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Journal articles on the topic 'Quantum chaotics probabilistic'

Author: Grafiati

Published: 7 June 2025

Last updated: 2 August 2025

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1

BISWAS, DEBABRATA. "EVOLUTION OF LIOUVILLE DENSITY IN BILLIARDS: THE QUANTUM CONNECTION." Modern Physics Letters B 20, no. 14 (2006): 795–813. http://dx.doi.org/10.1142/s0217984906011232.

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The study of classical Liouville density arises naturally in chaotic systems where a probabilistic treatment is more appropriate. In this review, we show that the evolution of a density projected onto the configuration space has a quantum connection in billiard systems. The eigenvalues and eigenfunctions of the concerned evolution operator have an approximate one-to-one correspondence with the quantum Neumann eigenvalues and eigenfunctions. For exceptional billiard shapes such as the rectangle, this correspondence is even exact. Despite the approximate nature of the correspondence, we demonstr

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2

Cipolloni, Giorgio, László Erdős, and Dominik Schröder. "Eigenstate Thermalization Hypothesis for Wigner Matrices." Communications in Mathematical Physics 388, no. 2 (2021): 1005–48. http://dx.doi.org/10.1007/s00220-021-04239-z.

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AbstractWe prove that any deterministic matrix is approximately the identity in the eigenbasis of a large random Wigner matrix with very high probability and with an optimal error inversely proportional to the square root of the dimension. Our theorem thus rigorously verifies the Eigenstate Thermalisation Hypothesis by Deutsch (Phys Rev A 43:2046–2049, 1991) for the simplest chaotic quantum system, the Wigner ensemble. In mathematical terms, we prove the strong form of Quantum Unique Ergodicity (QUE) with an optimal convergence rate for all eigenvectors simultaneously, generalizing previous pr

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3

HARRISON, JONATHAN M., and KLAUS KIRSTEN. "VACUUM ENERGY OF SCHRÖDINGER OPERATORS ON METRIC GRAPHS." International Journal of Modern Physics: Conference Series 14 (January 2012): 357–66. http://dx.doi.org/10.1142/s2010194512007477.

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We present an integral formulation of the vacuum energy of Schrödinger operators on finite metric graphs. Local vertex matching conditions on the graph are classified according to the general scheme of Kostrykin and Schrader. While the vacuum energy of the graph can contain finite ambiguities the Casimir force on a bond with compactly supported potential is well defined. The vacuum energy is determined from the zeta function of the graph Schrödinger operator which is derived from an appropriate secular equation via the argument principle. A quantum graph has an associated probabilistic classic

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4

Okabe, Yasunori, and Akihiko Inoue. "The theory of KM2O-Langevin equations and applications to data analysis (II): Causal analysis (1)." Nagoya Mathematical Journal 134 (June 1994): 1–28. http://dx.doi.org/10.1017/s0027763000004827.

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It is not too much to say that the problem of finding a cause-and-effect relationship is a fascinating and eternal theme in both natural and social sciences. It is often difficult to decide whether one is the cause of another in two related phenomena, but it is an important problem. It is related to the internal structure of phenomena which generate deterministic or random changes as time passes. We note that the phenomena to be considered are often not deterministic but random. For example, in physical systems such as quantum mechanics or chaotic classical mechanics, it is well known that cer

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5

Petrenko, A. S. "METHOD FOR CONSTRUCTING POST-QUANTUM ALGORITHMS OF EDS WITH TWO HIDDEN GROUPS." Voprosy kiberbezopasnosti 2, no. 66 (2025): 52–63. https://doi.org/10.21681/2311-3456-2025-2-52-63.

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Purpose of work is to develop and substantiate a method for constructing post-quantum EDS algorithms based on finite noncommutative associative algebras, which provides enhanced signature randomization due to double groups and chaotic mappings, compact key sizes and high performance, as well as automated evolutionary design of the multiplication table structure. Research methods: algebraic modeling of noncommutative structures and computer verification of the associativity of multiplication tables, mathematical modeling of the signature process and probabilistic assessment of cryptographic str

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6

Karwasz, Grzegorz. "On Determinism, Causality, and Free Will: Contribution from Physics." Roczniki Filozoficzne 69, no. 4 (2021): 5–24. http://dx.doi.org/10.18290/rf21694-1.

