Relaxation and Localization in Condensed Phases.
Abstract
This thesis consists of two parts. In the first part, relaxation dynamics and line broadening of a quantum mechanical system in condensed phases are studied. In the second part, we focus on the study of critical phenomena is disordered quantum mechanical systems. In Chapter 2, we consider a twolevel system (TLS) linearly and offdiagonally coupled to a harmonic bath. The equations of motion for the reduced TLS density matrix are obtained using projection operator techniques. Here, the factorization assumption for the initial density matrix is avoided. From a perturbation calculation to fourth order in the TLS/bath coupling, we find that the density matrix shows nonMarkovian behavior at short times. After this transient period, the Bloch equations of motion are recovered. For the complex OhmicLorentzian model, we found that the phase relaxation time, T_2 , can be greater than twice the population relaxation time, T_1, for a range of parameters. In Chapter 3, we calculate the absorption spectrum for the TLS, finding that the linewidth of the lineshape function can be smaller than 1/T_1, which seems to violate the energytime uncertainty principle. In Chapter 4, we study localization in energetically disordered systems. A standard diagonally disordered tight binding Hamiltonian is used. The critical disorder and critical exponents are determined using a numerical renormalization group method. By comparing the numerical results of the inverse participation ratio exponent and its generalizations, we show that the critical wave functions have a multifractal structure. Using a generalized phenomenological renormalization technique on the inverse participation ratio, the correlation length exponent nu = 0.99 +/ 0.04 is obtained, which is in agreement with experiments on compensated or amorphous doped semiconductors.
 Publication:

Ph.D. Thesis
 Pub Date:
 1992
 Bibcode:
 1992PhDT.......246C
 Keywords:

 Chemistry: Physical; Physics: Condensed Matter