相关论文: Arcsine Law as the Classical Limit for interacting…

Interacting Fock space connects the study of quantum probability theory, classical random variables, and orthogonal polynomials. It is a pre-Hilbert space associated with creation, preservation, and annihilation processes. We prove that if…

We prove that the Arcsine law as the time-averaged distribution for classical harmonic oscillators emerges from the distributions for quantum harmonic oscillators in terms of noncommutative algebraic probability. This is nothing but a…

We propose a model that interpolates between quantum walks and persistent (correlated) random walks using one parameter on the one-dimensional lattice. We show that the limit distribution is described by the normal variance mixture with the…

In this paper we suggest a simple mathematical procedure to derive the classical probability density of quantum systems via Bohr's correspondence principle. Using Fourier expansions for the classical and quantum distributions, we assume…

We provide an overview of a canonical formalism that describes mixed quantum-classical systems in terms of statistical ensembles on configuration space, and discuss applications to measurement theory. It is shown that the formalism allows a…

The construction of a consistent theory for structuring and representing how concepts combine and interact is one of the main challenges for the scholars involved in cognitive studies. All traditional approaches are still facing serious…

This paper extends the tools of C*-algebraic strict quantization toward analyzing the classical limits of unbounded quantities in quantum theories. We introduce the approach first in the simple case of finite systems. Then we apply this…

We study the convergence of the empirical distribution associated with a system of interacting kinetic particles subject to independent Brownian forcing in a finite horizon setting, using some recent progress on kinetic non-linear partial…

The rings of symmetric polynomials form an inverse system whose limit, the ring of symmetric functions, is the model for the bosonic Fock space representation of the affine Lie algebra. We categorify this construction by considering an…

A formalism is developed for describing approximate classical behaviour in finite (but possibly large) quantum systems. This is done in terms of a structure common to classical and quantum mechanics, viz. a Poisson space with a transition…

The classical limit problem of quantum mechanics is revisited on the basis of a scheme that enables a quantitative study of the way the quantum-classical agreement emerges while going through the intermediate mass range between the…

Building on earlier work introducing the notion of "mod-Gaussian" convergence of sequences of random variables, which arises naturally in Random Matrix Theory and number theory, we discuss the analogue notion of "mod-Poisson" convergence.…

Semiclassical limits of generic multiparameter quantized coordinate rings A = O_q(k^n) of affine spaces are constructed and related to A, for k an algebraically closed field of characteristic zero and q a multiplicatively antisymmetric…

Using Stein's method for the Beta distributions and a recent technique by Goldstein and Reinert of comparing the Stein characterization of the target distribution with that of the approximating distribution we prove a rate of convergence in…

We study the emergence of Boltzmann's law for the "single particle energy distribution" in a closed system of interacting classical spins. It is shown that for a large number of particles Boltzmann's law may occur, even if the interaction…

A consistent description of interactions between classical and quantum systems is relevant to quantum measurement theory, and to calculations in quantum chemistry and quantum gravity. A solution is offered here to this longstanding problem,…

In this paper we develop tools for studying limit theorems by means of convexity. We establish bounds for the discrepancy in total variation between probability measures $\mu$ and $\nu$ such that $\nu$ is log-concave with respect to $\mu$.…

The identification mentioned in the title allows a formulation of the multidi mensional Favard Lemma different from the ones currently used in the literature and which exactly parallels the original one dimensional formulation in the sense…

We continue our previous work [Ling-Bing He, Xuguang Lu and Mario Pulvirenti, Comm. Math. Phys., 386(2021), no. 1, 143223.] on the limit of the spatially homogeneous quantum Boltzmann equation as the Planck constant $\epsilon$ tends to…

We describe how a model of effective interactions between quantum fluctuations under certain assumptions can be constructed in a way so that the large-scale limit gives an effective theory that matches general relativity in vacuum regions.…