This article presents a brief account of Amir O. Caldeira's contributions to the theory of quantum Brownian motion. Motivated by its importance, we outline the description of Brownian motion in the quantum regime following Caldeira's first works. In this context, we particularly highlight the effect of dissipation on the tunneling rate out of a metastable state. We then journey along the alternative ways to approach quantum Brownian motion developed by Caldeira during his career, which go beyond the so-called Caldeira-Leggett model. We conclude by summarizing some of Caldeira's contributions to contemporary fields such as the theory of quantum decoherence and quantum thermodynamics, that were strongly inspired by his eponymous approach to quantum Brownian motion.This article presents a brief account of Amir O. Caldeira's contributions to the theory of quantum Brownian motion. Motivated by its importance, we outline the description of Brownian motion in the quantum regime following Caldeira's first works. In this context, we particularly highlight the effect of dissipation on the tunneling rate out of a metastable state. We then journey along the alternative ways to approach quantum Brownian motion developed by Caldeira during his career, which go beyond the so-called Caldeira-Leggett model. We conclude by summarizing some of Caldeira's contributions to contemporary fields such as the theory of quantum decoherence and quantum thermodynamics, that were strongly inspired by his eponymous approach to quantum Brownian motion.

quant-pharXiv:2604.26524Brazilian Journal of PhysicsApr 30, 20260 citations

Mean-field theory of quantum Brownian motion

ARMEN E. ALLAHVERDYAN, Roger Balian, Theo M. Nieuwenhuizen

arXiv:cond-mat/0102255The European Physical Journal BSep 1, 20010 citations

Derivation of the Schrödinger Equation from Newtonian Mechanics

EDWARD B. NELSON

We examine the hypothesis that every particle of mass $m$ is subject to a Brownian motion with diffusion coefficient $\frac{\ensuremath{\hbar}}{2m}$ and no friction. The influence of an external field is expressed by means of Newton's law $\mathbf{F}=m\mathbf{a}$ , as in the Ornstein-Uhlenbeck theory of macroscopic Brownian motion with friction. The hypothesis leads in a natural way to the Schr\"odinger equation, but the physical interpretation is entirely classical. Particles have continuous trajectories and the wave function is not a complete description of the state. Despite this opposition to quantum mechanics, an examination of the measurement process suggests that, within a limited framework, the two theories are equivalent.We examine the hypothesis that every particle of mass $m$ is subject to a Brownian motion with diffusion coefficient $\frac{\ensuremath{\hbar}}{2m}$ and no friction. The influence of an external field is expressed by means of Newton's law $\mathbf{F}=m\mathbf{a}$, as in the Ornstein-Uhlenbeck theory of macroscopic Brownian motion with friction. The hypothesis leads in a natural way to the Schr\"odinger equation, but the physical interpretation is entirely classical. Particles have continuous trajectories and the wave function is not a complete description of the state. Despite this opposition to quantum mechanics, an examination of the measurement process suggests that, within a limited framework, the two theories are equivalent.

Physical ReviewOct 28, 19661,717 citations

Quantum explanation of Brownian motion

Elias P. Gyftopoulos

Apr 1, 20050 citations

We examine the hypothesis that every particle of mass

m

is subject to a Brownian motion with diffusion coefficient $\frac{\ensuremath{\hbar}}{2m}$ and no friction. The influence of an external field is expressed by means of Newton's law

\mathbf{F}=m\mathbf{a}

, as in the Ornstein-Uhlenbeck theory of macroscopic Brownian motion with friction. The hypothesis leads in a natural way to the Schr\"odinger equation, but the physical interpretation is entirely classical. Particles have continuous trajectories and the wave function is not a complete description of the state. Despite this opposition to quantum mechanics, an examination of the measurement process suggests that, within a limited framework, the two theories are equivalent.