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Permanent URI for this collectionhttps://hdl.handle.net/20.500.14288/6

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1993 - 199929

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Start date: 1993End date: 1999

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    PublicationOpen Access
    Multidimensional wave packet dynamics within the fluid dynamical formulation of the Schrodinger equation
    (American Institute of Physics (AIP) Publishing, 1998) Rabitz, H.; Department of Mathematics; Aşkar, Attila; Dey, Bijoy K.; Faculty Member; Faculty Member; Department of Mathematics; College of Sciences; 178822; N/A
    This paper explores the quantum fluid dynamical (QFD) representation of the time-dependent Schrodinger equation for the motion of a wave packet in a high dimensional space. A novel alternating direction technique is utilized to single our each of the many dimensions in the QFD equations. This technique is used to solve the continuity equation for the density and the equation for the convection of the flux for the quantum particle. The ability of the present scheme to efficiently and accurately describe the dynamics of a quantum particle is demonstrated in four dimensions where analytical results are known. We also apply the technique to the photodissociation of NOCl and NO2 where the systems are reduced to two coordinates by freezing the angular variable at its equilibrium value.
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    PublicationOpen Access
    Generalized adiabatic product expansion: a nonperturbative method of solving the time-dependent Schrodinger equation
    (American Institute of Physics (AIP) Publishing, 1999) Department of Mathematics; Mostafazadeh, Ali; Faculty Member; Department of Mathematics; College of Sciences; 4231
    We outline a method based on successive canonical transformations which yields a product expansion for the evolution operator of a general (possibly non-Hermitian) Hamiltonian. For a class of such Hamiltonians this expansion involves a finite number of terms, and our method gives the exact solution of the corresponding time-dependent Schrödinger equation. We apply this method to study the dynamics of a general nondegenerate two-level quantum system, a time-dependent classical harmonic oscillator, and a degenerate system consisting of a spin 1 particle interacting with a time-dependent electric field ℰ→(t) through the Stark Hamiltonian H = λ(J→ · ℰ→)2.
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    PublicationOpen Access
    Quantum fluid dynamics in the Lagrangian representation and applications to photodissociation problems
    (American Institute of Physics (AIP) Publishing, 1999) Rabitz, H. A.; Department of Mathematics; Aşkar, Attila; Faculty Member; Department of Mathematics; College of Sciences; N/A; 178822
    This paper considers the practical utility of quantum fluid dynamics (QFD) whereby the time-dependent Schrodinger's equation is transformed to observing the dynamics of an equivalent "gas continuum." The density and velocity of this equivalent gas continuum are respectively the probability density and the gradient of the phase of the wave function. The numerical implementation of the QFD equations is carried out within the Lagrangian approach, which transforms the solution of Schrodinger's equation into following the trajectories of a set of mass points, i.e., subparticles, obtained by discretization of the continuum equations. The quantum dynamics of the subparticles which arise in the present formalism through numerical discretization are coupled by the density and the quantum potential. Numerical illustrations are performed for photodissociation of nocl and NO2 treated as two-dimensional models. The dissociation cross sections sigma(omega) are evaluated in the dramatically short CPU times of 33 s for nocl and 40 s for NO2 on a Pentium-200 mhz PC machine. The computational efficiency comes from a combination of (a) the QFD representation dealing with the near monotonic amplitude and phase as dependent variables, (b) the Lagrangian description concentrating the computation effort at all times into regions of highest probability as an optimal adaptive grid, and (c) the use of an explicit time integrator whereby the computational effort grows only linearly with the number of discrete points.
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    PublicationOpen Access
    Dimerization of pyrrole
    (TÜBİTAK, 1998) Yurtsever, Mine; Department of Chemistry; Yurtsever, İsmail Ersin; Faculty Member; Department of Chemistry; College of Sciences; 7129
    Accurate ab-inito quantum mechanical calculations of pyrrole dimers are reported. The thermodynamical stabilities of dimers with alpha - alpha, alpha -beta, and beta - beta type linkages are compared in order to predict the possibilities of branching in polypyrroles. Calculations employing large basis sets and including electron correlation effects predict the alpha - alpha dimers as the most stable form. However, an alpha - beta type bonding requires only 1.5-2.0 kcal/mol, and the energy necessary to introduce a beta - beta type bond is 3.6-4.0 kcal/mol. These values show that a high degree of branching is possible even at room temperatures.
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    PublicationOpen Access
    Transition from static to kinetic friction in a model lubricated system
    (American Institute of Physics (AIP) Publishing, 1998) Granick, S.; Department of Chemistry; Demirel, Adem Levent; Faculty Member; Department of Chemistry; College of Sciences; 6568
    Molecularly thin confined fluids were deformed in shear faster than structural relaxations in response to shear could be accomplished, such that with increasing deformation the systems passed from the rest state to sliding. The response of these systems-two atomically smooth mica sheets separated by a fluid comprised of globularly shaped molecules [octamethylcyclotetrasiloxane]-was studied as a function of film thickness of the fluid (from 80 to 10 Angstrom, i.e, from similar to 8 to similar to 1 molecular dimensions), as a function of normal pressure, and as a function of deformation rate, using a modified surface forces apparatus. Whereas the linear response was always liquid-like provided that the deformation rate was sufficiently slow, a "stick-slip" transition from the rest state to sliding was observed when the deformation rate was large, provided that the oscillatory frequency sufficiently exceeded the inverse intrinsic relaxation time of the confined fluid. This transition was monotonic and reversible without hysteresis for relatively thick films but for thinner films was discontinuous with hysteresis. For films thicker than 3 molecular layers (ML), two length scales in deformation were observed; the films showed nonlinear force-deformation response beginning at a deformation amplitude of 3 iq but in general showed stick slip only when the deformation was larger than this. The critical deformation at the point of stick slip decreased from 9 to 3 Angstrom with increasing normal pressure, indicating diminished plasticity of the confined structures with increasing normal pressure. The critical film thickness of 3 ML correlates with the possibility of one rather than more slip planes. The thinnest films under the highest compressive pressures showed moderate increase of the viscous shear force with increasing effective sliding velocity, but in general the viscous force reached a plateau in which force showed almost no dependence on sliding rate. In interpreting the results in the context of friction, static friction was identified with the elastic stress at rupture and kinetic friction was identified with the limiting maximum observed level of viscous force. After normalizing friction and normal forces by the contact area, the static friction coefficient was found to be 0.44 and the kinetic friction coefficient;to be 0.14, In other words, as the normal pressure increased, the elastic force needed to rupture the system increased more rapidly than the limiting shear stress. The magnitude of the limiting shear stress increased exponentially with decreasing film thickness with a decay length of 1 molecular dimension, This decay length correlates well with the known exponential decay of oscillations in the static force-distance profile, The critical shear amplitude of 3 Angstrom, relative to the molecular dimension of approximate to 9 Angstrom, is reminiscent of early estimates by Frenkel of the point of instability when planes of atoms slide over one another. (C) 1998 American Institute of Physics. [S0021-9606(98)52540-8].
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    PublicationOpen Access
    Comment on “Identical motion in classical and quantum mechanics”
    (American Physical Society (APS), 1999) Department of Mathematics; Department of Physics; Mostafazadeh, Ali; Faculty Member; Department of Mathematics; Department of Physics; College of Sciences; 4231
    Makowski and Konkel [Phys. Rev. A 58, 4975 (1998)] have obtained certain classes of potentials which lead to identical classical and quantum Hamilton-Jacobi equations. We obtain the most general form of these potentials.
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    PublicationOpen Access
    Modeling and experimental observation of parametric processes in segmented KTiOPO4 channel waveguides
    (American Institute of Physics (AIP) Publishing, 1999) Aschieri, P.; Baldi, P.; Bierlein, J.; Department of Physics; Sundheimer, Michael; Faculty Member; Department of Physics; College of Sciences
    This letter presents a modeling technique for quasiphase-matched parametric processes in segmented channel waveguides and the results of measurements of infrared parametric fluorescence in segmented KTiOPO4 channel waveguides. We demonstrate both theoretically and experimentally a strong dependence of optical parametric oscillator tuning curves and parametric conversion efficiency (parametric gain) on the segmentation duty cycle. We show that the optimum conversion efficiency for parametric interactions in segmented waveguides is obtained for duty cycles greater than 50%. Our results validate the use of an effective continuous waveguide model for segmented channel waveguide calculations over a wide range of wavelengths and duty cycles. (C) 1999 American Institute of Physics. [S0003-6951(99)02812-0].
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    PublicationOpen Access
    Erratum: Geometric phase, bundle classification, and group representation
    (American Institute of Physics (AIP) Publishing, 1999) Department of Mathematics; Department of Physics; Mostafazadeh, Ali; Faculty Member; Department of Mathematics; Department of Physics; College of Sciences; 4231
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    PublicationOpen Access
    Widely tunable continuous-wave solid-state red laser source using periodically-poled lithium niobate
    (Society of Photo-optical Instrumentation Engineers (SPIE), 1999) Department of Physics; Sundheimer, Michael; Sennaroğlu, Alphan; Faculty Member; Faculty Member; Department of Physics; College of Sciences; N/A; 23851
    In this work we have generated widely-tunable continuous-wave (CW) red light by second-harmonic generation (SHG) of the output of a Cr4+:forsterite laser, tunable from 1.206 to 1.320 mu m, using quasi-phasermatching (QPM) in periodically-poled lithium niobate (PPLN). For a given grating period in the PPLN, a combination of Cr4+:forsterite pump wavelength tuning and PPLN temperature tuning up to 200 degrees C provided continuous SHG tuning over a wavelength range of approximately 14 nm in the red. By translating the PPLN crystal to other periods, we have demonstrated SHG over the entire tuning range of the pump laser, yielding tunable CW output from 603 to 660 mu with maximum output powers of approximately 5 mW for a typical Cr4+:forsterite pump power of 500 mW.
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    PublicationOpen Access
    Labor market implications of the demographic window of opportunity
    (1996) Pritchett, Jonathan B.; Department of Economics; Tunalı, Fehmi İnsan; Faculty Member; Department of Economics; College of Administrative Sciences and Economics; 105635