Nonlinear Quantum Mechanics at the Planck Scale

Svetlichny, George

doi:10.1007/s10773-005-8983-1

Cited by 14 publications

(11 citation statements)

References 35 publications

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“…Advancing proposals-and-models [103][104][105][106][107][108][109][110][111] and other similar works, we conjecture one can formulate advantageous (0 + 1)-dimensional unitarily-evolving quantum many body systems from which both the local spacetime and geometric quantum matter emerge via 'state-history-driven self-organizations', by means of QMM-UEs (2.7,2.8;6.1;2.1).…”

Section: One-qubit Purely-qmm-ues: Selected General Highlightsmentioning

confidence: 80%

Unitary Evolutions From Interacting Quantum Memories: Closed Quantum Systems Directing Themselves Using Their State Histories

Tavanfar¹,

Aliasghar²,

Pezzutto³

2022

Preprint

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We propose, formulate and anlyze novel closed quantum systems whose unitary time evolutions, and internal interactions, emerge out of their linking quantum memories. In a closed system of the kind, the unitary evolution operator is updated, moment by moment, using the quantum state history as a compositional resource. The 'Quantum Memory Made' Hamiltonians (QMM-Hs) generating these unitary evolutions are Hermitian operators made of arbitrarily-chosen past-until-present density operators of the closed system, or its arbitrary subsystems. The time evolution is described by novel nonlocal and nonlinear von Neumann and Schrödinger equations. We establish that nontrivial Purely-QMM unitary evolutions are 'Robustly Non-Markovian', in the sense that the largest temporal distance between the compositional quantum memories admit finite lower bounds set by their interaction couplings. After general formulation and considerations, we take on the sufficiently-complex task of classifying the phases of one-qubit pure-state evolutions generated by specific choices of QMM-Hs, combining analytical methods with extensive numerical simulations, and using QMM two-point functions as natural signature probes. Analyzing Hamiltonians which are purely QMM, and those combined with the conventional Hamiltonians, we obtain and characterize specific families of analytical solutions, and then classify generic numerical solutions. We establish that QMM phase diagrams are outstandingly rich, containing wide classes of novel unitary evolutions with physically remarkable behaviours. Moreover, we show that QMM interactions give rise to novel purely internal dynamical phase transitions. We suggest several independent fundamental and applied domains and disciplines where QMM-UEs can be utilized advantageously.

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Section: One-qubit Purely-qmm-ues: Selected General Highlightsmentioning

confidence: 80%

Unitary Evolutions From Interacting Quantum Memories: Closed Quantum Systems Directing Themselves Using Their State Histories

Tavanfar¹,

Aliasghar²,

Pezzutto³

2022

Preprint

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“…Nonlinear quantum mechanics has been studied since the eighties [53] and several neural networks models and learning algorithms used nonlinear quantum computing [54,8,27,51], but the physical realizability of nonlinear quantum computing is still controversial [28,55]. A linear version of SAL needs investigation.…”

Section: Discussionmentioning

confidence: 99%

Quantum perceptron over a field and neural network architecture selection in a quantum computer

2016

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In this work, we propose a quantum neural network named quantum perceptron over a field (QPF). Quantum computers are not yet a reality and the models and algorithms proposed in this work cannot be simulated in actual (or classical) computers. QPF is a direct generalization of a classical perceptron and solves some drawbacks found in previous models of quantum perceptrons. We also present a learning algorithm named Superposition based Architecture Learning algorithm (SAL) that optimizes the neural network weights and architectures. SAL searches for the best architecture in a finite set of neural network architectures with linear time over the number of patterns in the training set. SAL is the first learning algorithm to determine neural network architectures in polynomial time. This speedup is obtained by the use of quantum parallelism and a non-linear quantum operator.

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“…In other words, for non-relativistic microscopic processes down to the atomic level, i.e. at scales of order 10 −10 m (for smaller scales, see [28]), could the Schrödinger equation in particular and the QM formalism in general have a nonlinear mathematical structure?…”

Section: (B) Can Quantum Mechanics Be Intrinsically Nonlinear?mentioning

confidence: 99%

Nonlinear dynamics in meso and nano scales: fundamental aspects and applications

Luz

Anteneodo

2011

Phil. Trans. R. Soc. A.

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This introduction to the special issue, Nonlinear dynamics in meso and nano scales: fundamental aspects and applications, gives a short overview about different contexts and current challenges posed by the emergence of nonlinearities at meso and nano characteristic sizes. It also addresses different aspects related to classical and quantum chaos. Moreover, it comments on the articles in this thematic publication, briefly summarizing their relevance in helping to understand the uprise of chaos and complex behaviour at those small scales.

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Nonlinear Quantum Mechanics at the Planck Scale

Cited by 14 publications

References 35 publications

Unitary Evolutions From Interacting Quantum Memories: Closed Quantum Systems Directing Themselves Using Their State Histories

Unitary Evolutions From Interacting Quantum Memories: Closed Quantum Systems Directing Themselves Using Their State Histories

Quantum perceptron over a field and neural network architecture selection in a quantum computer

Nonlinear dynamics in meso and nano scales: fundamental aspects and applications

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