Related papers: Internal nonlocality in generally dilated Hermitic…
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…
In most introductory courses on quantum mechanics one is taught that the Hamiltonian operator must be Hermitian in order that the energy levels be real and that the theory be unitary (probability conserving). To express the Hermiticity of a…
Given an initial quantum state |psi_I> and a final quantum state |psi_F> in a Hilbert space, there exist Hamiltonians H under which |psi_I> evolves into |psi_F>. Consider the following quantum brachistochrone problem: Subject to the…
We obtain a general concept of triplet of Hilbert spaces with closed (unbounded) embeddings instead of continuous (bounded) ones. The construction starts with a positive selfadjoint operator $H$, that is called the Hamiltonian of the…
One-dimensional scattering mediated by non-Hermitian Hamiltonians is studied. A schematic set of models is used which simulate two point interactions at a variable strength and distance. The feasibility of the exact construction of the…
When canonical Hamiltonians of local quantum field theories are transformed using a renormalization group procedure for effective particles, the resulting interaction terms are non-local. The range of their non-locality depends on the…
We consider a Hamiltonian $ H = H_0+ V $, in which $ H_0$ is a given non-random Hermitian matrix,and $V$ is an $N \times N$ Hermitian random matrix with a Gaussian probability distribution.We had shown before that Dyson's universality of…
We consider the simulation of the dynamics of one nonlocal Hamiltonian by another, allowing arbitrary local resources but no entanglement nor classical communication. We characterize notions of simulation, and proceed to focus on…
One of the postulates of quantum mechanics is that the Hamiltonian is Hermitian, as this guarantees that the eigenvalues are real. Recently there has been an interest in asking if $H^\dagger = H$ is a necessary condition, and has lead to…
We show in the present paper that pseudo-Hermitian Hamiltonian systems with even PT-symmetry admit a degeneracy structure. This kind of degeneracy is expected traditionally in the odd PT-symmetric systems which is appropriate to the…
We construct a discrete non-hermitean momentum operator, which implements faithfully the non self-adjoint nature of momentum for a particle in a box. Its eigenfunctions are strictly limited to the interior of the box in the continuum limit,…
Non-Hermitian quantum systems exhibit fascinating characteristics such as non-Hermitian topological phenomena and skin effect, yet their studies are limited by the intrinsic difficulties associated with their eigenvalue problems, especially…
When one applies a type of non-Hermitian effect, constant imaginary vector potential, to disordered systems, delocalization is induced even in two or lower dimension. By using the non-Hermitian induced transition as a probe, We propose a…
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…
We extend the application of the techniques developed within the framework of the pseudo-Hermitian quantum mechanics to study a unitary quantum system described by an imaginary PT-symmetric potential v(x) having a continuous real spectrum.…
Integrability is a cornerstone of classical mechanics, where it has a precise meaning. Extending this notion to quantum systems, however, remains subtle and unresolved. In particular, deciding whether a quantum Hamiltonian - viewed simply…
Non-Hermitian systems are widespread in both classical and quantum physics. The dynamics of such systems has recently become a focal point of research, showcasing surprising behaviors that include apparent violation of the adiabatic theorem…
A few recent innovations of applicability of standard textbook Quantum Theory are reviewed. The three-Hilbert-space formulation of the theory (known from the interacting boson models in nuclear physics) is discussed in its slightly…
The Dirac Hamiltonian in the (2+1) dimensional curved space-time has been studied with a metric for an expanding de Sitter space-time which is a two sphere. The spectrum and the exact solutions of the time dependent non-Hermitian and angle…
We describe a technique to emulate a two-level \PT-symmetric spin Hamiltonian, replete with gain and loss, using only the unitary dynamics of a larger quantum system. This we achieve by embedding the two-level system in question in a…