Related papers: Berezin-Toeplitz quantization and Berezin transfor…
An extension to computational mechanics complexity measure is proposed in order to tackle quantum states complexity quantification. The method is applicable to any $n-$partite state of qudits through some simple modifications. A Werner…
Toeplitz operators (also called localization operators) are a generalization of the well-known anti-Wick pseudodifferential operators studied by Berezin and Shubin. When a Toeplitz operator is positive semi-definite and has trace one we…
In this paper we develope the main ideas of the quantized version of affinely-rigid (homogeneously deformable) motion. We base our consideration on the usual Schr\"odinger formulation of quantum mechanics in the configuration manifold which…
In this short note we improve some of recent results of Cuckovic and Sahutoglu concerning regularity of the Berezin transform for a class of smooth pseudoconvex domains.
The boundedness and compactness of Toeplitz operator from $A_\omega^p$ to $A_\omega^q$ with doubling weights $\omega$ are studied in this paper. The characterizations of Schatten class Toeplitz operators and Volterra operators on…
In this paper, we study the basic properties of Toeplitz Operators with positive measures $\mu$ on harmonic Fock spaces. We prove equivalent conditions for boundedness, compactness and Schatten classes $S_{p}$ of $T_{\mu}$ by using the…
On a locally compact group we introduce covariant quantization schemes and analogs of phase space representations as well as mixed-state localization operators. These generalize corresponding notions for the affine group and the Heisenberg…
Recently, it has been proposed that the dimension of the Hilbert space of quantum gravity in deSitter space is finite and moreover it is expressed in terms of the coupling constants by using the entropy formula. A weaker conjecture would be…
An heuristic derivation of the tranformation law for the Berezin integration measure in noncompact supermanifolds, obtained by Roshstein \cite{Ro}, is presented.
In a recent paper [JFA, 278 (2020), 108401], Choe et al. obtained characterizations for bounded and compact differences of two weighted composition operators acting on standard weighted Bergman spaces over the unit disk in terms of Carleson…
We apply the Mellin-Barnes integral representation to several situations of interest in mathematical-physics. At the purely mathematical level, we derive useful asymptotic expansions of different zeta-functions and partition functions.…
We study whether essential positivity \[ \sigma_{\mathrm{ess}}(T_f)\subset [0,\infty) \] of a radial Toeplitz operator on Bergman and Fock spaces can be detected from the asymptotic behavior of its Berezin transform. For bounded real-valued…
We extend Fedosov deformation quantization to general contact manifolds. Unlike the case of symplectic manifolds, not every classical observable on a contact manifold is generally quantized. On examination of possible obstructions to…
In this paper, we focus on the weighted Bergman spaces $A_{\varphi}^{p}$ in $\mathbb{D}$ with $\varphi\in\mathcal{W}_{0}$. We first give characterizations of those finite positive Borel measures $\mu$ in $\mathbb{D}$ such that the embedding…
Quantum coherence is one of the fundamental aspects distinguishing classical and quantum theories. Coherence between different energy eigenstates is particularly important, as it serves as a valuable resource under the law of energy…
We first give simplified and corrected accounts of some results in \cite{PiRCP} on compactifications of pseudofinite groups. For instance, we use a classical theorem of Turing \cite{Turing} to give a simplified proof that any definable…
We present a controlled numerical study of the Berezinskii-Kosterlitz-Thouless (BKT) transition in the one-dimensional Bose-Hubbard model at unit filling, providing evidence of the characteristic logarithmic finite-size scaling of the BKT…
The Lorentz transformation properties of the equal-time bound-state Bethe-Salpeter amplitude in the two-dimensional massless quantum electrodynamics (the so called Schwinger Model) are considered. It is shown that while boosting a bound…
In this paper we prove that if S equals a finite sum of finite products of Toeplitz operators on the Bergman space of the unit disk, then S is compact if and only if the Berezin transform of S equals 0 on the boundary of the disk. This…
This is a written version of lectures that I would have given myself about aspects of the differential operator that is obtained from the linearized Kapustin-Witten equations on the product of the half-line with a compact, oriented,…