Biorthogonal system

About: Biorthogonal system is a research topic. Over the lifetime, 2190 publications have been published within this topic receiving 32209 citations.

The generalized lapped pseudo-biorthogonal transform

Abstract: We investigate a special class of N-channel oversampled linear-phase perfect reconstruction filter banks with a decimation factor M smaller than N. We deal with systems in which all analysis and synthesis filters have the same FIR length and share the same center of symmetry. We provide the general lattice factorization of a polyphase matrix of a particular class of these oversampled filter banks. The lattice structure is based on the singular value decomposition for non-square matrices. The resulting lattice structure is able to provide fast implementation and allows us to determine the filter coefficients by solving an unconstrained optimization problem. We show that the present systems with the lattice structure cover a wide range of linear-phase perfect reconstruction filter banks. We also show several design examples.

Topological invariants, zero mode edge states and finite size effect for a generalized non-reciprocal Su-Schrieffer-Heeger model

Abstract: Intriguing issues in one-dimensional non-reciprocal topological systems include the breakdown of usual bulk-edge correspondence and the occurrence of half-integer topological invariants. In order to understand these unusual topological properties, we investigate the topological phase diagrams and the zero-mode edge states of a generalized non-reciprocal Su-Schrieffer-Heeger model with a general form fulfilling the chiral symmetry, based on some analytical results. Meanwhile, we provide a concise geometrical interpretation of the bulk topological invariants in terms of two independent winding numbers and also give an alternative interpretation related to the linking properties of curves in three-dimensional space. For the system under the open boundary condition, we construct analytically the wavefunctions of zero-mode edge states by properly considering a hidden symmetry of the system and the normalization condition with the use of biorthogonal eigenvectors. Our analytical results directly give the phase boundary for the existence of zero-mode edge states and unveil clearly the evolution behavior of edge states. In comparison with results via exact diagonalization of finite-size systems, we find our analytical results agree with the numerical results very well.

Analysis of the CDF biorthogonal MRTD method with application to PEC targets

Abstract: We consider the biorthogonal Cohen-Daubechies- Feauveau (CDF) wavelet family in the context of a biorthogonal multiresolution time-domain (bi-MRTD) analysis. A disadvantage of previous bi-MRTD analyses is an inability to handle abrupt changes in material properties, particularly for a perfect electric conductor (PEC). A multiregion method is proposed to address PEC targets. The proposed method is based on the fact that the CDF bi-MRTD may be viewed as a linear combination of several conventional finite-difference time-domain (FDTD) solutions. The implementation of the connecting surface is also simplified. Several numerical results are presented, with comparison to analytic and FDTD results.

Phase Transitions and Generalized Biorthogonal Polarization in Non-Hermitian Systems.

Abstract: Non-Hermitian (NH) Hamiltonians can be used to describe dissipative systems, and are currently intensively studied in the context of topology A salient difference between Hermitian and NH models is the breakdown of the conventional bulk-boundary correspondence invalidating the use of topological invariants computed from the Bloch bands to characterize boundary modes in generic NH systems One way to overcome this difficulty is to use the framework of biorthogonal quantum mechanics to define a biorthogonal polarization, which functions as a real-space invariant signaling the presence of boundary states Here, we generalize the concept of the biorthogonal polarization beyond the previous results to systems with any number of boundary modes, and show that it is invariant under basis transformations as well as local unitary transformations Additionally, we propose a generalization of a perviously-developed method with which to find all the bulk states of system with open boundaries to NH models Using the exact solutions in combination with variational states, we elucidate genuinely NH aspects of the interplay between bulk and boundary at the phase transitions