Atılgan Büyükaşık, Şirin
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A. Büyükaşık, Şirin
Atılgan, Ş.
Buyukasik, Sirin A.
Büyükaşık, Şirin A.
Atilgan, S.
A. Buyukasik, Sirin
Atılgan, Ş.
Buyukasik, Sirin A.
Büyükaşık, Şirin A.
Atilgan, S.
A. Buyukasik, Sirin
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sirinatilgan@iyte.edu.tr
Main Affiliation
04.02. Department of Mathematics
Status
Current Staff
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Documents
10
Citations
68
h-index
5
Documents
13
Citations
82
Scholarly Output
18
Articles
10
Views / Downloads
37739/18330
Supervised MSc Theses
3
Supervised PhD Theses
2
WoS Citation Count
78
Scopus Citation Count
86
Patents
0
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0
WoS Citations per Publication
4.33
Scopus Citations per Publication
4.78
Open Access Source
17
Supervised Theses
5
| Journal | Count |
|---|---|
| Journal of Mathematical Physics | 6 |
| Communications in Nonlinear Science and Numerical Simulation | 3 |
| Journal of Physics: Conference Series | 2 |
| 32nd International Colloquium on Group Theoretical Methods in Physics (Group32) | 1 |
| Journal of Mathematical Chemistry | 1 |
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18 results
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Now showing 1 - 10 of 18
Conference Object Dynamics of Squeezed States of a Generalized Quantum Parametric Oscillator(IOP Publishing, 2019) Atılgan Büyükaşık, Şirin; Çayiç, ZehraTime-evolution of squeezed coherent states of a generalized Caldirola-Kanai type quantum parametric oscillator is found explicitly using the exact evolution operator obtained by the Wei-Norman algebraic approach. Properties of these states are investigated according to the parameters of the unitary squeeze operator and the time-variable parameters of the generalized quadratic Hamiltonian. As an application, we consider exactly solvable quantum models with specific frequency modification for which the corresponding classical oscillator is in underdamping case and driving forces are of sinusoidal type. For each model we explicitly provide the evolution of the squeezed coherent states and discuss their behavior.Article Exact Time-Evolution of a Generalized Two-Dimensional Quantum Parametric Oscillator in the Presence of Time-Variable Magnetic and Electric Fields(American Institute of Physics, 2022) Atılgan Büyükaşık, Şirin; Çayiç, ZehraThe time-dependent Schrodinger equation describing a generalized two-dimensional quantum parametric oscillator in the presence of time-variable external fields is solved using the evolution operator method. For this, the evolution operator is found as a product of exponential operators through the Wei-Norman Lie algebraic approach. Then, the propagator and time-evolution of eigenstates and coherent states are derived explicitly in terms of solutions to the corresponding system of coupled classical equations of motion. In addition, using the evolution operator formalism, we construct linear and quadratic quantum dynamical invariants that provide connection of the present results with those obtained via the Malkin-Man'ko-Trifonov and the Lewis-Riesenfeld approaches. Finally, as an exactly solvable model, we introduce a Cauchy-Euler type quantum oscillator with increasing mass and decreasing frequency in time-dependent magnetic and electric fields. Based on the explicit results for the uncertainties and expectations, squeezing properties of the wave packets and their trajectories in the two-dimensional configuration space are discussed according to the influence of the time-variable parameters and external fields. Published under an exclusive license by AIP Publishing.Article Citation - WoS: 4Citation - Scopus: 7Dirichlet Problem on the Half-Line for a Forced Burgers Equation With Time-Variable Coefficients and Exactly Solvable Models(Elsevier, 2020) Atılgan Büyükaşık, Şirin; Bozacı, AylinWe consider a forced Burgers equation with time-variable coefficients and solve the initial-boundary value problem on the half-line 0 < x < infinity with inhomogeneous Dirichlet boundary condition imposed at x = 0. Solution of this problem is obtained in terms of a corresponding second order ordinary differential equation and a second kind singular Volterra type integral equation. As an application of the general results, we introduce three different Burgers type models with specific damping, diffusion and forcing coefficients and construct classes of exactly solvable models. The Burgers problems with smooth time-dependent boundary data and an initial profile with pole type singularity have exact solutions with moving singularity. For each model we provide the solutions explicitly and describe the dynamical properties of the singularities depending on the time-variable coefficients and the given initial and boundary data. (C) 2019 Elsevier B.V. All rights reserved.Article