scholarly journals Bohm Quantum Trajectories of Scalar Field in Trans-Planckian Physics

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Jung-Jeng Huang
Keyword(s):  
Scalar Field ◽  
Wave Theory ◽  
Vacuum State ◽  
Quantum Trajectory ◽  
Quantum Trajectories ◽  
De Sitter ◽  
Pilot Wave ◽  
In Trans ◽  
Schrödinger Picture ◽  
Pilot Wave Theory

In lattice Schrödinger picture, we investigate the possible effects of trans-Planckian physics on the quantum trajectories of scalar field in de Sitter space within the framework of the pilot-wave theory of de Broglie and Bohm. For the massless minimally coupled scalar field and the Corley-Jacobson type dispersion relation with sextic correction to the standard-squared linear relation, we obtain the time evolution of vacuum state of the scalar field during slow-roll inflation. We find that there exists a transition in the evolution of the quantum trajectory from well before horizon exit to well after horizon exit, which provides a possible mechanism to solve the riddle of the smallness of the cosmological constant.

PILOT-WAVE SCALAR FIELD THEORY IN DE SITTER SPACE: LATTICE SCHRÖDINGER PICTURE

2010 ◽  
Vol 25 (01) ◽  
pp. 1-13 ◽  
Author(s):  
JUNG-JENG HUANG
Keyword(s):  
Scalar Field ◽  
Vacuum State ◽  
De Sitter Space ◽  
Quantum Trajectory ◽  
Quantum Trajectories ◽  
De Sitter ◽  
Minimal Coupling ◽  
Pilot Wave ◽  
The Difference ◽  
Schrödinger Picture

In the lattice Schrödinger picture, we find the de Broglie–Bohm quantum trajectories for the eigenstates of a generically coupled free real scalar field in de Sitter space. For the massless minimally coupled scalar field which has exact quantum trajectory, we evaluate both the time evolution of vacuum state and the possible effects of initial quantum nonequilibrium on the power spectrum of the primordial inflaton and curvature fluctuations in the slow-roll approximation. We reproduce the results that were already presented by Valentini who considered only the massless minimal coupling case. In addition we cover both massive minimal and massive non-minimal coupling cases which are the extension of Valentini's work. Finally we discuss the difference between de Broglie's first-order dynamics and Bohm's second-order dynamics in finding the quantum trajectories.

scholarly journals Hamiltonian formulation of the pilot-wave theory

2019 ◽  
Vol 97 (4) ◽  
pp. 431-435
Author(s):  
Dan N. Vollick
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Scalar Field ◽  
Relativistic Particle ◽  
Hamiltonian Formulation ◽  
Wave Theory ◽  
Schrödinger’S Equation ◽  
Pilot Wave ◽  
Schrödinger's Equation ◽  
Pilot Wave Theory

In the pilot-wave theory of quantum mechanics particles have definite positions and velocities and the system evolves deterministically. The velocity of a particle is determined by the wave function of the system (the guidance equation) and the wave function evolves according to Schrödinger’s equation. In this paper I first construct a Hamiltonian that gives Schrödinger’s equation and the guidance equation for the particle. I then find the Hamiltonian for a relativistic particle in Dirac’s theory and for a quantum scalar field.

scholarly journals Geometrical interpretation of the pilot wave theory and manifestation of spinor fields

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Mariya Iv. Trukhanova ◽  
Gennady Shipov
Keyword(s):  
Wave Theory ◽  
Geometrical Interpretation ◽  
Real Field ◽  
Spin Vector ◽  
Spinor Wave Function ◽  
Spinning Particle ◽  
Pilot Wave ◽  
Intrinsic Angular Momentum ◽  
Spinor Wave ◽  
Pilot Wave Theory

Abstract Using the hydrodynamical formalism of quantum mechanics for a Schrödinger spinning particle developed by Takabayashi, Vigier, and followers, which involves vortical flows, we propose a new geometrical interpretation of the pilot wave theory. The spinor wave in this interpretation represents an objectively real field, and the evolution of a material particle controlled by the wave is a manifestation of the geometry of space. We assume this field to have a geometrical nature, basing on the idea that the intrinsic angular momentum, the spin, modifies the geometry of the space, which becomes a manifold, represented as a vector bundle with a base formed by the translational coordinates and time, and the fiber of the bundle, specified at each point by the field of a tetrad $e^a_{\mu}$, forms from bilinear combinations of the spinor wave function. It has been shown that the spin vector rotates following the geodesic of the space with torsion, and the particle moves according to the geometrized guidance equation. This fact explains the self-action of the spinning particle. We show that the curvature and torsion of the spin vector line is determined by the space torsion of the absolute parallelism geometry.

Pilot-wave theory in retrospect

2013 ◽  
pp. 224-241
Author(s):  
Guido Bacciagaluppi ◽  
Antony Valentini
Keyword(s):  
Wave Theory ◽  
Pilot Wave ◽  
Pilot Wave Theory

scholarly journals Justifying Born’s Rule Pα = |Ψα|2 Using Deterministic Chaos, Decoherence, and the de Broglie-Bohm Quantum Theory

Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1371
Author(s):  
Aurélien Drezet
Keyword(s):  
Quantum Theory ◽  
Kinetic Theory ◽  
Deterministic Chaos ◽  
Wave Theory ◽  
Fast Relaxation ◽  
Pilot Wave ◽  
Born’S Rule ◽  
H Theorem ◽  
Pilot Wave Theory ◽  
De Broglie Bohm

In this work, we derive Born’s rule from the pilot-wave theory of de Broglie and Bohm. Based on a toy model involving a particle coupled to an environment made of “qubits” (i.e., Bohmian pointers), we show that entanglement together with deterministic chaos leads to a fast relaxation from any statistical distribution ρ(x) of finding a particle at point x to the Born probability law |Ψ(x)|2. Our model is discussed in the context of Boltzmann’s kinetic theory, and we demonstrate a kind of H theorem for the relaxation to the quantum equilibrium regime.

scholarly journals Energy velocity and reactive fields

2018 ◽  
Vol 376 (2134) ◽  
pp. 20170453 ◽  
Author(s):  
Hans G. Schantz
Keyword(s):  
Electromagnetic Fields ◽  
Logical Consequence ◽  
Plane Waves ◽  
Wave Theory ◽  
Radiation Reaction ◽  
Electromagnetic Theory ◽  
Subsequent Work ◽  
Pilot Wave ◽  
The Waves ◽  
Pilot Wave Theory

Conventional definitions of ‘near fields’ set bounds that describe where near fields may be found. These definitions tell us nothing about what near fields are, why they exist or how they work. In 1893, Heaviside derived the electromagnetic energy velocity for plane waves. Subsequent work demonstrated that although energy moves in synchronicity with radiated electromagnetic fields at the speed of light, in reactive fields the energy velocity slows down, converging to zero in the case of static fields. Combining Heaviside's energy velocity relation with the field Lagrangian yields a simple parametrization for the reactivity of electromagnetic fields that provides profound insights to the behaviour of electromagnetic systems. Fields guide energy. As waves interfere, they guide energy along paths that may be substantially different from the trajectories of the waves themselves. The results of this paper not only resolve the long-standing paradox of runaway acceleration from radiation reaction, but also make clear that pilot wave theory is the natural and logical consequence of the need for quantum mechanics correspond to the macroscopic results of the classical electromagnetic theory. This article is part of the theme issue ‘Celebrating 125 years of Oliver Heaviside's ‘Electromagnetic Theory’’.

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