Chaos and Quantum Mechanics

Habib, Salman; Bhattacharya, Tanmoy; Greenbaum, Benjamin; Jacobs, Kurt; Shizume, Kosuke; Sundaram, Bala

doi:10.1196/annals.1350.026

Cited by 8 publications

(10 citation statements)

References 58 publications

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“…coupled in some way to the external world, generically referred to as 'an environment', whether it is another system or a measuring device [42,43,58]. The interaction with the environment must be taken into account, and one distinguishes between two types of systems, depending on whether a measurement is performed on the environment or not [59,60,61]. If the environment is not observed, then the appropriate description of the system is in terms of the reduced density operator, obtained by tracing the full density matrix over the variables of the environment.…”

Section: The Quantum To Classical Transition (Qct)mentioning

confidence: 99%

Classical to quantum transition of a driven nonlinear nanomechanical resonator

et al. 2008

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Much experimental effort is invested these days in fabricating nanoelectromechanical systems (NEMS) that are sufficiently small, cold, and clean, so as to approach quantum mechanical behavior as their typical quantum energy scalē hΩ becomes comparable to that of the ambient thermal energy k B T . Such systems will hopefully enable one to observe the quantum behavior of human-made objects, and test some of the basic principles of quantum mechanics. Here we expand and elaborate on our recent suggestion [Phys. Rev. Lett. 99 (2007) 040404] to exploit the nonlinear nature of a nanoresonator in order to observe its transition into the quantum regime. We study this transition for an isolated resonator, as well as one that is coupled to a heat bath at either zero or finite temperature. We argue that by exploiting nonlinearities, quantum dynamics can be probed using technology that is almost within reach. Numerical solutions of the equations of motion display the first quantum corrections to classical dynamics that appear as the classical-to-quantum transition occurs. This provides practical signatures to look for in future experiments with NEMS resonators. † There exist other possibilities for describing quantum dynamics in phase space, see for example [42,43,44], but we find the Wigner function to be among the simplest.

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Section: The Quantum To Classical Transition (Qct)mentioning

confidence: 99%

Classical to quantum transition of a driven nonlinear nanomechanical resonator

et al. 2008

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“…Laws that govern matter are not as deterministic as we presumed them to be. At a sub-molecular level, some forces that govern the organisation of matter are, by their nature, unpredictable [22]. These forces provide the scientific explanation of the part of unpredictability that can be observed at other levels (molecular, biochemical, cellular, intercellular, organism, inter-organism, environment etc.)…”

Section: Ontological Positionsmentioning

confidence: 99%

Tackling Societal Challenges Related to Ageing and Transport Transition: An Introduction to Philosophical Principles of Causation Adapted to the Biopsychosocial Model

Vaucher

Favrat

2015

Geriatrics

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Abstract:In geriatrics, driving cessation is addressed within the biopsychosocial model. This has broadened the scope of practitioners, not only in terms of assessing fitness to drive, but also by helping to maintain social engagements and provide support for transport transition. Causes can be addressed at different levels by adapting medication, improving physical health, modifying behaviour, adapting lifestyle, or bringing changes to the environment. This transdisciplinary approach requires an understanding of how different disciplines are linked to each other. This article reviews the philosophical principles of causality between fields and provides a framework for understanding causality within the biopsychosocial model. Understanding interlevel constraints should help practitioners overcome their differences, and favor transversal approaches to driving cessation.Keywords: traffic medicine; behavioural science; causality; transversal research Clinical SituationA 78-year-old driver with a past history of cardiovascular disease was told his condition would not affect his fitness to drive, as long as he complied with his medication requirement to treat his arrhythmia. The patient is very attached to driving and attributes a feeling of freedom and independence to his car. He lives alone in a remote area and says he needs his car to do his shopping and meet with his friends and family. Recently, he has started suffering from mild cognitive impairment. A neuropsychologic assessment has nevertheless concluded that it was not yet severe enough to justify having to stop driving. It was therefore decided to monitor the situation and plan a transport transition phase within the next two years. He is now followed by an occupational therapist who has recently reported that the patient's condition has worsened and that the patient expresses strong resistance to the idea of giving up driving. A meeting with the physician, the patient's daughter, and the occupational therapist has been scheduled to discuss a solution to the problem and seriously consider driving cessation. Indeed, the patient's mental health state had worsened to a point where he frequently forwent his treatment and occasionally drove with heart palpitations. After forgetting to take his medication several days in a row, his heart condition severely worsened while he was driving. He lost consciousness and his vehicle hit the side of the road before

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“…The paradox is apparent: how can classical mechanics emerge from quantum mechanics in an appropriate macroscopic limit if the former manifestly exhibits the above mentioned property but the latter does not? One -and the dominant -way to resolve this is the observation of the fact that every experimental setup involves measurement, therefore open quantum systems [17].…”

Section: Joseph Fordmentioning

confidence: 99%

Paradigms for Quantum Feedback Control

Tóth

2012

Preprint

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In this review paper, we survey the main concepts and some of the recent developments in quantum feedback control. For consistency and clarity, essential ideas and notations in the theory of open quantum systems and quantum stochastic calculus, as well as continuous measurement theory are developed. We give a general description of quantum feedback control, set up a coherent model and compare it to open-loop designs. Objectives which can be achieved by feedback, such as rapid state preparation and purification or entanglement generation are formulated and analyzed, based on the relevant literature. The connection between quantum feedback and quantum chaos is also described and unravelled which, apart from its theoretical curiosity, can shed more light on some of the intrinsic properties of this control paradigm.

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Chaos and Quantum Mechanics

Cited by 8 publications

References 58 publications

Classical to quantum transition of a driven nonlinear nanomechanical resonator

Classical to quantum transition of a driven nonlinear nanomechanical resonator

Tackling Societal Challenges Related to Ageing and Transport Transition: An Introduction to Philosophical Principles of Causation Adapted to the Biopsychosocial Model

Paradigms for Quantum Feedback Control

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