling Hydrogen Bonding in Diblock Copolymer/Homopolymer Blends

Dehghan

Shi

2013

Macromolecules

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“…To calculate the solution for any frequency, a general formulation of the problem is proposed in § 3, obtaining a first order linear system of differential equations with varying coefficients. An analytical method to solve the differential equation is presented in § 4 using the Magnus expansion initially used to solve the Schrödinger equation (Sakurai & Tuan 1985) and the boundary conditions are discussed in § 5. Results and validations versus the linear steady velocity profile nozzle, numerical results and experimental data are illustrated in § 6 for different nozzle geometries and configurations; and conclusions are finally discussed in § 7.…”

Section: Introductionmentioning

confidence: 99%

Solution of the quasi-one-dimensional linearized Euler equations using flow invariants and the Magnus expansion

2013

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The acoustic and entropy transfer functions of quasi-one-dimensional nozzles are studied analytically for both subsonic and choked flows with and without shock waves. The present analytical study extends both the compact nozzle solution obtained by Marble & Candel (1977) and the effective nozzle length proposed by Stow et al. (2002) and by Goh & Morgans (2011a) to non-zero frequencies for both modulus and phase through an asymptotic expansion of the linearized Euler equations. It also extends the piecewiselinear approximation of the velocity profile in the nozzle proposed by Moase et al. (2007) to any arbitrary profile or equivalently any nozzle geometry. The equations are written as a function of three variables, namely the dimensionless mass, total temperature and entropy fluctuations, yielding a first order linear system of differential equations with varying coefficients, which is solved using the Magnus expansion. The solution shows that both the modulus and the phase of the transfer functions of the nozzle have a strong dependence on the frequency. This holds for both choked flows and subsonic converging diverging nozzles. The method is used to compare two different nozzle geometries with the same inlet and outlet Mach numbers showing that, even if the compact solution predicts no differences between the transfer functions of the two nozzles, significant differences are found at non-zero frequencies. A parametric study is finally performed to calculate the indirect to direct noise ratio for a model combustor, showing that this ratio decreases at higher frequencies.

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“…• Coupling terms The reduced matrix elements are assumed as known, so that one simple uses the Wigner-Eckart theorem [17] to evaluate the coupling coefficients in terms of the reduced matrix element. For convenience we introduce the (reduced) Rabi frequency:…”

Section: Outline Of Computational Methodsmentioning

confidence: 99%

Doppler cooling of gallium atoms: 2. Simulation in complex multilevel systems

Rutherford¹,

Lane²,

McCann³

2010

J. Phys. B: At. Mol. Opt. Phys.

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Abstract. This paper derives a general procedure for the numerical solution of the Lindblad equations that govern the coherences arising from multicoloured light interacting with a multilevel system. A systematic approach to finding the conservative and dissipative terms is derived and applied to the laser cooling of gallium. An improved numerical method is developed to solve the time-dependent master equation and results are presented for transient cooling processes. The method is significantly more robust, efficient and accurate than the standard method and can be applied to a broad range of atomic and molecular systems. Radiation pressure forces and the formation of dynamic dark-states are studied in the gallium isotope 66 Ga.

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Modern Quantum Mechanics

Cited by 105 publications

References 0 publications

Modeling Hydrogen Bonding in Diblock Copolymer/Homopolymer Blends

Modeling Hydrogen Bonding in Diblock Copolymer/Homopolymer Blends

Solution of the quasi-one-dimensional linearized Euler equations using flow invariants and the Magnus expansion

Doppler cooling of gallium atoms: 2. Simulation in complex multilevel systems

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