Related papers: Operator transpose within normal ordering and its …
We study a quasi-one-dimensional fluid of hard dumbbells with continuous orientational degrees of freedom using an exact transfer-matrix formulation. The model allows for a complete analytical characterization of thermodynamic properties,…
We derive simple formulas connecting the generalized Wigner functions for $s$-ordering with the density matrix, and vice-versa. These formulas proved very useful for quantum mechanical applications, as, for example, for connecting master…
It is widely believed that statistical interpretation of quantum mechanics requires that density operators representing quantum states be normalized. We present a description of selective measurements in terms of density operators. The…
The purpose of this paper is twofold. First, basic concepts such as Gamma function, almost convergence, fractional order difference operator and sequence spaces are given as a survey character. Thus, the current knowledge about those…
Quantum mechanics is often developed in the position representation, but this is not necessary, and one can perform calculations in a representation-independent fashion, even for wavefunctions. In this work, we illustrate how one can…
We perform conformal perturbation theory by marginal operators to first order. A suitable renormalization method is needed that makes the conformal invariance of the deformed correlation functions manifest. Combining the embedding space…
The transactional interpretation of quantum mechanics, which uses retarded and advanced solutions of the Schrodinger equation and its complex conjugate, offers an original way to visualize and understand quantum processes. After a brief…
Wiener-Hopf plus Hankel operators acting between Lebesgue spaces on the real line are studied in view of their invertibility, one sided-invertibility, Fredholm, and semi-Fredholm properties. This is done in two different cases: (i) when the…
The convolution operator is the fundamental building block of modern convolutional neural networks (CNNs), owing to its simplicity, translational equivariance, and efficient implementation. However, its structure as a fixed, linear,…
We introduce an entanglement branching operator to split a composite entanglement flow in a tensor network which is a promising theoretical tool for many-body systems. We can optimize an entanglement branching operator by solving a…
Given a weighted $\ell^2$ space with weights associated to an entire function, we consider pairs of weighted shift operators, whose commutators are diagonal operators, when considered as operators over a general Fock space. We establish a…
We discuss an application of the transfer operator approach to the analysis of the different spectral characteristics of 1d random band matrices (correlation functions of characteristic polynomials, density of states, spectral correlation…
Covariant affine integral quantization of the half-plane is studied and applied to the motion of a particle on the half-line. We examine the consequences of different quantizer operators built from weight functions on the half-plane. To…
Metaplectic Wigner distributions generalize the most popular time-frequency representations, such as the short-time Fourier transform (STFT) and $\tau$-Wigner distributions, using metaplectic operators. However, in order for a metaplectic…
In this paper, the order boundedness and essential norm of generalized weighted composition operators on Bergman spaces with doubling weights are characterized. Specially, we estimate the essential norm of these operators on weighted…
We trace back the phenomenon of "delayed-choice entanglement swapping" as it was realized in a recent experiment to the commutativity of the projection operators that are involved in the corresponding measurement process. We also propose an…
The Heisenberg evolution of a given unitary operator corresponds classically to a fixed canonical transformation that is viewed through a moving coordinate system. The operators that form the bases of the Weyl representation and its Fourier…
We discuss the entanglement properties of bipartite states with Gaussian Wigner functions. Separability and the positivity of the partial transpose are characterized in terms of the covariance matrix of the state, and it is shown that for…
Due to its effectiveness and performance, the Transformer translation model has attracted wide attention, most recently in terms of probing-based approaches. Previous work focuses on using or probing source linguistic features in the…
The need to retain the relative phases in quantum mechanics implies an addition law parametrized by a phase of two density operators required for the purification of a density matrix. This is shown with quantum tomography and the Wigner…