Related papers: Spectral Design for Matrix Hamiltonians: Different…
We show that a non-Hermitian operator with a tridiagonal matrix representation in a finite-dimensional vector space is similar to an Hermitian operator. The required condition is sufficient and simple examples show that it is not necessary.…
Correlated many-body problems ubiquitously appear in various fields of physics such as condensed matter physics, nuclear physics, and statistical physics. However, due to the interplay of the large number of degrees of freedom, it is…
We study the Hamiltonian truncation for the two-dimensional $\lambda\phi^4$ theory within the framework of Hamiltonian truncation effective theory, where truncation artifacts are mitigated through a systematic inclusion of corrective terms…
We establish a strong-weak coupling duality between two types of free matrix models. In the large-N limit, the real-symmetric matrix model is dual to the quaternionic-real matrix model. Using the large-N conformal invariant collective field…
We study a new class of matrix models, formulated on a lattice. On each site are $N$ states with random energies governed by a Gaussian random matrix Hamiltonian. The states on different sites are coupled randomly. We calculate the density…
We show that some non-Hermitian Hamiltonian operators with tridiagonal matrix representation may be quasi Hermitian or similar to Hermitian operators. In the class of Hamiltonian operators discussed here the transformation is given by a…
It is shown that the radial part of the Hydrogen Hamiltonian factorizes as the product of two not mutually adjoint first order differential operators plus a complex constant epsilon. The 1-susy approach is used to construct non-hermitian…
Operators that intertwine representations of a degenerate version of the double affine Hecke algebra are introduced. Each of the representations is related to multi-variable orthogonal polynomials associated with Calogero-Sutherland type…
We emphasize intertwining relations as a universal tool in constructing one-dimensional quasi-exactly solvable operators and offer their possible generalization to the multidimensional case. Considered examples include all quasi-exactly…
We discuss the computational problems when analyzing general, non-hermitian matrices and in particular the un-modified Wilson lattice Dirac operator. We report on our experiences with the Implicitly Restarted Arnoldi Method. The eigenstates…
An $n\times n$ matrix is said to have a self-interlacing spectrum if its eigenvalues $\lambda_k$, $k=1,\ldots,n$, are distributed as follows $$ \lambda_1>-\lambda_2>\lambda_3>\cdots>(-1)^{n-1}\lambda_n>0. $$ A method for constructing sign…
Intertwiners between representations of Lie groups can be used to obtain relations for matrix elements. We apply this technique to obtain different identities for the wave functions of the open Toda chain, in particular raising operators…
Intertwiners between \ade lattice models are presented and the general theory developed. The intertwiners are discussed at three levels: at the level of the adjacency matrices, at the level of the cell calculus intertwining the face…
A powerful method for calculating the eigenvalues of a Hamiltonian operator consists of converting the energy eigenvalue equation into a matrix equation by means of an appropriate basis set of functions. The convergence of the method can be…
Symplectic self-adjointness of Hamiltonian operator matrices is studied, which arises in symplectic elasticity and optimal control. For the cases of diagonal domain and off-diagonal domain, necessary and sufficient conditions are shown. The…
For a given standard Hamiltonian H=[p-A(x)]^2/(2m)+V(x) with arbitrary complex scalar potential V and vector potential A, with x real, we construct an invertible antilinear operator \tau such that H is \tau-anti-pseudo-Hermitian, i.e.,…
We introduce and analyze a novel class of binary operations on finite-dimensional vector spaces over a field K, defined by second-order multilinear expressions with linear shifts. These operations generate polynomials whose degree increases…
Using an isomorphism between Hilbert spaces $L^2$ and $\ell^{2}$ we consider Hamiltonians which have tridiagonal matrix representations (Jacobi matrices) in a discrete basis and an eigenvalue problem is reduced to solving a three term…
The large N spectrum of the quantum mechanical hamiltonian of two hermitean matrices in a harmonic potential is studied in a framework where one of the matrices is treated exactly and the other is treated as a creation operator impurity in…
By exhibiting the corresponding Lax pair representations we propose a wide class of integrable two-dimensional (2D) fermionic Toda lattice (TL) hierarchies which includes the 2D N=(2|2) and N=(0|2) supersymmetric TL hierarchies as…