The time dependence is completely described by the unitary matrix U(t, t0), or equivalently, by the hermitian Hamiltonian matrix H(t). This type of evolution is natural, but it is not the most general nor adequate for many applications such as relaxation phenomena and irreversibility. Quantum systems can rarely be thought of as being in total isolation. A system which is interacting with its su...

In this paper we define a new type of rings ”almost powerhermitian rings” (a generalization of almost hermitian rings) and establish several sufficient conditions over a ring R such that, every regular matrix admits a diagonal power-reduction.

A new iteration scheme for computing the sign of a matrix which has no pure imaginary eigenvalues is presented. Then, by applying a well-known identity in matrix functions theory, an algorithm for computing the geometric mean of two Hermitian positive definite matrices is constructed. Moreover, another efficient algorithm for this purpose is derived free from the computation of principal matrix...

We propose to uncover the topology of a pseudo-Hermitian Chern insulator by quantum quench dynamics. The Bloch Hamiltonian is defined in basis $q$-deformed Pauli matrices, which are related representation deformed algebras. show bulk-surface duality phases, then further build concrete relation between static band and dynamics, terms time-averaged spin textures. results also generalized into ful...

We study a bipartite Kronig-Penney model with negative Dirac-delta potentials that may be used, amongst other models, to interpret plasmon propagation in nanoparticle arrays. Such system can mapped into Su-Schrieffer-Heeger-like however, general, the overlap between 'atomic' wavefunctions of neighbouring sites is not negligible. In such case, edge states finite system, which retain their topolo...

We define pseudo-reality and pseudo-adjointness of a Hamiltonian, H, as ρHρ−1 = H∗ and μHμ−1 = H ′, respectively. We prove that the former yields the necessary condition for spectrum to be real whereas the latter helps in fixing a definition for inner-product of the eigenstates. Here we separate out adjointness of an operator from its Hermitian-adjointness. It turns out that a Hamiltonian posse...

We provide time-evolution operators, gauge transformations and a perturbative treatment for non-Hermitian Hamiltonian systems, which are explicitly timedependent. We determine various new equivalence pairs for Hermitian and non-Hermitian Hamiltonians, which are therefore pseudo-Hermitian and in addition in some cases also invariant under PT-symmetry. In particular, for the harmonic oscillator p...

A possible method to investigate non-Hermitian Hamiltonians is suggested through finding a Hermitian operator η+ and defining the annihilation and creation operators to be η+ -pseudo-Hermitian adjoint to each other. The operator η+ represents the η+ -pseudo-Hermiticity of Hamiltonians. As an example, a non-Hermitian and non-PT-symmetric Hamiltonian with imaginary linear coordinate and linear mo...

While Hermiticity of a time-independent Hamiltonian leads to unitary time evolution, in and of itself, the requirement of Hermiticity is only sufficient for unitary time evolution. In this paper, we provide conditions that are both necessary and sufficient. We show that PT symmetry of a time-independent Hamiltonian, or equivalently, reality of the secular equation that determines its eigenvalue...

We study a generalized Aubry-Andre model that obeys $\mathcal{PT}$-symmetry. observe robust $\mathcal{PT}$-symmetric phase with respect to system size and disorder strength, where all eigenvalues are real despite the Hamiltonian being non-hermitian. This can support an Anderson localization transition, giving rich diagram as result of interplay between Our provides perfect platform disorder-dri...