arXivDaily arXiv每日学术速递 周一至周五更新
2606.19414 2026-06-19 cond-mat.stat-mech nlin.CD 交叉投稿

Spectra as a classical phenomenon, and the Einstein classical program

光谱作为经典现象,以及爱因斯坦经典纲领

Andrea Carati, Luigi Galgani, Fabrizio Gangemi

AI总结 本文通过离子晶体红外光谱的经典计算,证明经典力学在宽温度范围内能复现实验数据,甚至优于现有量子计算,支持了爱因斯坦经典纲领。

Comments 23 Pages and 5 figures. Submitted to Journal Statistical Physics, for the special number on FPU problem

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AI中文摘要

根据玻恩(《原子物理学》,第103页),光谱是“量子现象,从经典立场来看完全不可理解”。然而,我们展示了离子晶体(实际为LiF)红外光谱的经典计算结果,表明情况更为复杂。事实上,结果发现:1)在室温及更高温度(高达1060 K)下,经典计算重现了实验数据,甚至比现有量子计算更好;2)在较低温度(甚至7.5 K)下,如果接受能斯特(第三定律的发明者)在1916年提出的零点能在经典物理学中也有容身之地的观点,经典计算也能很好地重现数据。最后指出,上述结果可被视为向实现爱因斯坦经典纲领迈出的第一步,该纲领旨在从实在论理论推导出量子物理学(公认的正确理论)。实际上,我们考虑的是极端版本的爱因斯坦经典纲领,其中实在论理论仅仅是(本质上,见下文)体相物质的经典电动力学,涉及相空间轨道、牛顿方程的解。附录致力于说明能斯特方法,该方法也涉及均分定律与普朗克定律之间的关系。

英文摘要

According to Born (\emph{Atomic Physics, page 103}), spectra are \emph{``quantum phenomena, which from a classical standpoint are perfectly unintelligible''}. However we illustrate results on classical calculations of infrared spectra of ionic crystals (actually LiF) which show that the situation is much more complex. Indeed it turns out that: 1) At room temperature and at higher ones (up to 1060 K) the classical computations reproduce the experimental data, even better than the \emph{presently available} quantum ones do; 2) At lower temperatures (even at 7.5 K), the classical computations reproduce pretty well the data, if one accepts the idea advanced in 1916 by Nernst (the inventor of the third principle) that zero-point energy has room in classical physics too. It is eventually pointed out that the mentioned results might be regarded as a first step towards an implementation of the Einstein Classical Program, which aims at deducing quantum physics (admittedly the correct theory) from a realistic theory. In fact, we are considering the Einstein classical program in the extreme version in which the realistic theory is just (\emph{essentially, see below}) classical electrodynamics of matter in bulk, involving phase space orbits, solutions of Newton equations. An Appendix is devoted to illustrate the Nernst approach, which concerns also the relation between equipartition and Planck's law.

2309.08484 2026-06-19 cond-mat.stat-mech hep-th nlin.CD physics.flu-dyn 版本更新

Fokker-Planck approach to wave turbulence

Daniel Schubring

Comments 30 pages, 7 figures

Journal ref J. Stat. Phys. 193 (2026) 75

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英文摘要

The Kolmogorov-Zakharov stationary states for weak wave turbulence involve solving a leading-order kinetic equation. Recent calculations of higher-order corrections to this kinetic equation using the Martin-Siggia-Rose path integral are reconsidered in terms of stationary states of a Fokker-Planck Hamiltonian. A non-perturbative relation closely related to the quantum mechanical Ehrenfest theorem is introduced and used to express the kinetic equation in terms of divergences of two-point expectation values in the limit of zero dissipation. Similar equations are associated to divergences in higher-order cumulants. It is additionally shown that the ordinary thermal equilibrium state is not actually a stationary state of the Fokker-Planck Hamiltonian, and a non-linear modification of dissipation is considered to remedy this.