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Determinism, causality, chance, free will and divine providence form a class of interlaced problems lying in three domains: philosophy, theology, and physics. Recent article by Dariusz Łukasiewicz in Roczniki Filozoficzne (no. 3, 2020) is a great example. Classical physics, that of Newton and Laplace, may lead to deism: God created the world, but then it goes like a mechanical clock. Quantum mechanics brought some “hope” for a rather naïve theology: God acts in gaps between quanta of indetermination. Obviously, any strict determinism jeopardizes the existence of free will. Yes, but only if hum

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7

CASUSO, E. "INTEGRAL TREATMENT FOR TIME EVOLUTION: THE GENERAL INTERACTIVITY." International Journal of Modern Physics A 14, no. 20 (1999): 3239–52. http://dx.doi.org/10.1142/s0217751x99001524.

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Assuming that the unpredictability associated with many dynamical systems is an artefact of the differential treatment of their time evolution, we propose here an integral treatment as an alternative. We make the assumption that time is two-dimensional, and that the time distribution in the past of observables characterizing the dynamical system, is some characteristic "projection" of its time distribution in the future. We show here how this method can be used to predict the time evolution of several dynamically complex systems over long time intervals. The present work can be considered as t

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8

Rabbani, Hassan. "Quantum-Chaotic Emotional Evolution A Mathematical and Computational Framework." May 8, 2025. https://doi.org/10.5281/zenodo.15368105.

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Classical psychology and neuroscience reduce emotions to neurochemical patterns and cognitive reactions. But such views lack explanatory power for recursive, oscillatory, and unpredictable emotional transitions. Recent findings in quantum cognition hint that emotional phenomena may exhibit interference, superposition, and recursive collapse—properties that are neither deterministic nor classically probabilistic. The Hypothesis: • Emotions evolve as dynamic quantum wavefunctions. • Their transitions are not arbitrary, but constrained by an internal logic—a recursive matrix

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9

Casagrande, Heitor P., Bo Xing, William J. Munro, Chu Guo, and Dario Poletti. "Tensor-networks-based learning of probabilistic cellular automata dynamics." Physical Review Research 6, no. 4 (2024). http://dx.doi.org/10.1103/physrevresearch.6.043202.

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Algorithms developed to solve many-body quantum problems, like tensor networks, can turn into powerful quantum-inspired tools to tackle issues in the classical domain. This work focuses on matrix product operators, a prominent numerical technique to study many-body quantum systems, especially in one dimension. It has been previously shown that such a tool can be used for classification, learning of deterministic sequence-to-sequence processes, and generic quantum processes. We further develop a matrix product operator algorithm to learn probabilistic sequence-to-sequence processes and apply th

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10

Lee, Kyle, Shuvro Chowdhury, and Kerem Y. Camsari. "Noise-augmented chaotic Ising machines for combinatorial optimization and sampling." Communications Physics 8, no. 1 (2025). https://doi.org/10.1038/s42005-025-01945-1.

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Abstract Ising machines are hardware accelerators for combinatorial optimization and probabilistic sampling, using stochasticity to explore spin configurations and avoid local minima. We refine the previously proposed coupled chaotic bits (c-bits), which operate deterministically, by introducing noise. This improves performance in combinatorial optimization, achieving algorithmic scaling comparable to probabilistic bits (p-bits). We show that c-bits follow the quantum Boltzmann law in a 1D transverse field Ising model. Furthermore, c-bits exhibit critical dynamics similar to p-bits in 2D Ising

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11

Jindal, Siddharth, and Pavan Hosur. "Generalized free cumulants for quantum chaotic systems." Journal of High Energy Physics 2024, no. 9 (2024). http://dx.doi.org/10.1007/jhep09(2024)066.

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Abstract The eigenstate thermalization hypothesis (ETH) is the leading conjecture for the emergence of statistical mechanics in generic isolated quantum systems and is formulated in terms of the matrix elements of operators. An analog known as the ergodic bipartition (EB) describes entanglement and locality and is formulated in terms of the components of eigenstates. In this paper, we significantly generalize the EB and unify it with the ETH, extending the EB to study higher correlations and systems out of equilibrium. Our main result is a diagrammatic formalism that computes arbitrary correla

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12

Cavedon, Michael. "Supersolid Dark Matter and the Fabric of Spacetime." IPI Letters, May 16, 2025, O81—O85. https://doi.org/10.59973/ipil.197.

