Related papers: Milne quantization for non-Hermitian systems
We present an asymptotically exact solution of a paradigmatic non-Hermitian model: the disordered interacting fermionic Hatano-Nelson model, or equivalently, the non-Hermitian spin-1/2 XXZ model. We use a renormalization group method suited…
Non-Hermitian systems with parity-time symmetry have been developed rapidly and hold great promise for future applications. Unlike most existing works considering the symmetry of the free energy terms (e.g., gain-loss system), in this…
In the context of non-Hermitian quantum mechanics, many systems are known to possess a pseudo PT symmetry , i.e. the non-Hermitian Hamiltonian H is related to its adjoint H^{{\dag}} via the relation, H^{{\dag}}=PTHPT . We propose a…
In this work we consider a generalization of the symmetry classification of topological insulators to non-Hermitian Hamiltonians which satisfy a combined $PT$-symmetry (parity and time-reversal). We show via examples, and explicit bulk and…
Non-Hermitian systems display remarkable response effects that reflect a variety of distinct spectral scenarios, such as exceptional points where the eigensystem becomes defective. However, present frameworks treat the different scenarios…
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…
We consider the description of open quantum systems with probability sinks (or sources) in terms of general non-Hermitian Hamiltonians.~Within such a framework, we study novel possible definitions of the quantum linear entropy as an…
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…
Nonlinear Hamiltonian systems describing the abstract Vlasov and Hartree equations are considered in the framework of algebraic Poissonian theory. The concept of uniformization is introduced; it generalizes the method of second quantization…
We associate the stationary harmonic oscillator with time-dependent systems exhibiting non-Hermiticity by means of point transformations. The new systems are exactly solvable, with all-real spectrum, and transit to the Hermitian…
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…
Non-Hermitian Hamiltonians possessing a discrete real spectrum motivated a remarkable research activity in quantum physics and new insights have emerged. In this paper we formulate concepts of statistical thermodynamics for systems…
A consistent physical theory of quantum mechanics can be built on a complex Hamiltonian that is not Hermitian but instead satisfies the physical condition of space-time reflection symmetry (PT symmetry). Thus, there are infinitely many new…
Recently developed parity (P) and time-reversal (T) symmetric non-Hermitian systems govern a rich variety of new and characteristically distinct physical properties, which may or may not have a direct analog in their Hermitian counterparts.…
It is generally assumed that a Hamiltonian for a physically acceptable quantum system (one that has a positive-definite spectrum and obeys the requirement of unitarity) must be Hermitian. However, a PT-symmetric Hamiltonian can also define…
We fill some of existed gaps in the correspondence between Supersymmetric Quantum Mechanics and the Inverse Scattering Transform by extending the consideration to the case of paired stationary and non-stationary Hamiltonians. We formulate…
Simple examples of non-Hermitian Hamiltonians with purely real spectra defined in $L^2(R^+)$ having spectral singularities inside the continuous spectrum are given. It is shown that such Hamiltonians may appear by shifting the ndependent…
The standard $\mathcal{PT}$-symmetric dimer is a linearly-coupled two-site discrete nonlinear Schr\"odinger equation with one site losing and the other one gaining energy at the same rate. We show that despite gain and loss, the standard…
I will provide a pedagogical introduction to non-Hermitian quantum systems that are PT-symmetric, that is they are left invariant under a simultaneous parity transformation (P) and time-reversal (T). I will explain how generalised versions…
Recently, apparent nonphysical implications of non-Hermitian quantum mechanics (NHQM) have been discussed in the literature. In particular, the apparent violation of the no-signaling theorem, discrimination of nonorthogonal states, and the…