Hydrodynamic derivation of the Schr\"odinger equation and spacetime
curvature of a quantum particle
- URL: http://arxiv.org/abs/2202.08999v1
- Date: Fri, 18 Feb 2022 03:08:49 GMT
- Title: Hydrodynamic derivation of the Schr\"odinger equation and spacetime
curvature of a quantum particle
- Authors: Naoki Sato
- Abstract summary: We show that spin represents the angular momentum associated with the rotation of a charged fluid within a massive particle.
The rotation velocity can be evaluated through the current density of the fourth Maxwell equation.
The hydrodynamic representation is then used to obtain the stress-energy-momentum tensor for a quantum particle.
- Score: 0.2741266294612775
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We report a hydrodynamic derivation of the Schr\"odinger equation. The
derivation only assumes that spin represents the angular momentum associated
with the rotation of a charged fluid within a massive particle. The rotation
velocity can be evaluated through the current density of the fourth Maxwell
equation, leading to a quantum correction of the classical fluid energy. The
Schr\"odinger equation then follows in Madelung form by application of the
Poisson operator of the Euler equations for an ideal fluid to the total fluid
energy including the quantum effect of internal spin. The hydrodynamic
representation is then used to obtain the stress-energy-momentum tensor for a
quantum particle. We find that the trace of the quantum modification to the
stress-energy-momentum tensor expresses the energy density of an oscillator
with frequency given by the vorticity of the internal rotation velocity.
Finally, the stress-energy-momentum tensor is used to determine the
relationship between the Ricci scalar curvature arising from the Einstein field
equations and the fluid density associated with the hydrodynamic representation
of the quantum particle in a static spherically symmetric configuration.
Related papers
- A Formulation of Quantum Fluid Mechanics and Trajectories [0.0]
A formalism of classical mechanics is given for time-dependent many-body states of quantum mechanics.
The familiar equations of energy, motion, and those of Lagrangian mechanics are obtained.
arXiv Detail & Related papers (2024-05-02T17:22:12Z) - A Theory of Quantum Jumps [44.99833362998488]
We study fluorescence and the phenomenon of quantum jumps'' in idealized models of atoms coupled to the quantized electromagnetic field.
Our results amount to a derivation of the fundamental randomness in the quantum-mechanical description of microscopic systems.
arXiv Detail & Related papers (2024-04-16T11:00:46Z) - Unveiling the Quantum Toroidal Dipole in Nanosystems: Quantization,
Interaction Energy, and Measurement [44.99833362998488]
We investigate a quantum particle confined to a toroidal surface in the presence of a filiform current along the system's rotational axis.
Our analysis reveals that the interaction between the particle and the current induces a non-zero toroidal dipole in the particle's stationary states.
arXiv Detail & Related papers (2024-01-26T13:31:32Z) - Quantum mechanics without quantum potentials [0.0]
Non-locality in quantum mechanics can be resolved by considering relativistically covariant diffusion in spacetime.
We introduce the concept of momentum equilinear to replace the second-order Bohm-Newton equations of motion.
arXiv Detail & Related papers (2024-01-08T18:51:38Z) - Energetics of the dissipative quantum oscillator [22.76327908349951]
We discuss some aspects of the energetics of a quantum Brownian particle placed in a harmonic trap.
Based on the fluctuation-dissipation theorem, we analyze two distinct notions of thermally-averaged energy.
We generalize our analysis to the case of the three-dimensional dissipative magneto-oscillator.
arXiv Detail & Related papers (2023-10-05T15:18:56Z) - Quantum wave representation of dissipative fluids [0.0]
We present a mapping between a Schr"odinger equation with a shifted non-linear potential and the Navier-Stokes equation.
The inclusion of the Bohm quantum potential plus the laplacian of the phase field in the non-linear term leads to continuity and momentum equations for a dissipative incompressible Navier-Stokes fluid.
arXiv Detail & Related papers (2023-08-10T23:44:27Z) - Thermal masses and trapped-ion quantum spin models: a self-consistent approach to Yukawa-type interactions in the $λ\!φ^4$ model [44.99833362998488]
A quantum simulation of magnetism in trapped-ion systems makes use of the crystal vibrations to mediate pairwise interactions between spins.
These interactions can be accounted for by a long-wavelength relativistic theory, where the phonons are described by a coarse-grained Klein-Gordon field.
We show that thermal effects, which can be controlled by laser cooling, can unveil this flow through the appearance of thermal masses in interacting QFTs.
arXiv Detail & Related papers (2023-05-10T12:59:07Z) - Fields and Equations of Classical Mechanics for Quantum Mechanics [0.0]
An equation is also derived that is equivalent to the main equation of Bohmian mechanics.
For one-body systems, the Eulerian Eq. can model either a fluid or particle description of quantum states.
arXiv Detail & Related papers (2022-07-09T23:28:27Z) - Quantum kinetic theory of flux-carrying Brownian particles [0.0]
We develop the kinetic theory of the flux-carrying Brownian motion recently introduced in the context of open quantum systems.
This model constitutes an effective description of two-dimensional dissipative particles violating both time-reversal and parity.
arXiv Detail & Related papers (2021-10-29T09:54:53Z) - Quantum dynamics and relaxation in comb turbulent diffusion [91.3755431537592]
Continuous time quantum walks in the form of quantum counterparts of turbulent diffusion in comb geometry are considered.
Operators of the form $hatcal H=hatA+ihatB$ are described.
Rigorous analytical analysis is performed for both wave and Green's functions.
arXiv Detail & Related papers (2020-10-13T15:50:49Z) - Theory of waveguide-QED with moving emitters [68.8204255655161]
We study a system composed by a waveguide and a moving quantum emitter in the single excitation subspace.
We first characterize single-photon scattering off a single moving quantum emitter, showing both nonreciprocal transmission and recoil-induced reduction of the quantum emitter motional energy.
arXiv Detail & Related papers (2020-03-20T12:14:10Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.