Quantum Fluctuations and Wigner Dynamics of a Carbon Nanotube Oscillator Driven by an Atomic Force Microscope
Abstract
Suspended carbon nanotubes provide a useful platform for studying controlled nanomechanical motion in regimes where environmental fluctuations, memory effects, and quantum coherence can all influence the dynamics. We model the fundamental flexural mode of a carbon nanotube driven by an atomic force microscope as a harmonic quantum Brownian oscillator subject to a prescribed classical force and coupled linearly to a thermal environment. Starting from the generalized Langevin equation, we formulate the reduced dynamics directly in phase space, where the Wigner function evolves through a Gaussian propagator determined by dissipative linear transport, a deterministic force-induced displacement, and bath-induced fluctuations. For a Drude memory kernel, the retarded response is expressed through the three roots of a characteristic cubic equation. In the classical-noise limit, the three independent entries of the finite-time covariance matrix reduce to explicit finite sums over these response poles, eliminating numerical double-time covariance integration. We extend the construction to the full quantum fluctuation spectrum, obtaining a thermal frequency series representation that retains zero-point and low-temperature fluctuations. For an initial two-packet superposition, we examine interference attenuation and the integrated negative part of the Wigner function, which provides a phase space measure of nonclassicality. These results provide an explicit analytical framework for finite-memory quantum Brownian motion of bound oscillators and a tractable phase space description of driven carbon nanotube dynamics relevant to future quantum state preparation and quantum tomography experiments.
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BibTeX
@misc{silio2026quantum,
title = {{Quantum Fluctuations and Wigner Dynamics of a Carbon Nanotube Oscillator Driven by an Atomic Force Microscope}},
author = {Conrad Silio and Cristian Staii},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.27167},
eprint = {2610.27167},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.27167},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Quantum Fluctuations and Wigner Dynamics of a Carbon Nanotube Oscillator Driven by an Atomic Force Microscope
AU - Conrad Silio
AU - Cristian Staii
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.27167
UR - https://arxiv.org/abs/2610.27167
AB - Suspended carbon nanotubes provide a useful platform for studying controlled nanomechanical motion in regimes where environmental fluctuations, memory effects, and quantum coherence can all influence the dynamics. We model the fundamental flexural mode of a carbon nanotube driven by an atomic force microscope as a harmonic quantum Brownian oscillator subject to a prescribed classical force and coupled linearly to a thermal environment. Starting from the generalized Langevin equation, we formulate the reduced dynamics directly in phase space, where the Wigner function evolves through a Gaussian propagator determined by dissipative linear transport, a deterministic force-induced displacement, and bath-induced fluctuations. For a Drude memory kernel, the retarded response is expressed through the three roots of a characteristic cubic equation. In the classical-noise limit, the three independent entries of the finite-time covariance matrix reduce to explicit finite sums over these response poles, eliminating numerical double-time covariance integration. We extend the construction to the full quantum fluctuation spectrum, obtaining a thermal frequency series representation that retains zero-point and low-temperature fluctuations. For an initial two-packet superposition, we examine interference attenuation and the integrated negative part of the Wigner function, which provides a phase space measure of nonclassicality. These results provide an explicit analytical framework for finite-memory quantum Brownian motion of bound oscillators and a tractable phase space description of driven carbon nanotube dynamics relevant to future quantum state preparation and quantum tomography experiments.
ER -