Browsing by Subject "Schrödinger equation"

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    Existence of unattainable states for Schrödinger type flows on the half-line
    (Oxford University Press, 2023-12-01) Özsarı, Türker; Kalimeris, Konstantinos
    We prove that the solutions of the Schrödinger and biharmonic Schrödinger equations do not have the exact boundary controllability property on the half-line by showing that the associated adjoint models lack observability. We consider the framework of L2 boundary controls with data spaces H−1(R+) and H−2(R+) for the classical and biharmonic Schrödinger equations, respectively. The lack of controllability on the half-line contrasts with the corresponding dynamics on a finite interval for a similar regularity setting. Our proof is based on an argument that uses the sharp fractional time trace estimates for solutions of the adjoint models. We also make several remarks on the connection of controllability and temporal regularity of spatial traces.
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    The interior-boundary Strichartz estimate for the Schrödinger equation on the half-line revisited
    (TÜBİTAK, 2022-01-01) Köksal, Bilge; Özsarı, Türker
    In recent papers, it was shown for the biharmonic Schrödinger equation and 2D Schrödinger equation that Fokas method-based formulas are capable of defining weak solutions of associated nonlinear initial boundary value problems (ibvps) below the Banach algebra threshold. In view of these results, we revisit the theory of interiorboundary Strichartz estimates for the Schrödinger equation posed on the right half line, considering both Dirichlet and Neumann cases. Finally, we apply these estimates to obtain low regularity solutions for the nonlinear Schrödinger equation (NLS) with Neumann boundary condition and a coupled system of NLS equations defined on the half line with Dirichlet/Neumann boundary conditions. © This work is licensed under a Creative Commons Attribution 4.0 International License.
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    A time-dependent study of bistability in resonant tunneling structures
    (1997) Keçecioğlu, Ersin
    A comjDutational time-dependent study of the bistability in resonant tunneling structures including the electron-electron interactions is presented. A new computational method for the investigation of many jDarticle interacting systems for the study of quantum transport in small systems is introduced. The timedependence of the wave-function in the Schrödinger equation is studied by discretizing the energy spectrum and the time steps. A simple model for a double barrier resonant tunneling structure is introduced. The method is then applied to this simple model of double barrier resonant tunneling structure, and this geometry is investigated systematically in terms of inter-pcirticle interaction strength and number of particles. By applying the method to this simple geometry it is shown that there exists instabilities which occur a.s oscillcitions in the current-voltage characteristics of the model geometry.