Related papers: The Energy Operator for a Model with a Multiparame…
The exchange operator formalism in polar coordinates, previously considered for the Calogero-Marchioro-Wolfes problem, is generalized to a recently introduced, infinite family of exactly solvable and integrable Hamiltonians $H_k$, $k=1$, 2,…
We show the natural relation between the Wigner Hamiltonian and the conformal Hamiltonian. It is presented a model in (super)conformal quantum mechanics with (super)conformal symmetry in the Wigner-Heisenberg algebra picture $ [x,p_{x}]=…
We study two-dimensional Hamiltonians in phase space with noncommutativity both in coordinates and momenta. We consider the generator of rotations on the noncommutative plane and the Lie algebra generated by Hermitian rotationally invariant…
We consider time-dependent perturbations which are relatively bounded with respect to the square root of an unperturbed Hamiltonian operator, and whose commutator with the latter is controlled by the full perturbed Hamiltonian. The…
In this work we present a general formalism to treat non-Hermitian and noncommutative Hamiltonians. This is done employing the phase-space formalism of quantum mechanics, which allows to write a set of robust maps connecting the Hamitonians…
The Jordan-Wigner transformation is frequently utilised to rewrite quantum spin chains in terms of fermionic operators. When the resulting Hamiltonian is bilinear in these fermions, i.e. the fermions are free, the exact spectrum follows…
In this article, we have introduced a $\mathcal{PT}$ symmetric non-Hermitian Hamiltonian model which is given as $\hat{\mathcal{H}}=\omega (\hat{b}^{\dag}\hat{b}+1/2)+ \alpha (\hat{b}^{2}-(\hat{b}^{\dag})^{2})$ where $\omega$ and $\alpha$…
We study the most general continuous transformation on the generators of bilinear master equations of a quantum oscillator. We find that transformation operators that preserve the hermiticity of density operators and conserve the…
Operator method and cumulant expansion are used for nonperturbative calculation of the partition function and the free energy in quantum statistics. It is shown for Boltzmann diatomic molecular gas with some model intermolecular potentials…
We establish a physically meaningful representation of a quantum energy density for use in Quantum Monte Carlo calculations. The energy density operator, defined in terms of Hamiltonian components and density operators, returns the correct…
A quasi-Hermitian operator is an operator that is similar to its adjoint in some sense, via a metric operator, i.e., a strictly positive self-adjoint operator. Whereas those metric operators are in general assumed to be bounded, we analyze…
Starting on the basis of the non-commutative q-differential calculus, we introduce a generalized q-deformed Schr\"odinger equation. It can be viewed as the quantum stochastic counterpart of a generalized classical kinetic equation, which…
We give an explicit characterization of the most general quasi-Hermitian operator H, the associated metric operators \eta_+, and \eta_+-pseudo-Hermitian operators acting in two-dimensional complex Euclidean space C^2. These operators…
We investigate systematically dimension-9 operators in the standard model effective field theory which contains only standard model fields and respects its gauge symmetry. With the help of the Hilbert series approach to classifying…
We consider real mass and FI deformations of ABJM theory preserving supersymmetry in the large $N$ limit, and compare with holographic results. On the field theory side, the problems amounts to a spectral problem of a non-Hermitian…
We present a method to compute the genus expansion of the free energy of Hermitian matrix models from the large N expansion of the recurrence coefficients of the associated family of orthogonal polynomials. The method is based on the…
In this paper, we propose an adaptive fast solver for a general class of symmetric positive definite (SPD) matrices which include the well-known graph Laplacian. We achieve this by developing an adaptive operator compression scheme and a…
The spectral analysis of a non-Hermitian unbounded operator appearing in quantum physics is our main concern. The properties of such an operator are essentially different from those of Hermitian Hamiltonians, namely due to spectral…
In this paper we commence the study of discrete harmonic analysis associated with Jacobi orthogonal polynomials of order $(\alpha,\beta)$. Particularly, we give the solution $W^{(\alpha,\beta)}_t$, $t\ge 0$, and some properties of the heat…
Multiple Operator Integrals (MOIs) have played a foundational role in operator theory and functional calculus, particularly for analyzing Hermitian matrices via spectral decomposition. Conventional MOIs rely on the assumption of…