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In classical dynamical systems, chaotic behavior is often associated with exponential sensitivity to initial conditions together with global phase-space structure. Translating this geometric concept to the strictly linear framework of…

Quantum Physics · Physics 2026-03-24 Stephen Wiggins

Classical limits of quantum systems are shown to lead to different conceptions of spaces different from the classical one underlying the process of quantization of such systems. The accent is put in situations where traces of…

Quantum Physics · Physics 2022-07-22 Thierry Paul

We study nonclassical effects in the dynamics of an open quantum system. The model involves a harmonic oscillator coupled to a reservoir of non-interacting harmonic oscillators. Different system-bath interaction schemes as well as reservoir…

Quantum Physics · Physics 2023-05-17 Mehdi Abdi , Moslem Zarei

Motivated by the famous ink-drop experiment, where ink droplets are used to determine the chaoticity of a fluid, we propose an experimentally implementable method for measuring the scrambling capacity of quantum processes. Here, a system of…

Quantum Physics · Physics 2023-07-19 Magdalini Zonnios , Jesper Levinsen , Meera M. Parish , Felix A. Pollock , Kavan Modi

Computational mechanics, an approach to structural complexity, defines a process's causal states and gives a procedure for finding them. We show that the causal-state representation--an $\epsilon$-machine--is the minimal one consistent with…

Statistical Mechanics · Physics 2022-02-17 Cosma Rohilla Shalizi , James P. Crutchfield

We consider stationary stochastic dynamical systems evolving on a compact metric space, by perturbing a deterministic dynamics with a random noise, added according to an arbitrary probabilistic distribution. We prove the maximal and…

Dynamical Systems · Mathematics 2018-07-10 Eleonora Catsigeras

The underlying physical concept of computing out-of-time-ordered correlation (OTOC) is a significant new tool within the framework of quantum field theory, which now-a-days is treated as a measure of random fluctuations. In this paper, by…

General Physics · Physics 2021-06-03 Sayantan Choudhury

Depth is a complexity measure for natural systems of the kind studied in statistical physics and is defined in terms of computational complexity. Depth quantifies the length of the shortest parallel computation required to construct a…

Popular Physics · Physics 2011-11-14 Jon Machta

A novel probabilistic approach for the design of mechanical structures with friction interfaces is proposed. The objective function is defined as the probability that a specified performance measure of the forced vibration response is…

Computational Engineering, Finance, and Science · Computer Science 2021-01-01 Malte Krack , Sebastian Tatzko , Lars Panning-von Scheidt , Jörg Wallaschek

We tackle the dynamical description of the quantum measurement process, by explicitly addressing the interaction between the system under investigation with the measurement apparatus, the latter ultimately considered as macroscopic quantum…

Quantum Physics · Physics 2019-07-31 A. De Pasquale , C. Foti , A. Cuccoli , V. Giovannetti , P. Verrucchi

We introduce a new tool for the quantitative characterisation of the departure form Markovianity of a given dynamical process. Our tool can be applied to a generic $N$-level system and extended straightforwardly to Gaussian…

Quantum Physics · Physics 2015-06-15 S. Lorenzo , F. Plastina , M. Paternostro

The modal interpretation of quantum mechanics allows one to keep the standard classical definition of realism intact. That is, variables have a definite status for all time and a measurement only tells us which value it had. However, at…

Quantum Physics · Physics 2009-11-10 Jay Gambetta , H. M. Wiseman

Even simply-defined, finite-state generators produce stochastic processes that require tracking an uncountable infinity of probabilistic features for optimal prediction. For processes generated by hidden Markov chains the consequences are…

Statistical Mechanics · Physics 2021-09-15 Alexandra M. Jurgens , James P. Crutchfield

The article is devoted to stochastic processes with values in finite- and infinite-dimensional vector spaces over infinite fields $\bf K$ of zero characteristics with non-trivial non-archimedean norms. For different types of stochastic…

Probability · Mathematics 2018-12-18 S. V. Ludkovsky

This paper presents Orthogonal Subspace Clustering (OSC), an innovative method for high-dimensional data clustering. We first establish a theoretical theorem proving that high-dimensional data can be decomposed into orthogonal subspaces in…

Machine Learning · Computer Science 2026-03-17 Qing-Yuan Wen , Da-Qing Zhang

A causal set is a partially ordered set on a countably infinite ground-set such that each element is above finitely many others. A natural extension of a causal set is an enumeration of its elements which respects the order. We bring…

Probability · Mathematics 2011-09-22 Graham Brightwell , Malwina Luczak

We derive exceedingly simple practical procedures revealing the quantum nature of states and measurements by the violation of classical upper bounds on the statistics of arbitrary measurements. Data analysis is minimum and definite…

Quantum Physics · Physics 2009-04-28 Ángel Rivas , Alfredo Luis

Stochastic exclusion processes play an integral role in the physics of non-equilibrium statistical mechanics. These models are Markovian processes, described by a classical master equation. In this paper a quantum mechanical version of a…

Quantum Physics · Physics 2015-03-13 Kristan Temme , Michael M. Wolf , Frank Verstraete

We introduce a quantum-optical notion of nonclassicality that we call as the process output nonclassicality for multimode quantum channels. The motivation comes from an information-theoretic point of view and the emphasis is on the output…

Quantum Physics · Physics 2016-04-28 Krishna Kumar Sabapathy

The nonlinear oscillator model allows a basic understanding of all nonlinear processes and can be adopted to analyse optical vibrational modes and electronic transition in molecules and crystals, in order to derive general properties of…

Optics · Physics 2015-06-26 F. Bassani , V. Lucarini