Structural Properties Of One-dimensional PT Symmetric Polymers

The observability in quantum mechanics can be represented by the Hermitian operator whose corresponding eigenvalues are real numbers.However,in 1998,Bender et al.found that for PT-symmetry(space-time inverse symmetry,abbreviation for Parity-Time)non-Hermitian Hamiltonians of quantum systems could also have real eigenvalues.There are not the PT-symmetry quantum systems in nature.Until 2010,Christian et al.firstly implemented experimental simulation in the PT-symmetry optical coupling system.In this thsis,the dispersion characteristics and the evolution of light intensity are studied for the polymer waveguide system,because it can promote the further study of the properties of PT-symmetry optical coupling system.In order to study the properties of one-dimensional PT-symmetry polymer waveguides with different geometric structures,In this thesis,the optical coupling system properties of PT-symmetry one-dimensional oligophenyl-like waveguide(with armchair boundary)and PT-symmetry one-dimensional oligoacene-like waveguide(with zigzag boundary)are studied,and the evolution of light intensity under different initial conditions and the influence of symmetry-broken phase transition(the ratio of?/v)and topological phase transition(the ratio of coupling coefficients between waveguides:v/v' and v/v").The main contents of this paper are as follows:Firstly,we briefly introduce the main properties of PT-symmetry quantum system,polymer waveguide,tightly-bounding model,Bloch's theorem,and the calculation method of the of the energy eigenvalue of periodic structures.secondly,the Hamiltonian matrix of the model,the calculation of the eigenvalue energy and the related expressions are introduced by taking a one-dimensional infinite trimer waveguide as an example.The light intensity evolution of the system under broken state and unbroken PT-symmetry state is simulated.thirdly,the dispersion characteristics of PT-symmetry one-dimensional oligophenyl-like hexamer waveguide model in broken and unbroken PT-symmetry state are studied,and the evolution law of light wave in waveguide with time transmission under different initial conditions is studied.It is found that the evolution law of light intensity is asymmetric whether the system is in PT-symmetry broken or not.When the system is in the PT-symmetry unbroken state,the light intensity shape(two Gaussian-like distribution modes)in the light intensity evolution region is the same,and the larger the PT-symmetry breaking phase transition,the greater the light intensity in the evolution region.When the initial incident light is at different positions,the maximum light intensity of the gain waveguide is greater than that of the loss waveguide.However,the evolution region of the light intensity of the two waveguides in different states presents two Gaussian distribution modes.lastly,in the fourth chapter,the same research ideas and methods are used to study the dispersion characteristics of PT-symmetry one-dimensional oligoacene-like waveguide model and the evolution law of light wave in waveguide with time propagation under different initial conditions.It is found that the distribution of light intensity in the evolution region in the PT-symmetry unbroken state is symmetric about the structure of the intermediate unit.With the increase of v/v',the light intensity is closer to the middle,and the maximum of the light intensity appears after a period of evolution time.When the value ? is greater than one threshold,the system transforms into the PT broken state,and the distribution of light intensity in the evolutionary region is a symmetric and presents a Gaussian function distribution mode.It is found that in the waveguide structure of one-dimensional oligoacene-like,the distribution of light intensity in the evolution region is the same when the PT-symmetry phase transition is greater than 0.The maximum light intensity increases with the increase of PTsymmetry phase transition.When the initial incident light is located in the middle unit waveguide,the light intensity evolution of the gain waveguide is similar to the forward propagation of water ripple.When the initial incident light is located in waveguides with different gain and loss states,the light intensity evolution of two waveguides with the same unit structure is symmetric at the same time point.