Related papers: Correspondence principle for idempotent calculus a…
A unifying approach to software and hardware design generated by ideas of Idempotent Mathematics is discussed. The so-called idempotent correspondence principle for algorithms, programs and hardware units is described. A software project…
A unifying approach to software and hardware design generated by ideas of Idempotent Mathematics is discussed. The so-called idempotent correspondence principle for algorithms, programs and hardware units is described. A software project…
This is a survey paper on applications of mathematics of semirings to numerical analysis and computing. Concepts of universal algorithm and generic program are discussed. Relations between these concepts and mathematics of semirings are…
General potential theories concern the study of functions which are subharmonic with respect to a suitable constraint set (called a subequation) in the space of 2-jets. While interesting in their own right, general potential theories are…
Quantum mechanics and classical mechanics are two very different theories, but the correspondence principle states that quantum particles behave classically in the limit of high quantum number. In recent years much research has been done on…
In a companion paper (hereafter referred to as Paper I), we have presented an attempt to derive the finite-dimensional abstract quantum formalism within the framework of information geometry. In this paper, we formulate a correspondence…
Many problems in optimization theory are strongly nonlinear in the traditional sense but possess a hidden linear structure over suitable idempotent semirings. After an overview of `Idempotent Mathematics' with an emphasis on matrix theory,…
A brief survey of some basic ideas of the so-called Idempotent Mathematics is presented; an "idempotent" version of the representation theory is discussed. The Idempotent Mathematics can be treated as a result of a dequantization of the…
To apply the abstract quantum formalism to a particular physical system, one must specify the precise form of the relevant measurement and symmetry transformation operators. These operators are determined by a set of rules, the…
In this paper we consider Idempotent Functional Analysis, an `abstract' version of Idempotent Analysis developed by V. P. Maslov and his collaborators. We give a review of the basic ideas of Idempotent Analysis. The correspondence between…
The oracle model of computation is believed to allow a rigorous proof of quantum over classical computational superiority. Since quantum and classical oracles are essentially different, a correspondence principle is commonly implicitly used…
The problem of consistent formulation of the correspondence principle in quantum gravity is considered. The usual approach based on the use of the two-particle scattering amplitudes is shown to be in disagreement with the classical result…
It is noted that quantum theory includes the correspondence principle which is independent of the value of quantum corrections. Some consequences of this generalized correspondence principle are considered. For example, it is discussed how…
Mathematical proofs are often said to justify their conclusions by indicating the existence of a corresponding formal derivation. We argue that this widespread view relies on an under-examined notion of correspondence, or what it means for…
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…
Based on the Bohr's correspondence principle it is shown that relativistic mechanics and quantum mechanics may be considered as generalizations of classical mechanics. A comparative description of relativistic and classical mechanics is…
Problems of interacting quantum magnetic moments become exponentially complex with increasing number of particles. As a result, classical equations are often used but the validity of reduction of a quantum problem to a classical problem…
In a companion paper (hereafter referred to as Paper I), we have presented an attempt to derive the finite-dimensional abstract quantum formalism from a set of physically comprehensible assumptions. In this paper, we formulate a…
It is demonstrated that the the statistics for a joint measurement of two conjugate variables in Quantum Mechanics are expressed through an equation identical to the classical one, provided that joint classical probabilities are substituted…
Correspondence identifies relationships among objects via similarities among their components; it is ubiquitous in the analysis of spatial datasets, including images, weather maps, and computational simulations. This paper develops a novel…