Related papers: On computing quantum waves and spin from classical and relativistic action

On computing quantum waves and spin from classical and relativistic action

URL: http://arxiv.org/abs/2405.06328v4
Date: Tue, 05 Nov 2024 19:48:13 GMT
Title: On computing quantum waves and spin from classical and relativistic action
Authors: Winfried Lohmiller, Jean-Jacques Slotine,
Abstract summary: We show that the Schroedinger equation of quantum physics can be solved using a generalized form of the classical Hamilton-Jacobi least action equation. The results, which extend to the relativistic setting, build on two developments. They suggest a smooth transition between physics across scales, with the Hamilton-Jacobi formalism extending to general relativity.
Score: 0.0
License:
Abstract: We show that the Schroedinger equation of quantum physics can be solved using a generalized form of the classical Hamilton-Jacobi least action equation, extending a key result of Feynman applicable only to quadratic actions. The results, which extend to the relativistic setting, build on two developments. The first is incorporating geometric constraints directly in the classical least action problem. This leads to multi-valued least action solutions where each local action is its own set element. The multiple solutions replace in part the probabilistic setting by the non-uniqueness of solutions of the constrained problem. For instance, in the double slit experiment or for a particle in a box, spatial inequality constraints create impulsive constraint forces, which lead to multiple path solutions. Second, an approximate mapping $ \ \Psi \approx e^{\frac{i }{\hbar} \Phi } \ $ between action $\Phi$ and wave function $\Psi$ has been known since Dirac and even Schroedinger. We show that this mapping can be made exact by introducing a compression ratio of the proposed multi-valued action, which can in turn be interpreted as a probability density on classical trajectories of a fluid flow field. Branch points of the multi-valued least action imply a quantum wave collapse. These developments leave the results of associated Feynman path integrals unchanged, but the computation can be greatly simplified as only multi-valued least actions are used, avoiding time-slicing and zig-zag trajectories altogether. They also suggest a smooth transition between physics across scales, with the Hamilton-Jacobi formalism extending to general relativity, in a coordinate-invariant framework. In particular, the Klein-Gordon equation may have a natural extension to general relativity.

Related papers

Classical and Quantum Phase Transitions in Multiscale Media: Universality and Critical Exponents in the Fractional Ising Model [0.0]
We show that for $q 1$ in the classical regime and $q 2$ in the quantum regime, fractional interactions allow phase transitions in one dimension. This work establishes fractional derivatives as a powerful tool for engineering critical behavior.
arXiv Detail & Related papers (2025-01-23T23:21:00Z)
Efficient Quantum Simulation Algorithms in the Path Integral Formulation [0.5729426778193399]
We provide two novel quantum algorithms based on Hamiltonian versions of the path integral formulation and another for Lagrangians of the form $fracm2dotx2 - V(x)$. We show that our Lagrangian simulation algorithm requires a number of queries to an oracle that computes the discrete Lagrangian that scales for a system with $eta$ particles in $D+1$ dimensions, in the continuum limit, as $widetildeO(eta D t2/epsilon)$ if $V(x)$ is bounded
arXiv Detail & Related papers (2024-05-11T15:48:04Z)
A hybrid quantum algorithm to detect conical intersections [39.58317527488534]
We show that for real molecular Hamiltonians, the Berry phase can be obtained by tracing a local optimum of a variational ansatz along the chosen path. We demonstrate numerically the application of our algorithm on small toy models of the formaldimine molecule.
arXiv Detail & Related papers (2023-04-12T18:00:01Z)
Correspondence between open bosonic systems and stochastic differential equations [77.34726150561087]
We show that there can also be an exact correspondence at finite $n$ when the bosonic system is generalized to include interactions with the environment. A particular system with the form of a discrete nonlinear Schr"odinger equation is analyzed in more detail.
arXiv Detail & Related papers (2023-02-03T19:17:37Z)
A shortcut to adiabaticity in a cavity with a moving mirror [58.720142291102135]
We describe for the first time how to implement shortcuts to adiabaticity in quantum field theory. The shortcuts take place whenever there is no dynamical Casimir effect. We obtain a fundamental limit for the efficiency of an Otto cycle with the quantum field as a working system.
arXiv Detail & Related papers (2022-02-01T20:40:57Z)
How does the Planck scale affect qubits? [0.0]
We present a new model of nonlocal geometry in which the Planck-scale smearing of classical points generates GURs for angular momentum. The relations correspond to a novel representation of rm SU(2) that acts nontrivially on both subspaces of the composite state describing matter-geometry interactions. In addition to the canonical qubits states, $ket0 = ketuparrow$ and $ket1 = ketdownarrow$, there exist two new eigenstates in which the spin of the particle becomes entangled with the spin
arXiv Detail & Related papers (2021-03-04T15:20:05Z)
Effective Theory for the Measurement-Induced Phase Transition of Dirac Fermions [0.0]
A wave function exposed to measurements undergoes pure state dynamics. For many-particle systems, the competition of these different elements of dynamics can give rise to a scenario similar to quantum phase transitions. A key finding is that this field theory decouples into one set of degrees of freedom that heats up indefinitely.
arXiv Detail & Related papers (2021-02-16T19:00:00Z)
Probing quantum effects with classical stochastic analogs [0.0]
We propose a method to construct a classical analog of an open quantum system. The classical analog is made out of a collection of identical wells where classical particles of mass $m$ are trapped.
arXiv Detail & Related papers (2020-12-13T18:02:27Z)
Random quantum circuits anti-concentrate in log depth [118.18170052022323]
We study the number of gates needed for the distribution over measurement outcomes for typical circuit instances to be anti-concentrated. Our definition of anti-concentration is that the expected collision probability is only a constant factor larger than if the distribution were uniform. In both the case where the gates are nearest-neighbor on a 1D ring and the case where gates are long-range, we show $O(n log(n)) gates are also sufficient.
arXiv Detail & Related papers (2020-11-24T18:44:57Z)
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)
External and internal wave functions: de Broglie's double-solution theory? [77.34726150561087]
We propose an interpretative framework for quantum mechanics corresponding to the specifications of Louis de Broglie's double-solution theory. The principle is to decompose the evolution of a quantum system into two wave functions. For Schr"odinger, the particles are extended and the square of the module of the (internal) wave function of an electron corresponds to the density of its charge in space.
arXiv Detail & Related papers (2020-01-13T13:41:24Z)

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