## Abstract

We study the small mass limit (or: the Smoluchowski–Kramers limit) of a class of quantum Brownian motions with inhomogeneous damping and diffusion. For Ohmic bath spectral density with a Lorentz–Drude cutoff, we derive the Heisenberg–Langevin equations for the particle’s observables using a quantum stochastic calculus approach. We set the mass of the particle to equal m= m_{0}ϵ, the reduced Planck constant to equal ħ= ϵ and the cutoff frequency to equal Λ= E_{Λ}/ ϵ, where m_{0} and E_{Λ} are positive constants, so that the particle’s de Broglie wavelength and the largest energy scale of the bath are fixed as ϵ→ 0. We study the limit as ϵ→ 0 of the rescaled model and derive a limiting equation for the (slow) particle’s position variable. We find that the limiting equation contains several drift correction terms, the quantum noise-induced drifts, including terms of purely quantum nature, with no classical counterparts.

Original language | English (US) |
---|---|

Pages (from-to) | 351-377 |

Number of pages | 27 |

Journal | Journal of Statistical Physics |

Volume | 170 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 2018 |

## Keywords

- Heisenberg–Langevin equation
- Noise-induced drifts
- Quantum Brownian motion
- Quantum stochastic calculus
- Small mass limit
- Smoluchowski–Kramers limit

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics