相关论文: Berezin-Toeplitz quantization and Berezin transfor…

We study the near diagonal asymptotic expansion of the generalized Bergman kernel of the renormalized Bochner-Laplacian on high tensor powers of a positive line bundle over a compact symplectic manifold. We show how to compute the…

We study the asymptotic expansion of the product of two Toeplitz operators on the Fock space. In comparison to earlier results we require significantly less derivatives and get the expansion to arbitrary order. This, in particular, improves…

In this paper, we study the asymptotic behaviour of plane partitions distributed according to a $q^{\text{Volume}}$-weighted Muttalib--Borodin ensemble and its associated discrete point process. We establish a Large Deviation Principle for…

In studies of quantum squeezing, the emphasis is typically placed more on specific squeezed states and their evolution rather than on the dynamical operations that could simultaneously squeeze a broader range of quantum states, regardless…

We give estimates for the essential norms of a positive Toeplitz operator on the Bergman space of a minimal bounded homogeneous domain in terms of the Berezin transform or the averaging function of the symbol. Using these estimates, we also…

This work mainly addresses a construction of Gazeau-Klauder type coherent states for a P\"oschl-Teller model. Relevant characteristics are investigated. Induced geometry and statistics are studied. Then the Berezin - Klauder - Toeplitz…

We compute the asymptotics of matrix elements in canonical bases of irreducible representations of the unitary group as the highest weight goes to infinity, in terms of the symplectic geometry of the associated coadjoint orbit. This uses…

We study the asymptotic behavior of the generalized Bergman kernel of the renormalized Bochner-Laplacian on high tensor powers of a positive line bundle on a symplectic manifold of bounded geometry. First, we establish the off-diagonal…

We propose a two-dimensional hard-core loop-gas model as a way to regularize the asymptotically free massive continuum quantum field theory that emerges at the Berezinskii-Kosterlitz-Thouless transition. Without fine-tuning, our model can…

We analyze in detail, beyond the usual scaling hypothesis, the finite-size convergence of static quantities toward the thermodynamic limit. In this way we are able to obtain sequences of pseudo-critical points which display a faster…

The basic theory of semi-measures on locally compact Abelian groups is extended to prove the existence of a generalised Eberlein decomposition into such semi-measures.

This paper studies the boundary behavior of the Berezin transform on the C*-algebra generated by the analytic Toeplitz operators on the Bergman space.

We give a proof of a slightly refined version of Gammelgaard's graph theoretic formula for Berezin-Toeplitz quantization on (pseudo-)Kaehler manifolds. Our proof has the merit of giving an alternative approach to Karabegov-Schlichenmaier's…

We study an unorthodox variant of the Berezin-Toeplitz type of quantization scheme, on a reproducing kernel Hilbert space generated by the real Hermite polynomials and work out the associated semi-classical asymptotics.

The purpose of this article is to prove sharp $L^p$ bounds for quasimodes of Berezin-Toeplitz operators. We consider examples with explicit computations and a general situation on compact spaces and $\mathbb{C}^n$. In both cases the…

Deformation quantization and geometric quantization on K\"ahler manifolds give the mathematical description of the algebra of quantum observables and the Hilbert spaces respectively, where the later forms a representation of quantum…

We establish that Hitchin's connection exist for any rigid holomorphic family of Kahler structures on any compact pre-quantizable symplectic manifold which satisfies certain simple topological constraints. Using Toeplitz operators we prove…

We study Toeplitz operators on the Bargmann space, with Toeplitz symbols given by exponentials of complex quadratic forms. We show that the boundedness of the corresponding Weyl symbols is necessary for the boundedness of the operators,…

We initiate the study of weighted multi-Toeplitz operators associated with noncommutative regular domains in B(H)^n. These operators are acting on the full Fock space with n generators and have as symbols free pluriharmonic functions.…

We characterise the boundedness of a Toeplitz operator on the Bergman space with an L^1 symbol.We also prove that the compactness of a Toeplitz operator on the Bergman space with an L^1 symbol is completely determined by the boundary…