Related papers: Spectral aspects of the Berezin transform
A vertex operator approach for form factors of Belavin's $(\mathbb{Z}/n\mathbb{Z})$-symmetric model is constructed on the basis of bosonization of vertex operators in the $A^{(1)}_{n-1}$ model and vertex-face transformation. As simple…
We present a microscopic theory for nonlinear optical spectroscopy of N molecules in an optical cavity. A quantum Langevin analytical expression is derived for the time- and frequency-resolved signals accounting for arbitrary numbers of…
We extend the construction of generalized Berezin and Berezin-Toeplitz quantization to the case of compact Hodge supermanifolds. Our approach is based on certain super-analogues of Rawnsley's coherent states. As applications, we discuss the…
Koopman operators and transfer operators represent dynamical systems through their induced linear action on vector spaces of observables, enabling the use of operator-theoretic techniques to analyze nonlinear dynamics in state space. The…
How much unavoidable randomness is generated by a Positive Operator Valued Measure (POVM)? We address this question using two complementary approaches. First we study the variance of a real variable associated to the POVM outcomes. In this…
This paper investigates the concept of the $q$-Berezin range and $q$-Berezin number of bounded linear operators acting on Hardy space. We obtain the $q$-Berezin range of some classes of operators on Hardy space. In addition, the convexity…
We study wave propagation in periodic and frequency dependent materials. The approach in this paper leads to spectral analysis of a quadratic operator pencil where the spectral parameter relates to the quasimomentum and the frequency is a…
We investigate the Berezin-Toeplitz operators that operate on the geometric quantized space corresponding to the $SO(3)$-Witten-Chern-Simons theory. We conjecture that the $SO(3)$-Berezin-Toeplitz operators quantized from the A-polynomial…
The paper develops theory of covariant transform, which is inspired by the wavelet construction. It was observed that many interesting types of wavelets (or coherent states) arise from group representations which are not square integrable…
Our main purpose of this article is to study the convergence and other related properties of q-Bernstein-Kantorovich operators including the shifted knots of real positive numbers. We design the shifted knots of Bernstein-Kantorovich…
The transfer tensor method is a versatile tool for analyzing and propagating general open quantum systems. It captures in a compact manner all memory effects in a non-Markovian system through a straightforward transformation of a set of…
Bopp shifts, introduced in 1956, played a pivotal role in the statistical interpretation of quantum mechanics. As demonstrated in our previous work, Bopp's construction provides a phase-space perspective of quantum mechanics that is closely…
Completely positive quantum operations are frequently discussed in the contexts of statistical mechanics and quantum information. They are customarily given by maps forming positive operator-values measures. To intuitively understand…
We define a Hermitian phase operator for zero mass spin one particles (photons) by taking account polarization. The Hilbert space includes the positive helicity states and negative helicity states with opposite circular polarization. We…
We define essentially positive operators on Hilbert space as a class of self-adjoint operators whose essential spectra is contained in the nonnegative real numbers and describe their basic properties. Using Toeplitz operators and the…
Among certification techniques, those based on the violation of Bell inequalities are appealing because they do not require assumptions on the underlying Hilbert space dimension and on the accuracy of calibration methods. Such…
Nonlinearities in finite dimensions can be linearized by projecting them into infinite dimensions. Unfortunately, often the linear operator techniques that one would then use simply fail since the operators cannot be diagonalized. This…
Following Nag-Sullivan, we study the representation of the group ${\rm Diff}^+(S^1)$ of diffeomorphisms of the circle on the Hilbert space of holomorphic functions. Conformal welding provides a triangular decompositions for the…
Spectral density functions quantify how environmental modes couple to quantum systems and govern their open dynamics. Inferring such frequency-dependent functions from time-domain measurements is an ill-conditioned inverse problem. Here, we…
We discuss a generalization of POVM which is used in quantum-like modeling of mental processing.