Related papers: Time-dependent $\mathcal{PT}$-symmetric quantum me…
While a Hamiltonian can be both Hermitian and $PT$ symmetric, it is $PT$ symmetry that is the more general, as it can lead to real energy eigenvalues even if the Hamiltonian is not Hermitian. We discuss some specific ways in which $PT$…
We provide the first solution of a time-dependent metric operator for the non-Hermitian Jaynes-Cummings Hamiltonian. We use this solution to calculate the entanglement between two identical isolated such Hamiltonians. The presence of a…
Canonical quantum mechanics postulates Hermitian Hamiltonians to ensure real eigenvalues. Counterintuitively, a non-Hermitian Hamiltonian, satisfying combined parity-time (PT) symmetry, could display entirely real spectra above some…
Parity-time ($PT$) symmetric Hamiltonians are generally non-Hermitian and give rise to exotic behaviour in quantum systems at exceptional points, where eigenvectors coalesce. The recent realisation of $PT$-symmetric Hamiltonians in quantum…
Over the past decade, non-Hermitian, $\mathcal{PT}$-symmetric Hamiltonians have been investigated as candidates for both, a fundamental, unitary, quantum theory, and open systems with a non-unitary time evolution. In this paper, we…
We propose a new point of view regarding the problem of time in quantum mechanics, based on the idea of replacing the usual time operator $\mathbf{T}$ with a suitable real-valued function $T$ on the space of physical states. The proper…
We propose a scheme to deal with certain time-dependent non-Hermitian Hamiltonian operators $H(t)$ that generate a real phase in their time-evolution. This involves the use of invariant operators $I_{PH}(t)$ that are pseudo-Hermitian with…
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…
We propose random non-Hermitian Hamiltonians to model the generic stochastic nonlinear dynamics of a quantum state in Hilbert space. Our approach features an underlying linearity in the dynamical equations, ensuring the applicability of…
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…
The parity-time-reversal- ($\mathcal{PT}$) symmetric quantum mechanics (PTQM) has developed into a noteworthy area of research. However, to date most known studies of PTQM focused on the spectral properties of non-Hermitian Hamiltonian…
Recently Bender, Brody, Jones and Meister found that in the quantum brachistochrone problem the passage time needed for the evolution of certain initial states into specified final states can be made arbitrarily small, when the…
The quantum measurement axiom dictates that physical observables and in particular the Hamiltonian must be diagonalizable and have a real spectrum. For a time-independent Hamiltonian (with a discrete spectrum) these conditions ensure the…
Non-Hermitian systems with parity-time ($\mathcal{PT}$) symmetry give rise to exceptional points (EPs) with exceptional properties that arise due to the coalescence of eigenvectors. Such systems have been extensively explored in the…
The explorations of the quantum-inspired symmetries in optical and photonic systems have witnessed immense research interests both fundamentally and technologically in a wide range of subjects of physics and engineering. One of the…
Open classical and quantum systems have attracted great interest in the past two decades. These include systems described by non-Hermitian Hamiltonians with parity-time $(\mathcal{PT})$ symmetry that are best understood as systems with…
The physics of systems that cannot be described by a Hermitian Hamiltonian, has been attracting a great deal of attention in recent years, motivated by their nontrivial responses and by a plethora of applications for sensing, lasing, energy…
Parity-Time (PT) symmetric quantum mechanics is a complex extension of conventional Hermitian quantum mechanics in which physical observables possess a real eigenvalue spectrum. However, an experimental demonstration of the true quantum…
We review the methodology to theoretically treat parity-time- ($\mathcal{PT}$-) symmetric, non-Hermitian quantum many-body systems... (For the full abstract see paper)
It is well known that nonrelativistic quantum mechanics presents a clear asymmetry between space and time. Much of this asymmetry is attributed to the lack of Lorentz invariance of the theory. Nonetheless, a recent work [Phys. Rev. A…