Classicality of single quantum particles in curved spacetime through the hydrodynamical reformulation of quantum mechanics

Research output: Contribution to journalArticlepeer-review


Single-particle physics focuses on the behavior and properties of individual particles, providing insight into the building blocks of quantum mechanics. The theory of quantum particles in curved spacetime has been getting attention in recent years for gaining a deeper understanding of the relationship between quantum mechanics and general relativity, the two pillars of modern physics. In this note, we show how single quantum particles can obtain classical behavior. In particular, for a quantum particle that follows the Klein-Gordon equation in curved spacetime in the presence of external potential, we show that when the amplitude of its wavefunction follows the Klein-Gordon equation with an arbitrary effective mass, empty curved spacetime, but with the same curved geometry appearing in the original Klein-Gordon equation of the wavefunction, the quantum force of the particle vanishes, providing a classical description of the quantum particle using a system of coupled classical equations. The result relies on the Madelung hydrodynamical reformulation of quantum mechanics. Understanding how quantum systems transition to a classical behavior is a long-standing challenge in mesoscopic physics, with important implications for a wide range of applications, from quantum computing to condensed matter physics. The result provides a fresh perspective on the relations between quantum and classical effects in curved spacetime.

Original languageAmerican English
Article number365301
JournalJournal of Physics A: Mathematical and Theoretical
Issue number36
StatePublished - 8 Sep 2023


  • Klein-Gordon equation
  • Madelung equations
  • curved spacetime
  • quantum foundations
  • quantum potential

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • General Physics and Astronomy
  • Statistics and Probability
  • Mathematical Physics
  • Modelling and Simulation


Dive into the research topics of 'Classicality of single quantum particles in curved spacetime through the hydrodynamical reformulation of quantum mechanics'. Together they form a unique fingerprint.

Cite this