Browsing by Subject "Hamiltonian systems."

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    Integrable systems on regular time scales
    (2009) Yantır, Burcu Silindir
    We present two approaches to unify the integrable systems. Both approaches are based on the classical R-matrix formalism. The first approach proceeds from the construction of (1 + 1)-dimensional integrable ∆-differential systems on regular time scales together with bi-Hamiltonian structures and conserved quantities. The second approach is established upon the general framework of integrable discrete systems on R and integrable dispersionless systems. We discuss the deformation quantization scheme for the dispersionless systems. We also apply the theories presented in this dissertation, to several well-known examples.
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    Limiting Gibbs measures in some one and two dimensional models
    (2005) Tülü, Serdar
    We give the definitions of finite volume Gibbs measure and limit Gibbs states. In one dimensional Ising model with arbitrary boundary conditions we calculate correlation functions in explicit way. In one dimension, conditions for uniqueness of Gibbs state are considered. We also discuss two dimensional Ising model.
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    Low-temperature thermodynamics of finite and discrete quartic quantum oscillator in one dimension
    (1999) Sıddıki, Afif
    I.' this work we examined a quartic Hamiltonian using two different approaches. We first introduced a mean-field Gaussian approximation in order to handle this Hamiltonian analytically and observed that this approximation is insufficient for all coupling strengths. Hence we applied second and third order non-degenerate time-independent perturbation and obtained third or- ■ ler correcHo