相关论文: Phase Operator Problem and Macroscopic Extension o…

The position operator (defined within Schroedinger representation as usual) becomes meaningless when the usual Born-von Karman periodic boundary conditions are adopted: this fact is at the root of the polarization problem. I show how to…

The spectral analysis of a non-Hermitian unbounded operator appearing in quantum physics is our main concern. The properties of such an operator are essentially different from those of Hermitian Hamiltonians, namely due to spectral…

The phase resolution of interferometers is limited by the so-called Heisenberg limit, which states that the optimum phase sensitivity is inversely proportional to the number of interfering particles N, a 1/sqrt{N} improvement over the…

The main achievements of Pseudo-Hermitian Quantum Mechanics and its distinction with the indefinite-metric quantum theories are reviewed. The issue of the non-uniqueness of the metric operator and its consequences for defining the…

We study solutions of the collisionless Boltzmann equation (CBE) in a functional Koopman representation. This facilitates the use of linear spectral techniques characteristic of the analysis of Schrodinger-type equations. For illustrative…

Position deformation of a Heisenberg algebra and Hilbert space representation of both maximal length and minimal momentum uncertainties may lead to loss of Hermiticity of some operators that generate this algebra. Consequently, the…

Spectral equivalences of the quasi-exactly solvable sectors of two classes of Schrodinger operators are established, using Gaudin-type Bethe ansatz equations. In some instances the results can be extended leading to full isospectrality. In…

Phase estimation, at the heart of many quantum metrology and communication schemes, can be strongly affected by noise, whose amplitude may not be known, or might be subject to drift. Here, we investigate the joint estimation of a phase…

An integral of the Wigner function of a wavefunction |psi >, over some region S in classical phase space is identified as a (quasi) probability measure (QPM) of S, and it can be expressed by the |psi > average of an operator referred to as…

We address the problem of phase shift operator acting as time evolution operator in Pegg-Barnett formalism. It is argued that standard shift operator is inconsistent with the behaviour of the state vector under cyclic evolution. We consider…

Requirements of a conjugate operator are emphasized, especially in its role in uncertainty relations.It is argued that in many contexts it is necessary to extend the Hilbert space in order to define a conjugate operator as in gauge…

It is well known that the unboundedness of operators in Hilbert space entails domain troubles. It is also well known that most domain troubles can be surmounted by extending the Hilbert space to a rigged Hilbert space. In this note, we…

Pseudo-Hermitian operators generalize the concept of Hermiticity. This class of operators includes the quasi-Hermitian operators, which reformulate quantum theory while retaining real-valued measurement outcomes and unitary time evolution.…

It is often inevitable to introduce an indefinite-metric space in quantum field theory. There is a problem to determine the metric structure of a given representation space of field operators. We show the systematic method to determine such…

We propose a new generalised formalism for estimating the quantum phase uncertainty of pure and mixed continuous-variable quantum states and compare this with the phase uncertainty given by the quantum Fisher information. In order to…

In quantum mechanics the position and momentum operators are related to each other via the Fourier transform. In the same way, here we show that the so-called Pegg-Barnett phase operator can be obtained by the application of the discrete…

We present a systematic perturbative construction of the most general metric operator (and positive-definite inner product) for quasi-Hermitian Hamiltonians of the standard form, H= p^2/2 + v(x), in one dimension. We show that this problem…

A complex function is associated to each bounded linear operator

In this paper we obtain a description of the Hermitian operators acting on the Hilbert space $\C^n$, description which gives a complete solution to the over parameterization problem. More precisely we provide an explicit parameterization of…

Describing systems with non-Hermitian (NH) operators remains a challenge in quantum theory due to instabilities (e.g., exceptional points and decoherence) arising from interactions with the environment. We propose a framework to express the…