Nonlinear friction forces are a problem in classical Brownian motion for a long time [1]. They are described either by Langevin or by Fokker-Planck equations [2-4]. However, the rigorous generalized Langevin equation is linear, which points out that nonlinear friction forces possess a macroscopic hydrodynamic origin [1]. For this reason, they are not present in the modern quantum theory of open systems [5]. The scope of the present paper is to investigate the nonlinear friction effect on quantum mechanics. The analysis is based on a dissipative Madelung quantum hydrodynamics. Thus, the nonlinear friction is a result of nonlinear non-equilibrium thermodynamics in contrast to the traditional mechanical nonlinear friction forces. A quantum particle in vacuum is described by the Schrodinger equationNonlinear friction forces are a problem in classical Brownian motion for a long time [1]. They are described either by Langevin or by Fokker-Planck equations [2-4]. However, the rigorous generalized Langevin equation is linear, which points out that nonlinear friction forces possess a macroscopic hydrodynamic origin [1]. For this reason, they are not present in the modern quantum theory of open systems [5]. The scope of the present paper is to investigate the nonlinear friction effect on quantum mechanics. The analysis is based on a dissipative Madelung quantum hydrodynamics. Thus, the nonlinear friction is a result of nonlinear non-equilibrium thermodynamics in contrast to the traditional mechanical nonlinear friction forces. A quantum particle in vacuum is described by the Schrodinger equation

Jan 1, 20123 citations

Quantum-mechanical description of friction

I.R. Svin'in

Theoretical and Mathematical PhysicsFeb 1, 197520 citations

Rotational Vacuum Friction of Nonabsorbing Particles

F. Javier García de Abajo, Alejandro Manjavacas

A nonabsorbing particle rotating in vacuum can lose angular momentum only by converting mechanical energy into electromagnetic radiation. Here, we develop a quantum theory of rotational vacuum friction for small lossless particles and show that axial symmetry qualitatively changes the leading dissipation channel. At zero temperature, the frictional torque scales as $M\proptoΩ^7$ with rotation frequency $\ Omega$ in anisotropic particles due to the emission of correlated photon pairs whose frequencies sum to $2Ω$ , while a contribution to the torque linear in $\ Omega$ is found at finite temperature. In contrast, axisymmetric particles are protected against photon-assisted friction regardless of temperature.A nonabsorbing particle rotating in vacuum can lose angular momentum only by converting mechanical energy into electromagnetic radiation. Here, we develop a quantum theory of rotational vacuum friction for small lossless particles and show that axial symmetry qualitatively changes the leading dissipation channel. At zero temperature, the frictional torque scales as $M\proptoΩ^7$ with rotation frequency $\ Omega$ in anisotropic particles due to the emission of correlated photon pairs whose frequencies sum to $2Ω$, while a contribution to the torque linear in $\ Omega$ is found at finite temperature. In contrast, axisymmetric particles are protected against photon-assisted friction regardless of temperature.

quant-pharXiv:2606.24723Jun 24, 2026

On a quantum-mechanical description of motion with friction

B. A. Arbuzov

Theoretical and Mathematical PhysicsFeb 1, 19969 citations

M\proptoΩ^7

with rotation frequency

\ Omega

in anisotropic particles due to the emission of correlated photon pairs whose frequencies sum to

2Ω

, while a contribution to the torque linear in

\ Omega

is found at finite temperature. In contrast, axisymmetric particles are protected against photon-assisted friction regardless of temperature.