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Yayın Compressive spectral renormalization method(Işık University Press, 2018-09-09) Bayındır, CihanIn this paper a novel numerical scheme for finding the sparse self-localized states of a nonlinear system of equations with missing spectral data is introduced. As in the Petviashivili's and the spectral renormalization method, the governing equation is transformed into Fourier domain, but the iterations are performed for far fewer number of spectral components (M) than classical versions of the these methods with higher number of spectral components (N). After the converge criteria is achieved for M components, N component signal is reconstructed from M components by using the l(1) minimization technique of the compressive sampling. This method can be named as compressive spectral renormalization (CSRM) method. The main advantage of the CSRM is that, it is capable of finding the sparse self-localized states of the evolution equation(s) with many spectral data missing.Yayın Engineering four-qubit fuel states for protecting quantum thermalization machine from decoherence(Multidisciplinary Digital Publishing Institute (MDPI), 2024-01-10) Özaydın, Fatih; Sarkar, Ramita; Bayrakçı, Veysel; Bayındır, Cihan; Altıntaş, Azmi Ali; Müstecaplıoğlu, Özgür E.Decoherence is a major issue in quantum information processing, degrading the performance of tasks or even precluding them. Quantum error-correcting codes, creating decoherence-free subspaces, and the quantum Zeno effect are among the major means for protecting quantum systems from decoherence. Increasing the number of qubits of a quantum system to be utilized in a quantum information task as a resource expands the quantum state space. This creates the opportunity to engineer the quantum state of the system in a way that improves the performance of the task and even to protect the system against decoherence. Here, we consider a quantum thermalization machine and four-qubit atomic states as its resource. Taking into account the realistic conditions such as cavity loss and atomic decoherence due to ambient temperature, we design a quantum state for the atomic resource as a classical mixture of Dicke and W states. We show that using the mixture probability as the control parameter, the negative effects of the inevitable decoherence on the machine performance almost vanish. Our work paves the way for optimizing resource systems consisting of a higher number of atoms.Yayın A split-step Fourier scheme for the dissipative Kundu-Eckhaus equation and its rogue wave dynamics(Işık University Press, 2021-01) Bayındır, Cihan; Yurtbak, HazalWe investigate the rogue wave dynamics of the dissipative Kundu-Eckhaus equation. With this motivation, we propose a split-step Fourier scheme for its numerical solution. After testing the accuracy and stability of the scheme using an analytical solution as a benchmark problem, we analyze the chaotic wave fields generated by the modulation instability within the frame of the dissipative Kundu-Eckhaus equation. We discuss the effects of various parameters on rogue wave formation probability and we also discuss the role of dissipation on occurrences of such waves.
