Related papers: Sharp correspondence principle and quantum measure…

The principles are elaborated which underlie the applications of general nonclassical states to communication and measurement systems. Relevant classical communication concepts are reviewed. Communication and measurement processes are…

We apply a quantum version of dimensional reduction to Gaussian coherent states in Bargmann space to obtain squeezed states on complex projective spaces. This leads to a definition of a family of squeezed spin states with excellent…

We show sharp bounds for probabilities of large deviations for sums of independent random variables satisfying Bernstein's condition. One such bound is very close to the tail of the standard Gaussian law in certain case; other bounds…

Pollet et al have questioned our claim staked in Phys. Rev. Lett. 103, 085701 (2009) that from the location of sharp features in the compressibility in the trap, it is possible to map out the phase boundary between two phases within…

We consider Berezin-Toeplitz operators whose multipliers are compactly supported densities carried by a submanifold of ${\mathbb C}^N$ . We compute asymptotically the moments of their spectral measures, and we prove Szeg\"o limit theorems…

We establish a sharp upper bound for the bottom spectrum of the Beltrami Laplacian on universal covers of closed Riemannian manifolds with scalar curvature lower bound. Moreover, we prove a scalar curvature rigidity theorem when this bound…

In this semi-expository paper, we define certain Rawnsley-type coherent and squeezed states on an integral K\"ahler manifold (after possibly removing a set of measure zero) and show that they satisfy some properties which are akin to…

We prove a Tauberian theorem for singular values of noncommuting operators which allows us to prove exact asymptotic formulas in noncommutative geometry at a high degree of generality. We explain how, via the Birman--Schwinger principle,…

We prove an effective version of the Shafarevich conjecture (as proven by Faltings) for smooth quartic curves. To do so, we establish an effective version of Scholl's finiteness result for smooth del Pezzo surfaces of degree at most four.

A generalized approach to the quantization of a large class of maps on a torus, i.e. quantization via the von Neumann Equation, is described and a number of issues related to the quantization of model systems are discussed. The approach…

The correspondence principle is important in quantum theory on both the fundamental and practical levels: it is needed to connect theory to experiment, and for calculations in the technologically important domain lying between the atomic…

The main purpose of the note is to explore the invariant properties of sphericalization and flattening and their applications in quasi-metric spaces. We show that sphericalization and flattening procedures on a quasimetric spaces preserving…

In this paper we revisit several recent results on monotone and strictly monotone Hurwitz numbers, providing new proofs. In particular, we use various versions of these numbers to discuss methods of derivation of quantum spectral curves…

We develop a systematic approach to determine and measure numerically the geometry of generic quantum or "fuzzy" geometries realized by a set of finite-dimensional hermitian matrices. The method is designed to recover the semi-classical…

In this article, we study the geometry of compact quasi-Einstein manifolds with boundary. We establish sharp boundary estimates for compact quasi-Einstein manifolds with boundary that improve some previous results. Moreover, we obtain a…

Quantification of coherence lies at the heart of quantum information processing and fundamental physics. Exact evaluation of coherence measures generally needs a full reconstruction of the density matrix, which becomes intractable for…

Traditionally, finite differences and finite element methods have been by many regarded as the basic tools for obtaining numerical solutions in a variety of quantum mechanical problems emerging in atomic, nuclear and particle physics,…

We prove a quantum version of the Sabine law from acoustics describing the location of resonances in transmission problems. This work extends the author's previous work to a broader class of systems. Our main applications are to scattering…

Coherence is a basic phenomenon in quantum mechanics and considered to be an essential resource in quantum information processing. Although the quantification of coherence has attracted a lot of interest, the lack of efficient methods to…

We study a quantum and classical correspondence related to the Strichartz estimates. First we consider the orthonormal Strichartz estimates on manifolds with ends. Under the nontrapping condition we prove the global-in-time estimates on…