Related papers: Two simple models derived from a quantum-mechanica…
We formulate the coherent state path integral on a two dimensional noncommutative plane using the fact that noncommuative quantum mechanics can be viewed as a quantum system on the Hilbert space of Hilbert-Schmidt operators acting on…
We describe quantum behaviors of a simple harmonic oscillator, starting from the classical mechanics. By imposing two conditions on the phase points generated from a symplectic algorithm, we obtain discrete energy levels, satisfying $E_n…
A general strategy is provided to identify the most general metric for diagonalizable pseudo-Hermitian and anti-pseudo-Hermitian Hamilton operators represented by two-dimensional matrices. It is investigated how a permutation of the…
Since the realization of quantum systems described by non-Hermitian Hamiltonians with parity-time (PT) symmetry, interest in non-Hermitian, quantum many-body models has steadily grown. Most studies to-date map to traditional quantum spin…
In this paper we consider energy operator (a free Hamiltonian), in the second-quantized approach, for the multiparameter quon algebras: $a_{i}a_{j}^{\dagger}-q_{ij}a_{j}^{\dagger}a_{i} = \delta_{ij}, i,j\in I$ with $(q_{ij})_{i,j\in I}$ any…
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…
We propose an approximate mapping of a molecular Hamiltonian to a Hamiltonian of qubits, which allows for high accuracy quantum chemistry calculations of vertical excitation energies of some molecules. The mapping is based on separating of…
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 $\alpha$…
A set of Hamiltonians that are not self-adjoint but have the spectrum of the harmonic oscillator is studied. The eigenvectors of these operators and those of their Hermitian conjugates form a bi-orthogonal system that provides a…
We provide time-evolution operators, gauge transformations and a perturbative treatment for non-Hermitian Hamiltonian systems, which are explicitly time-dependent. We determine various new equivalence pairs for Hermitian and non-Hermitian…
One of the unique features of non-Hermitian~(NH) systems is the appearance of non-Hermitian degeneracies known as exceptional points~(EPs). The extensively studied defective EPs occur when the Hamiltonian becomes non-diagonalizable. Aside…
A time operator is a Hermitian operator that is canonically conjugate to a given Hamiltonian. For a particle in 1-dimension, a Hamiltonian conjugate operator in position representation can be obtained by solving a hyperbolic second-order…
A series of recent papers ``Faster than Hermitian Quantum Mechanics'' and related articles made a point of the possibility of a non-Hermitian, but PT-symmetric, operator to play the role of a Hamiltonian. In particular, they show that with…
We give a simple proof of the fact that every diagonalizable operator that has a real spectrum is quasi-Hermitian and show how the metric operators associated with a quasi-Hermitian Hamiltonian are related to the symmetry generators of an…
We study the path integral solution of a system of particle moving in certain class of PT symmetric non-Hermitian and non-central potential. The Hamil- tonian of the system is converted to a separable Hamiltonian of Liouville type in…
In this paper we revisit the problem of finding hidden symmetries in quantum mechanical systems. Our interest in this problem was renewed by nontrivial degeneracies of a simple spin Hamiltonian used to model spin relaxation in alkali-metal…
We introduce a general framework for realizing $\mathcal{PT}$-like phase transitions in non-Hermitian systems without imposing explicit parity--time ($\mathcal{PT}$) symmetry. The approach is based on constructing a Hamiltonian as the…
We study non-Hermitian quantum mechanics in the presence of a minimal length. In particular we obtain exact solutions of a non-Hermitian displaced harmonic oscillator and the Swanson model with minimal length uncertainty. The spectrum in…
Usually duality process keeps energy spectrum invariant. In this paper, we provide a duality, which keeps entanglement spectrum invariant, in order to diagnose quantum entanglement of non-Hermitian non-interacting fermionic systems. We…
We consider the simplest nontrivial supersymmetric quantum mechanical system involving higher derivatives. We unravel the existence of additional bosonic and fermionic integrals of motion forming a nontrivial algebra. This allows one to…