Related papers: Equivalence Principle for Quantum Mechanics in the Heisenberg Picture

Equivalence Principle for Quantum Mechanics in the Heisenberg Picture

URL: http://arxiv.org/abs/2309.03095v2
Date: Tue, 14 May 2024 08:50:47 GMT
Title: Equivalence Principle for Quantum Mechanics in the Heisenberg Picture
Authors: Otto C. W. Kong,
Abstract summary: We present an exact quantum observable analog of the weak equivalence principle for a relativistic' quantum particle. The quantum geodesic equations are obtained from Heisenberg equations of motion as an exact analog of a fully covariant classical Hamiltonian evolution picture.
Score: 0.0
License: http://creativecommons.org/licenses/by/4.0/
Abstract: We present an exact quantum observable analog of the weak equivalence principle for a `relativistic' quantum particle. The quantum geodesic equations are obtained from Heisenberg equations of motion as an exact analog of a fully covariant classical Hamiltonian evolution picture, with the proper identification of the canonical momentum variables as $p_\mu$, rather than $p^\mu$. We discuss the meaning of the equations in relation to projective measurements as well as equations with solution curves as ones in the noncommutative geometric picture of spacetime, and a plausible approach to quantum gravity as a theory about quantum observables as physical quantities including the notion of quantum coordinate transformation.

Related papers

Semiclassical gravity phenomenology under the causal-conditional quantum measurement prescription II: Heisenberg picture and apparent optical entanglement [13.04737397490371]
In quantum gravity theory, a state-dependent gravitational potential introduces nonlinearity into the state evolution. The formalism for understanding the continuous quantum measurement process on the quantum state has been previously discussed using the Schr"odinger picture. In this work, an equivalent formalism using the Heisenberg picture is developed and applied to the analysis of two optomechanical experiment protocols.
arXiv Detail & Related papers (2024-11-08T14:07:18Z)
Quantum Mechanics in Curved Space(time) with a Noncommutative Geometric Perspective [0.0]
We take seriously the noncommutative symplectic geometry corresponding to the quantum observable algebra. The work points to a very different approach to quantum gravity.
arXiv Detail & Related papers (2024-06-20T10:44:06Z)
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)
A dynamic programming interpretation of quantum mechanics [0.0]
We introduce a transformation of the quantum phase $S'=S+frachbar2logrho$, which converts the deterministic equations of quantum mechanics into the Lagrangian reference frame of particles. We show that the quantum potential can be removed from the transformed quantum Hamilton-Jacobi equations if they are solved as Hamilton-Jacobi-Bellman equations.
arXiv Detail & Related papers (2024-01-08T18:43:40Z)
Quantumness and quantum to classical transition in the generalized Rabi model [17.03191662568079]
We define the quantumness of a Hamiltonian by the free energy difference between its quantum and classical descriptions. We show that the Jaynes-Cummings and anti Jaynes-Cummings models exhibit greater quantumness than the Rabi model.
arXiv Detail & Related papers (2023-11-12T18:24:36Z)
Earthquake Quantization [0.0]
We propose a novel quantization prescription, where the paths of a path-integral are not random, but rather solutions of a geodesic equation in a random background. We show that this change of perspective can be made mathematically equivalent to the usual formulations of non-relativistic quantum mechanics.
arXiv Detail & Related papers (2023-03-10T19:00:03Z)
Quantum simulation of partial differential equations via Schrodingerisation [31.986350313948435]
We present a simple new way to simulate general linear partial differential equations via quantum simulation. Using a simple new transform, referred to as the warped phase transformation, any linear partial differential equation can be recast into a system of Schrodinger's equations. This can be seen directly on the level of the dynamical equations without more sophisticated methods.
arXiv Detail & Related papers (2022-12-28T17:32:38Z)
Quantum dynamics corresponding to chaotic BKL scenario [62.997667081978825]
Quantization smears the gravitational singularity avoiding its localization in the configuration space. Results suggest that the generic singularity of general relativity can be avoided at quantum level.
arXiv Detail & Related papers (2022-04-24T13:32:45Z)
Lyapunov equation in open quantum systems and non-Hermitian physics [0.0]
The continuous-time differential Lyapunov equation is widely used in linear optimal control theory. In quantum physics, it is known to appear in Markovian descriptions of linear (quadratic Hamiltonian, linear equations of motion) open quantum systems. We establish the Lyapunov equation as a fundamental and efficient formalism for linear open quantum systems.
arXiv Detail & Related papers (2022-01-03T14:40:07Z)
Quantum indistinguishability through exchangeable desirable gambles [69.62715388742298]
Two particles are identical if all their intrinsic properties, such as spin and charge, are the same. Quantum mechanics is seen as a normative and algorithmic theory guiding an agent to assess her subjective beliefs represented as (coherent) sets of gambles. We show how sets of exchangeable observables (gambles) may be updated after a measurement and discuss the issue of defining entanglement for indistinguishable particle systems.
arXiv Detail & Related papers (2021-05-10T13:11:59Z)

This list is automatically generated from the titles and abstracts of the papers in this site.