Citation - WoS: 23Citation - Scopus: 24Exact Solutions of Forced Burgers Equations With Time Variable Coefficients(Elsevier Ltd., 2013) Atılgan Büyükaşık, Şirin; Pashaev, OktayIn this paper, we consider a forced Burgers equation with time variable coefficients of the form Ut+(μ̇(t)/μ(t))U+UUx=(1/2μ(t))Uxx-ω2(t)x, and obtain an explicit solution of the general initial value problem in terms of a corresponding second order linear ordinary differential equation. Special exact solutions such as generalized shock and multi-shock waves, triangular wave, N-wave and rational type solutions are found and discussed. Then, we introduce forced Burgers equations with constant damping and an exponentially decaying diffusion coefficient as exactly solvable models. Different type of exact solutions are obtained for the critical, over and under damping cases, and their behavior is illustrated explicitly. In particular, the existence of inelastic type of collisions is observed by constructing multi-shock wave solutions, and for the rational type solutions the motion of the pole singularities is described.Master Thesis Exactly Solvable Generalized Quantum Harmonic Oscillators Related With the Classical Orthogonal Polynomials(Izmir Institute of Technology, 2016) Çayiç, Zehra; Atılgan Büyükaşık, ŞirinIn this thesis, we study exactly solvable generalized parametric oscillators related with the classical orthogonal polynomials of Hermite, Laguerre and Jacobi type. These quantum models with specific damping term, frequency and external forces are solved using Wei-Norman Lie algebraic approach. The exact form of the evolution operator is explicitly obtained in terms of two linearly independent homogeneous solutions and a particular solution of the corresponding classical equation of motion. Then, time evolution of wave functions and Glauber coherent states are constructed. Probability densities, expectation values and uncertainty relations are found and their properties are investigated according to the influence of the external forces. Besides, some examples with explicit solutions are given and their plots are constructed for the probability densities and uncertainty relations.Doctoral Thesis Exactly Solvable Burgers Type Equations With Variable Coefficients and Moving Boundary Conditions(01. Izmir Institute of Technology, 2022) Bozacı, Aylin; Atılgan Büyükaşık, ŞirinIn this thesis, firstly, a generalized diffusion type equation is considered. A family of analytical solutions to an initial value problem on the whole line for this equation is obtained in terms of solutions to the characteristic ordinary differential equation and the standard heat model by using Wei-Norman Lie algebraic approach for finding the evolution operator of the associated diffusion type equation. Then, initial-boundary value problems on half-line and an initial-boundary value problem with moving boundary for this equation are studied. It is shown that if the boundary propagates according to an associated classical equation of motion determined by the time-dependent parameters, then the analytical solution is obtained in terms of the heat problem on the half-line. For this, a non-linear Riccati type dynamical system, that simultaneously determines the solution of the diffusion type problem and the moving boundary is solved by a linearization procedure. The mean position of the solutions, the influence of the moving boundaries and the variable parameters are examined by constructing exactly solvable models. Then, an initial value problem for a generalized Burgers type equation on whole real line is discussed. By using Cole-Hopf linearization and solution of the corresponding generalized linear diffusion type equation, a family of analytical solution is obtained in terms of solutions to the characteristic equation and the standard heat or Burgers model. Exactly solvable models are constructed and the influence of the variable coefficients are examined. Later, an initial-boundary value problem for the generalized Burgers type equation with Dirichlet boundary condition defined on the half-line is studied. Finally, an initial-boundary value problem for the generalized Burgers type equations with Dirichlet boundary condition imposed at a moving boundary is considered. The analytical solution is obtained in terms of solution to characteristic equation and the standard heat or Burgers model, if the moving boundary propagates according to an associated classical equation of motion. In order to show certain aspects of the general results, some exactly solvable models are introduced and solutions corresponding to different types of initial and homogeneous/inhomogeneous boundary conditions are discussed by examining the influence of the moving boundaries.Conference Object Citation - WoS: 1Citation - Scopus: 1Exact Quantization of Cauchy-Euler Type Forced Parametric Oscillator(IOP Publishing