Related papers: A self-consistent criterion for the range of valid…
A quantitative test for the validity of the semi-classical approximation in gravity is given. The criterion proposed is that solutions to the semi-classical Einstein equations should be stable to linearized perturbations, in the sense that…
This theoretical work considers the following conundrum: linear response theory is successfully used by scientists in numerous fields, but mathematicians have shown that typical low-dimensional dynamical systems violate the theory's…
From previous work arXiv:2010.09811, the semiclassical backreaction equation in 1+1 dimensions was solved and a criterion was implemented to assess the validity of the semiclassical approximation in this case. The criterion involves the…
We address the issue of the validity of linear response theory for a closed quantum system subject to a periodic external driving. Linear response theory (LRT) predicts energy absorption at frequencies of the external driving where the…
The aim of this paper is to clarify the relation between three different approaches of theories with a minimal length scale: A modification of the Lorentz-group in the 'Deformed Special Relativity', theories with a 'Generalized Uncertainty…
An investigation of the validity of the semiclassical approximation to quantum electrodynamics in 1+1 dimensions is given. The criterion for validity used here involves the impact of quantum fluctuations introduced through a two-point…
We study a system of all-to-all weakly coupled uniformly expanding circle maps in the thermodynamic limit. The state of the system is described by a probability measure and its evolution is given by the action of a nonlinear operator, also…
Coherent states provide a natural connection of quantum systems to their classical limit and are employed in various fields of physics. Here we derive general systematic expansions, with respect to quantum parameters, of expectation values…
Analytical work probability distributions for open classical systems are scarce; they can only be calculated in a few examples. In this work, I present a new method to derive such quantities for weakly driven processes in the overdamped…
The validity of the fluctuation theorem for entropy production as deduced from the observation of trajectories implicitly requires that all slow degrees of freedom are accessible. We experimentally investigate the role of hidden slow…
We present exact analytical solutions to the classical equations of motion and analyze the dynamical consequences of the existence of a minimal length for the free particle, particle in a linear potential, anti-symmetric constant force…
A well motivated method for demonstrating that an experiment resists any classical explanation is to show that its statistics violate generalized noncontextuality. We here formulate this problem as a linear program and provide an…
We propose a quantitative test for the validity of the semi-classical approximation in gravity, namely that the solutions to the semi-classical equations should be stable to linearized perturbations, in the sense that no gauge invariant…
This work explores the consistency of small LLMs (2B-8B parameters) in answering multiple times the same question. We present a study on known, open-source LLMs responding to 10 repetitions of questions from the multiple-choice benchmarks…
Finite-time coherent sets represent minimally mixing objects in general nonlinear dynamics, and are spatially mobile features that are the most predictable in the medium term. When the dynamical system is subjected to small parameter…
This paper addresses the following classical question: giving a sequence of identically distributed random variables in the domain of attraction of a normal law, does the associated linear process satisfy the central limit theorem? We study…
Systems often repeat the same prompt to large language models (LLMs) and aggregate responses to improve reliability. This short note analyzes an estimator of the self-consistency of LLMs and the tradeoffs it induces under a fixed compute…
In this work we formulate the problem of satisfying a linear temporal logic formula on a linear plant with output feedback, through a recent hybrid systems formalism. We relate this problem to the notion of recurrence introduced for the…
We consider the on-line predictive version of the standard problem of linear regression; the goal is to predict each consecutive response given the corresponding explanatory variables and all the previous observations. The standard…
It is shown that the psychometric test reliability, based on any true-score model with randomly sampled items and conditionally independent errors, converges to 1 as the test length goes to infinity, assuming some fairly general regularity…