Related papers: Operator Space Manifold Theory: Modeling Quantum O…
Unlike standard quantum mechanics, dynamical reduction models assign no particular a priori status to `measurement processes', `apparata', and `observables', nor self-adjoint operators and positive operator valued measures enter the…
We review "quantum" invariants of closed oriented 3-dimensional manifolds arising from operator algebras.
We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…
Harmonic inversion is introduced as a powerful tool for both the analysis of quantum spectra and semiclassical periodic orbit quantization. The method allows to circumvent the uncertainty principle of the conventional Fourier transform and…
We introduce a quantum phase space representation for the orientation state of extended quantum objects, using the Euler angles and their conjugate momenta as phase space coordinates. It exhibits the same properties as the standard Wigner…
Utilizing the previously established general formalism for quantum symmetry reduction in the framework of loop quantum gravity the spectrum of the area operator acting on spherically symmetric states in 4 dimensional pure gravity is…
The Variational Quantum Eigensolver approach to the electronic structure problem on a quantum computer involves measurement of the Hamiltonian expectation value. Formally, quantum mechanics allows one to measure all mutually commuting or…
We study the mirror-field interaction in several frameworks: when it is driven, when it is affected by an environment and when a two-level atom is introduced in the cavity. By using operator techniques we show how these problems may be…
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.…
Let $\alpha\in \mathbb{R}\backslash \mathbb{Q}$ and $\beta(\alpha) = \limsup _{n \to \infty}(\ln q_{n+1})/ q_n <\infty$, where $p_n/q_n$ is the continued fraction approximations to $\alpha$. Let $(H_{\lambda,\alpha,\theta}u)…
In this work, we present an abstract theory for the approximation of operator-valued Riccati equations posed on Hilbert spaces. It is demonstrated here that the error of the approximate solution to the operator-valued Riccati equation is…
In a series of papers on Bohr-Sommerfeld-Heisenberg quantization of completely integrable systems we interpreted shifting operators as quantization of functions ${\mathrm{e}}^{ \pm i{\theta}_j}$ , where $(I_j , {\theta}_j )$ are action…
In this paper, we propose a new perspective of quantum spin (angular momentum) in which the Boltzmann constant \(k_{\beta}\), Planck temperature \(T_{P}\), Planck mass \(m_{P}\) and Planck area \(l_{P}^{2}\) are the integral part of the…
In this note we present a operator formulation of gauge theories in a quantum phase space which is specified by a operator algebra. For simplicity we work with the Heisenberg algebra. We introduce the notion of the derivative (transport)…
In this paper we examine one of the multiple applications of the theta operator xd/dx in quantum mechanics, namely, in the formalism of generalized hypergeometric coherent states (GHG CSs). These states are the most general coherent states,…
Let $T\in B(\mathcal{H})$ be an invertible operator. From the 1940's, Gelfand, Hille and Wermer investigated the invariant subspaces of $T$ by analyzing the growth of $\|T^n\|$, where $n\in \mathbb{Z}$. In this paper, we study the invariant…
Recent advancements in quantum computing suggest the potential to revolutionize computational algorithms across various scientific domains including oceanography and atmospheric science. The field is still relatively young and quantum…
Motivated by the construction of spectral manifolds in noncommutative geometry, we introduce a higher degree Heisenberg commutation relation involving the Dirac operator and the Feynman slash of scalar fields. This commutation relation…
For quantum mechanics of a charged particle in a classical external electromagnetic field, there is an apparent puzzle that the matrix element of the canonical momentum and Hamiltonian operators is gauge dependent. A resolution to this…
We consider questions related to a quantization scheme in which a classical variable f:\Omega\to R on a phase space \Omega is associated with a semispectral measure E^f, such that the moment operators of E^f are required to be of the form…