Hydrodynamic quantum field theory: the free particle

Dagan, Yuval; Bush, John W. M.

doi:10.5802/crmeca.34

Cited by 21 publications

(40 citation statements)

References 66 publications

(132 reference statements)

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“…While the possibilities for alternative wave-particle couplings are numerous, we expect the in-line speed oscillations elucidated here to be a generic feature of pilot-wave systems with a quasimonochromatic guiding field; indeed, such speed oscillations have already been seen to emerge in HQFT [56].…”

Section: Discussionmentioning

confidence: 63%

“…Andersen et al [55] explored a model in which the pilot wave is generated by localized periodic particle excitation of the Schrödinger equation, and considered the particle velocity as being proportional to the gradient of the wave phase. In the hydrodynamic quantum field theory (HQFT) of Dagan & Bush [56], the authors explore a variant of de Broglie’s original formulation: the particle velocity is proportional to the slope of the pilot wave generated by localized periodic particle excitation of the Klein–Gordon equation. While the possibilities for alternative wave-particle couplings are numerous, we expect the in-line speed oscillations elucidated here to be a generic feature of pilot-wave systems with a quasi-monochromatic guiding field; indeed, such speed oscillations have already been seen to emerge in HQFT [56].…”

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

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Speed oscillations in classical pilot-wave dynamics

2020

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We present the results of a theoretical investigation of a dynamical system consisting of a particle self-propelling through a resonant interaction with its own quasi-monochromatic pilot-wave field. We rationalize two distinct mechanisms, arising in different regions of parameter space, that may lead to a wavelike statistical signature with the pilot-wavelength. First, resonant speed oscillations with the wavelength of the guiding wave may arise when the particle is perturbed from its steady self-propelling state. Second, a random-walk-like motion may set in when the decay rate of the pilot-wave field is sufficiently small. The implications for the emergent statistics in classical pilot-wave systems are discussed.

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Section: Discussionmentioning

confidence: 63%

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

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Speed oscillations in classical pilot-wave dynamics

2020

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“…De qualquer maneira "destacamos que nossos resultados não fecham a porta para a busca de difração e interferência das [gotas] errantes, apenas para as condições de contorno consideradas aqui, para o qual o comportamento do sistema é dominado pelas interações gota errante-anteparo" [37, p. 1152]. Além desse último artigo, vale a pena destacar outros trabalhos também de John W. M. Bush e colaboradores que têm se debruçado sobre essa analogia de maneira meticulosa, tal como o Hydrodynamic quantum field theory: the free particle e o Hydrodynamic quantum field theory: The onset of particle motion and the form of the pilot wave [38,39], a ponto de estabelecerem um modelo hidrodinâmico para a spintrônica em Emergent order in hydrodynamic spin lattices, observando uma histerese na transição de antiferromagnético para ferromagnético [40].…”

Section: Novo Interesse: As Gotas Errantesunclassified

Uma tradução comentada do artigo “A Termodinâmica Oculta das Partículas” de Louis de Broglie

Lima

Chaib

2021

Rev. Bras. Ensino Fís.

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Louis de Broglie é principalmente lembrado por sua contribuição no que se refere à dualidade onda-partícula e à expressão que relaciona o momento linear e o comprimento de onda no desenvolvimento da Teoria Quântica, contribuições dadas no período de 1922–1924. Entretanto, pouco se fala de sua postura e atividade crítica a interpretações afins da Complementaridade de Niels Bohr, e sua proposta de novas bases para uma teoria quântica alternativa, de caráter realista e determinista. Assim, no sentido de apresentar textos históricos originais e contribuir para o resgate das ideias de Louis de Broglie, apresentamos uma tradução comentada do artigo “A Termodinâmica Oculta das Partículas”, publicado em 1964, em que de Broglie sintetiza sua proposta teórica e apresenta dois resultados importantes, a saber: que o caminho de menor ação percorrido por uma partícula é aquele que maximiza a entropia do meio subquântico; e que os estados de transição em um átomo teria uma entropia menor do que os estados estacionários, justificando termodinamicamente porque os estados estacionários têm maior probabilidade de acontecerem.

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“…Walkers have also been predicted to show anomalous two-droplet correlations 23,24 . Recently, efforts have also been made to develop a hydrodynamic quantum field theory for the walking-droplet system 25,26 . A detailed review of hydrodynamic quantum analogues for walking droplets is provided by Bush 27 and Bush and Oza 28 .…”

Section: Introductionmentioning

confidence: 99%

Lorenz-like systems emerging from an integro-differential trajectory equation of a one-dimensional wave-particle entity

Valani

2021

Preprint

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Vertically vibrating a liquid bath can give rise to a self-propelled wave-particle entity on its free surface. The horizontal walking dynamics of this wave-particle entity can be described adequately by an integro-differential trajectory equation. By transforming this integro-differential equation of motion for a one-dimensional wave-particle entity into a system of ordinary differential equations (ODEs), we show the emergence of Lorenz-like dynamical systems for various spatial wave forms of the entity. Specifically, we present and give examples of Lorenz-like dynamical systems that emerge when the wave form gradient is (i) a solution of a linear homogeneous constant coefficient ODE, (ii) a polynomial and (iii) a periodic function. Understanding the dynamics of the wave-particle entity in terms of Lorenz-like systems may provide to be useful in rationalizing emergent statistical behavior from underlying chaotic dynamics in hydrodynamic quantum analogs of walking droplets. Moreover, the results presented here provide an alternative physical interpretation of various Lorenz-like dynamical systems in terms of the walking dynamics of a wave-particle entity.A droplet of oil may walk horizontally while bouncing vertically when placed on a vertically vibrating bath of the same liquid. Each bounce of the droplet creates a localized decaying standing wave which in turn guides the horizontal motion of the droplet, resulting in a self-propelled wave-particle entity. Such entities have been shown to mimic several features that were thought to be exclusive to the quantum realm. In this paper, we show that for certain spatial forms of the waves, Lorenz-like dynamical systems emerge from the trajectory equation of the waveparticle entity. We do this by transforming the integrodifferential trajectory equation of motion into a system of infinite ODEs and show that for certain choice of wave forms, the system of infinite ODEs can be reduced to a finite system that have Lorenz-system-like structure in both the equations and the underlying strange attractor.

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Hydrodynamic quantum field theory: the free particle

Cited by 21 publications

References 66 publications

Speed oscillations in classical pilot-wave dynamics

Speed oscillations in classical pilot-wave dynamics

Uma tradução comentada do artigo “A Termodinâmica Oculta das Partículas” de Louis de Broglie

Lorenz-like systems emerging from an integro-differential trajectory equation of a one-dimensional wave-particle entity

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