Ltd., 2016) Atılgan Büyükaşık, Şirin; Çayiç, ZehraDriven and damped parametric quantum oscillator is solved by Wei-Norman Lie algebraic approach, which gives the exact form of the evolution operator. This allows us to obtain explicitly the probability densities, time-evolution of initially Glauber coherent states, expectation values and uncertainty relations. Then, as an exactly solvable model, we introduce the driven Cauchy-Euler type quantum parametric oscillator, which appears as self-adjoint quantization of the classical Cauchy-Euler differential equation. We discuss some typical behavior of this oscillator under the influence of external terms and give a concrete example.Master Thesis Solutions of Initial and Boundary Value Problems for Inhomogeneous Burgers Equations With Time-Variable Coefficients(Izmir Institute of Technology, 2016) Bozacı, Aylin; Atılgan Büyükaşık, ŞirinIn this thesis, we have investigated initial-boundary value problems on semiinfinite line for inhomogeneous Burgers equation with time-variable coecients. We have formulated the solutions for the cases with Dirichlet and Neumann boundary conditions. We showed that the Dirichlet problem for the variable parametric Burgers equation is solvable in terms of a linear ordinary dierential equation and a linear second kind singular Volterra integral equation. Then, for particular models with special initial and Dirichlet boundary conditions we found a class of exact solutions. Next, we considered the Neumann problem and showed that it reduces to a second order linear ordinary dierential equation and the standard heat equation with initial and nonlinear boundary conditions. Finally, we formulated the Cauchy problem for the variable parametric Burgers equation on the non-characteristic line, and obtained its solution in terms of a linear ODE and the series solution of the corresponding Cauchy problem for the heat equation. We gave examples to illustrate how some well known solutions of the Burgers equation can be recovered by solving a corresponding Cauchy problem.Article Citation - WoS: 8Citation - Scopus: 7Time-Evolution of Squeezed Coherent States of a Generalized Quantum Parametric Oscillator(American Institute of Physics, 2019) Atılgan Büyükaşık, Şirin; Çayiç, ZehraTime evolution of squeezed coherent states for a quantum parametric oscillator with the most general self-adjoint quadratic Hamiltonian is found explicitly. For this, we use the unitary displacement and squeeze operators in coordinate representation and the evolution operator obtained by the Wei-Norman Lie algebraic approach. Then, we analyze squeezing properties of the wave packets according to the complex parameter of the squeeze operator and the time-variable parameters of the Hamiltonian. As an application, we construct all exactly solvable generalized quantum oscillator models classically corresponding to a driven simple harmonic oscillator. For each model, defined according to the frequency modification in position space, we describe explicitly the squeezing and displacement properties of the wave packets. This allows us to see the exact influence of all parameters and make a basic comparison between the different models.Master Thesis Algebraic Methods and Exact Solutions of Quantum Parametric Oscillators(Izmir Institute of Technology, 2019) Çetindaş, Osman; Atılgan Büyükaşık, Şirin; Pashaev, OktayIn this thesis, we study different approaches for solving the Schrödinger equation for quantum parametric oscillators. The Wei-Norman algebraic approach, the Lewis- Riesenfeld invariant approach, the Malkin-Manko-Trifonov approach are investigated. For each approach, the wave function solutions of the Schrödinger equation, the propagator and dynamical invariants are found and their relations with each other are shown. In the Wei-Norman Algebraic approach, for constructing wave functions, explicit form of evolution operator is obtained uniquely in terms of two linearly independent classical solutions of the corresponding classical equation of motion. In Lewis-Riesenfeld approach, quadratic invariants are found in terms of the solution of Ermakov-Pinney equation and using the eigenstates of these invariants, wave function solutions are constructed. Setting initial values for Ermakov-Pinney solution, results of Wei-Norman and Lewis- Riesenfeld approaches are compared, then this solution is expressed in terms of same two linearly independent classical solutions. In Malkin-Manko-Trifonov approach, linear invariants which are symmetry operators for the Schrödinger equation, are constructed in terms of complex-valued solutions of the classical equation. Using these invariants, quadratic invariants are constructed and their eigenstates are used to find wave function solutions. Moreover, initial values for complex solutions of classical equation of motion are posed, and comparison of the three approaches is given.