The Analysis of Eigenstates of a Few Generalized Quantum Baker's Maps Using Hadamard and Related Transforms

摘要

Application of the Hadamard and related transforms on a few generalized quantum baker's maps have been studied. Effectiveness of the Hadamard transform and a new transform which combines the Fourier and the Hadamard transforms, for simplifying the eigenstates or resonances of the quantization of a few generalized baker's map namely tetradic baker and lazy baker's map when the Hilbert space dimension is power of 2 has been done by comparing the participation ratios in the transformed basis with respect to the position basis. Several special family of states based on their maximal compression in either Hadamard transform or the new transform are identified and they are related to the ubiquitous Thue-Morse and allied sequences. Evidence is provided that these special family of states as well as average over all eigenstates exhibits multifractal nature.