Related papers: Oscillation probabilities for a PT-symmetric non-H…
The eigenvalue problem of the spherically symmetric oscillator Hamiltonian is revisited in the context of canonical raising and lowering operators. The Hamiltonian is then factorized in terms of two not mutually adjoint factorizing…
Open classical and quantum systems with effective parity-time ($\mathcal{PT}$) symmetry, over the past five years, have shown tremendous promise for advances in lasers, sensing, and non-reciprocal devices. And yet, how such effective…
We introduce a class of PT-symmetric systems which include mutually matched nonlinear loss and gain (inother words, a class of PT-invariant Hamiltonians in which both the harmonic and anharmonic parts are non-Hermitian). For a basic system…
A new class of non-Hermitian Hamiltonians with real spectrum, which are written as a real linear combination of su(2) generators in the form $ H=\omega J_{3}+\alpha J_{-}+\beta J_{+}$, $\alpha \neq \beta$, is analyzed. The metrics which…
We investigate PT -symmetry breaking transitions in a dimer comprising two LC oscillators, one with loss and the second with gain. The electric energy of this four-mode model oscillates between the two LC circuits, and between capacitive…
The non-Hermitian but $\mathcal{PT}$-symmetric quantum field theories are known to have a pseudo-Hermitian interpretation. However the corresponding intertwining operator happens to be nonlocal that raises the question to what extent this…
Harmonic oscillator in noncommutative two dimensional lattice are investigated. Using the properties of non-differential calculus and its applications to quantum mechanics, we provide the eigenvalues and eigenfunctions of the corresponding…
We show that and how point interactions offer one of the most suitable guides towards a quantitative analysis of properties of certain specific non-Hermitian (usually called PT-symmetric) quantum-mechanical systems. A double-well model is…
A quantum state for being an eigenstate of some local Hamiltonian should be constraint by zero energy variance and consequently, the constraint is rather strong that a single eigenstate may uniquely determine the Hamiltonian. For…
Some PT-symmetric non-hermitean Hamiltonians have only real eigenvalues. There is numerical evidence that the associated PT-invariant energy eigenstates satisfy an unconventional completeness relation. An ad hoc scalar product among the…
Neutrino oscillation phenomenon is a definite evidence of physics beyond the Standard Model (SM) and high precision measurement of neutrino properties will certainly give us clue about what lies beyond the SM. In particular, precise…
During the recent developments of quantum theory it has been clarified that the observable quantities (like energy or position) may be represented by operators (with real spectra) which are manifestly non-Hermitian. The mathematical…
We briefly explain some simple arguments based on pseudo Hermiticity, supersymmetry and PT-symmetry which explain the reality of the spectrum of some non-Hermitian Hamiltonians. Subsequently we employ PT-symmetry as a guiding principle to…
We extend the study of supersymmetric tridiagonal Hamiltonians to the case of non-Hermitian Hamiltonians with real or complex conjugate eigenvalues. We find the relation between matrix elements of the non-Hermitian Hamiltonian $H$ and its…
We show that a quantum system possessing an exact antilinear symmetry, in particular PT-symmetry, is equivalent to a quantum system having a Hermitian Hamiltonian. We construct the unitary operator relating an arbitrary non-Hermitian…
Non-Hermitian systems exhibiting topological properties are attracting growing interest. In this work, we propose an algorithm for solving the ground state of a non-Hermitian system in the matrix product state (MPS) formalism based on a…
We notice that PT symmetric non-Hermitian one dimensional simple Harmonic Oscillator under simultaneous transformation of co-ordinate and momentum with proper choice of positive oscillating frequency can reflect negative spectrum with well…
The Hamiltonian for quantum electrodynamics becomes non-Hermitian if the unrenormalized electric charge $e$ is taken to be imaginary. However, if one also specifies that the potential $A^\mu$ in such a theory transforms as a pseudovector…
We show that several Hamiltonians that are $\mathcal{PT}$ symmetric may be taken to Hermitian Hamiltonians via a non-unitary transformation and vice versa. We also show that for some specific Hamiltonians such non-unitary transformations…
The complex eigenvalues of some non-Hermitian Hamiltonians, e.g. parity-time symmetric Hamiltonians, come in complex-conjugate pairs. We show that for non-Hermitian scattering Hamiltonians (of a structureless particle in one dimension)…