Related papers: Constructing Exactly Solvable Pseudo-hermitian Man…
A method to construct non-Dirac-hermitian supersymmetric quantum system that is isospectral with a Dirac-hermitian Hamiltonian is presented. The general technique involves a realization of the basic canonical (anti-)commutation relations…
A class of pseudo-hermitian quantum system with an explicit form of the positive-definite metric in the Hilbert space is presented. The general method involves a realization of the basic canonical commutation relations defining the quantum…
A method to construct non-dissipative non-Dirac-hermitian relativistic quantum system that is isospectral with a Dirac-hermitian Hamiltonian is presented. The general technique involves a realization of the basic canonical…
A non-hermitian deformation of the one-dimensional transverse Ising model is shown to have the property of quasi-hermiticity. The transverse Ising chain is obtained from the starting non-hermitian Hamiltonian through a similarity…
The construction of exactly-solvable models has recently been advanced by considering integrable $T\bar{T}$ deformations and related Hamiltonian deformations in quantum mechanics. We introduce a broader class of non-Hermitian Hamiltonian…
We show that a Dicke-type pseudo-hermitian Hamiltonian undergoes quantum phase transition by mapping it to the "Dressed Dicke Model" through a similarity transformation. We find the positive-definite metric in the Hilbert space of the…
We examine the properties and consequences of pseudo-supersymmetry for quantum systems admitting a pseudo-Hermitian Hamiltonian. We explore the Witten index of pseudo-supersymmetry and show that every pair of diagonalizable (not necessarily…
It is well known that the unitary evolution of a closed $M-$level quantum system can be generated by a non-Hermitian Hamiltonian $H$ with real spectrum. Its Hermiticity can be restored via an amended inner-product metric $\Theta$. In…
The energy spectra of two different quantum systems are paired through supersymmetric algorithms. One of the systems is Hermitian and the other is characterized by a complex-valued potential, both of them with only real eigenvalues in their…
This work outlines a consistent method of identifying subsystems in finite-dimensional Hilbert spaces, independent of the underlying inner-product structure. Such Hilbert spaces arise in $\mathcal{P}\mathcal{T}$-symmetric quantum mechanics,…
We discuss the basic theoretical framework for non-Hermitian quantum systems with particular emphasis on the diagonalizability of non-Hermitian Hamiltonians and their $GL(1,\mathbb{C})$ gauge freedom, which are relevant to the adiabatic…
Non-stationary version of unitary quantum mechanics formulated in non-Hermitian (or, more precisely, in hiddenly Hermitian) interaction-picture representation is illustrated via an elementary $N$ by $N$ matrix Hamiltonian $H(t)$ mimicking a…
We provide exact analytical solutions for a two dimensional explicitly time-dependent non-Hermitian quantum system. While the time-independent variant of the model studied is in the broken PT-symmetric phase for the entire range of the…
Unitarity is a cornerstone of quantum theory, ensuring the conservation of probability and information. Although non-Hermitian Hamiltonians are typically associated with open or dissipative systems, pseudo-Hermitian quantum mechanics shows…
We discuss the dynamical quantum systems which turn out to be bi-unitary with respect to the same alternative Hermitian structures in a infinite-dimensional complex Hilbert space. We give a necessary and sufficient condition so that the…
Several explicit examples of multi-particle quasi exactly solvable `discrete' quantum mechanical Hamiltonians are derived by deforming the well-known exactly solvable multi-particle Hamiltonians, the Ruijsenaars-Schneider-van Diejen…
A diagonalizable non-Hermitian Hamiltonian having a real spectrum may be used to define a unitary quantum system, if one modifies the inner product of the Hilbert space properly. We give a comprehensive and essentially self-contained review…
To overcome the fast oscillatory behavior of correlation functions for extracting scattering phase shift in real-time quantum simulations encountered in Ref.\cite{Guo:2026qkx}, we propose and test two solutions in the present work. One is…
We demonstrate how to discriminate two non-orthogonal, entangled quantum state which are slightly different from each other by using pseudo-Hermitian system. The positive definite metric operator which makes the pseudo-Hermitian systems…
A universal algorithm to construct N-particle (classical and quantum) completely integrable Hamiltonian systems from representations of coalgebras with Casimir element is presented. In particular, this construction shows that quantum…