Principe (philosophie)

Résumé

Le principe est un concept philosophique polysémique qui désigne ou bien une source, un fondement, une vérité première d'idées ou d'autres choses. On parle ainsi de la conscience ou l'âme comme principe de vie. Concept Chez les présocratiques Les philosophes présocratiques s’étaient donné pour tâche de connaître le principe de toute chose, l’arkhè, principe premier. Ils entendaient par là l’étude de ce qui était le fondement de l’existence de l’ensemble des réalités empiriquement observables, qu'ils réduisaient à des matières fondamentales (les quatre éléments). Le premier présocratique à utiliser le terme darkhè serait Anaximandre, quoique cela soit discuté. Pour Théophraste, il s’agit d’un . Le principe est à la fois association et, pour ainsi dire, union intime entre eux des éléments intelligibles et des éléments physiques. Chez Platon Platon, disciple de Socrate, pense à son tour l'arkhè dans ses dialogues. C'est notamment le cas dans

Source officielle

https://fr.wikipedia.org/wiki/Principe_(philosophie)

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Time-evolution of local information: Thermalization dynamics of local observables

Loïc Jean Pierre Herviou

Quantum many-body dynamics generically result in increasing entanglement that eventually leads to thermalization of local observables. This makes the exact description of the dynamics complex despite the apparent simplicity of (high-temperature) thermal states. For accurate but approximate simulations one needs a way to keep track of essential (quantum) information while discarding inessential one. To this end, we first introduce the concept of the information lattice, which supplements the physical spatial lattice with an additional dimension and where a local Hamiltonian gives rise to well-defined locally conserved von Neumann information current. This provides a convenient and insightful way of capturing the flow, through time and space, of information during quantum time-evolution, and gives a distinct signature of when local degrees of freedom decouple from long-range entanglement. As an example, we describe such de-coupling of local degrees of freedom for the mixed-field transverse Ising model. Building on this, we secondly construct algorithms to time-evolve sets of local density matrices without any reference to a global state. With the notion of information currents, we motivate algorithms based on the intuition that information for statistical reasons flows from small to large scales. Using this guiding principle, we construct an algorithm that, at worst, shows two-digit convergence in time-evolutions up to very late times for diffusion process governed by the mixed-field transverse Ising Hamiltonian. While we focus on dynamics in 1D with nearest-neighbor Hamiltonians, the algorithms do not essentially rely on these assumptions and can in principle be generalized to higher dimensions and more complicated Hamiltonians.

SCIPOST FOUNDATION2022

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Algebraic Nahm transform for parabolic Higgs bundles on P^1

Szilárd Szabó

We formulate the Nahm transform in the context of parabolic Higgs bundles on P^1 and extend its scope in completely algebraic terms. This transform requires parabolic Higgs bundles to satisfy an admissibility condition and allows Higgs fields to have poles of arbitrary order and arbitrary behavior. Our methods are constructive in nature and examples are provided. The extended Nahm transform is established as an algebraic duality between moduli spaces of parabolic Higgs bundles. The guiding principle behind the construction is to investigate the behavior of spectral data near the poles of Higgs fields.

2014

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This paper is concerned with frequency domain theory for functional time series, which are temporally dependent sequences of functions in a Hilbert space. We consider a variance decomposition, which is more suitable for such a data structure than the variance decomposition based on the Karhunen-Loeve expansion. The decomposition we study uses eigenvalues of spectral density operators, which are functional analogs of the spectral density of a stationary scalar time series. We propose estimators of the variance components and derive convergence rates for their mean square error as well as their asymptotic normality. The latter is derived from a frequency domain invariance principle for the estimators of the spectral density operators. This principle is established for a broad class of linear time series models. It is a main contribution of the paper.

INT STATISTICAL INST2020

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