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The nature of dark matter and its role in the universe remains one of the most profound mysteries in modern physics. This paper proposes a unifying framework in which dark matter is a supersolid that fills the vacuum of space itself. In this model, the supersolid dark matter is the fabric of spacetime - whose state of displacement gives rise to gravitational phenomena. Ordinary matter moving through this supersolid displaces it, generating gravitational forces via a ”displacing back” mechanism. The supersolid dark matter is also what waves in wave-particle duality, and its chaotic nature gives

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13

Pelliconi, Pietro, Julian Sonner, and Herman Verlinde. "Gravity as a mesoscopic system." Journal of High Energy Physics 2025, no. 4 (2025). https://doi.org/10.1007/jhep04(2025)097.

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Abstract We employ a probabilistic mesoscopic description to draw conceptual and quantitative analogies between Brownian motion and late-time fluctuations of thermal correlation functions in generic chaotic systems respecting ETH. In this framework, thermal correlation functions of ‘simple’ operators are described by stochastic processes, which are able to probe features of the microscopic theory only in a probabilistic sense. We apply this formalism to the case of semiclassical gravity in AdS3, showing that wormhole contributions can be naturally identified as moments of stochastic processes.

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14

Bielińska, Marta, Michał Eckstein, and Horodecki Paweł. "Superluminal signalling and chaos in nonlinear quantum dynamics." New Journal of Physics, April 9, 2025. https://doi.org/10.1088/1367-2630/adcae1.

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Abstract Nonlinear quantum dynamics is often invoked in models trying to bridge the gap between the quantum micro-world and the classical macro-world. Such endeavors, however, encounter challenges at the nexus with relativity. In 1989 Nicolas Gisin proved a powerful no-go theorem, according to which nonlinear quantum dynamics would lead to superluminal signalling, violating Einstein’s causality. Here we analyse the theorem from the perspective of recent developments. First, we observe that it harmonises with the no-restriction hypothesis from General Probabilistic Theories. Second, we note tha

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15

-, Srikanth Jonnakuti. "Quantum-Inspired Heuristics for Optimizing Cloud Infrastructure Usage." International Journal of Leading Research Publication 5, no. 6 (2024). https://doi.org/10.70528/ijlrp.v5.i6.1557.

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The age of multi-region cloud computing, optimal resource-packing and task scheduling are key to realizing the highest system performance as well as lowered operational expense. This paper examines the use of quantum-inspired approximation algorithms (QIAAs) in the form of QAOA-like methodologies to mitigate large-scale resource assignment and scheduling complications in heterogeneous, multi-tenant cloud systems. Drawn from the concepts of quantum mechanics, these algorithms take advantage of probabilistic modeling and superposition to traverse multiple solution spaces with minimal waste. Unli

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16

Bary, Ghulam, Waqar Ahmed, and Riaz Ahmad. "Demonstration of chaotic–coherent strength to explore the intrinsic peculiarities of the complex dynamical systems." Chaos: An Interdisciplinary Journal of Nonlinear Science 35, no. 4 (2025). https://doi.org/10.1063/5.0244816.

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In this paper, we illustrate the innovative techniques to explore the dynamical properties of the hybrid complex systems by various parameters and demonstrate the clusters under the chaotic-condensation peculiarities to accentuate the different technological challenges in the modern world. The complex dynamic characteristics of the contemplated systems are explored with interferometry techniques, which play key roles in examining the consequences of intricate features to interpreting the dynamics of an assemblage that possesses the ability to traverse along dependable tracks of particles, and

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17

Gurikar, Shivaraj G. "CHAOS THEORY AND ITS IMPLICATIONS IN PHYSICAL SYSTEMS." ShodhKosh: Journal of Visual and Performing Arts 5, no. 1 (2024). https://doi.org/10.29121/shodhkosh.v5.i1.2024.4285.

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Chaos theory is a transformative field of mathematics and science that examines the behavior of dynamic systems highly sensitive to initial conditions. Often described as the "butterfly effect," this sensitivity implies that even minuscule changes in a system's starting state can result in vastly different outcomes, making long-term predictions challenging despite deterministic governing laws. Originating from studies of non-linear dynamics, chaos theory has redefined our understanding of predictability and randomness, offering profound insights into physical systems and beyond. In physical sy

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18

Aynur, Saran. "On the Ground of Politics and Political Life Quantum Leadership Paradigm." November 9, 2022. https://doi.org/10.5281/zenodo.7578028.

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Express the same meaning in our language, it is understood that the words politics and politics originating from Ancient Greek and Arabic are related to the city, state, society, and administration; however, the primary field of study of politics is political power. Because politics is a social activity, the first of the conditions that create politics is social life; later conditions that create politics are differentiation, conflict, and reconciliation resulting from differences. The field of study known as political science, in which political thinkers restricted their subject to the "

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