Related papers: Counting operator analysis of the discrete spectru…

In a pre-selected Hilbert space of quantum states the unitarity of the evolution is usually guaranteed via a pre-selection of the generator (i.e., of the Hamiltonian operator) in self-adjoint form. In fact, the simultaneous use of both of…

We introduce and study in a general setting the concept of homogeneity of an operator and, in particular, the notion of homogeneity of an integral operator. In the latter case, homogeneous kernels of such operators are also studied. The…

This article studies sharp norm estimates for the commutator of pseudo-differential operators with multiplication operators on closed Heisenberg manifolds. In particular, we obtain a Calderon commutator estimate: If $D$ is a first-order…

We prove that any $n$-dimensional Hamiltonian operator with pure point spectrum is completely integrable via self-adjoint first integrals. Furthermore, we establish that given any closed set $\Sigma\subset\mathbb R$ there exists an…

As a continuum work of Bhaumik et al who derived the common eigenvector of the number-difference operator Q and pair-annihilation operator ab (J. Phys. A9 (1976) 1507) we search for the simultaneous eigenvector of Q and (ab-a^{+}b^{+}) by…

In this paper we are developing a theory of rational (pseudo) difference Hamiltonian operators, focusing in particular on its algebraic aspects. We show that a pseudo--difference Hamiltonian operator can be represented as a ratio $AB^{-1}$…

The spectral properties of the Frobenius-Perron operator of one-dimensional maps are studied when approaching a weakly intermittent situation. Numerical investigation of a particular family of maps shows that the spectrum becomes extremely…

A non-Hermitian operator with a real spectrum and a complete set of eigenvectors may serve as the Hamiltonian operator for a unitary quantum system provided that one makes an appropriate choice for the defining inner product of the physical…

Optimized, necessary and sufficient conditions for the identification of the Schmidt number will be derived in terms of general Hermitian operators. These conditions apply to arbitrary mixed quantum states. The optimization procedure…

We achieve query-optimal quantum simulations of non-Hermitian Hamiltonians $H_{\mathrm{eff}} = H_R + iH_I$, where $H_R$ is Hermitian and $H_I \succeq 0$, using a bivariate extension of quantum signal processing (QSP) with non-commuting…

Consider a Hermitian operator $A$ acting on a complex Hilbert space of dimension $2^n$. We show that when $A$ has small degree in the Pauli expansion, or in other words, $A$ is a local $n$-qubit Hamiltonian, its operator norm can be…

We show that a diagonalizable (non-Hermitian) Hamiltonian H is pseudo-Hermitian if and only if it has an antilinear symmetry, i.e., a symmetry generated by an invertible antilinear operator. This implies that the eigenvalues of H are real…

The concept of operator frame can be considered as a generalization of frame. Firstly, we introduce the notion of operator frame for the set of all adjointable operators $Hom_{\mathcal{A}}^{\ast}(\mathcal{X})$ on a Hilbert…

Let $H$ be a self-adjoint operator, bounded from below and let $O$ be a bounded self-adjoint operator with purely discrete spectrum. Suppose that (i) $E(H)=\inf \mathrm{spec}(H)$ is a simple eigenvalue, and (ii) $H$ strongly commutes with…

In this work, we revisit several families of standard Hamiltonians that appear in the literature and discuss their symmetries and conserved quantities in the language of commutant algebras. In particular, we start with families of…

The eigenvalue equation of a band or a block tridiagonal matrix, the tight binding model for a crystal, a molecule, or a particle in a lattice with random potential or hopping amplitudes: these and other problems lead to three-term…

This article proposed a new approach to the determination of the spectrum for nonlinear continuous operators in the Banach spaces and using it investigated the spectrum of some classes of operators. Here shows that in nonlinear operators…

This work continues \cite{bib1} where the construction of Hamiltonian $H$ for the system of three quantum particles is considered. Namely the system consists of two fermions with mass $1$ and another particle with mass $m>0$. In the present…

A scalar valued random field is called operator-scaling if it satisfies a self-similarity property for some matrix E with positive real parts of the eigenvalues. We present a moving average and a harmonizable representation of stable…

We investigate properties of the most general PT-symmetric non-Hermitian Hamiltonian of cubic order in the annihilation and creation operators as a ten parameter family. For various choices of the parameters we systematically construct an…