Abstract
Recent simulations and experiments with aqueous quadrupole micro-traps have confirmed a possibility for control and localization of motion of a charged particle in a water environment, also predicting a possibility of further reduction of the trap size to tens of nano-meters for trapping charged bio-molecules and DNA segments. We study the random thermal noise due to Brownian motion in water which significantly influences the trapping of particles in an aqueous environment. We derive the exact, closed-form expressions for the thermal fluctuations of position and velocity of a trapped particle and thoroughly examine the properties of the rms for the fluctuations as functions of the system parameters and time. The instantaneous signal transferring mechanism between the velocity and position fluctuations could not be achieved in the previous phase-average approaches.
Highlights
Conventional quadrupole Paul traps [1,2] are used to confine the charged particles to narrow three-dimensional (3-D) or two-dimensional (2-D) regions by the combination of static (DC) and radio-frequency oscillating electric fields in vacuum or in gaseous environment
Presence of aqueous and possible electrolytic [10,11] environment is of the key importance for chemical stability of charged bio-molecules
Control of translocation of a singlestranded DNA by aqueous Paul nano-trap (APT) may improve the performance of the third generation of DNA sequencing devices
Summary
Conventional quadrupole Paul traps [1,2] are used to confine the charged particles (e.g., atomic and molecular ions) to narrow three-dimensional (3-D) or two-dimensional (2-D) regions by the combination of static (DC) and radio-frequency (rf, AC) oscillating electric fields in vacuum or in gaseous environment. An important factor in designing an aqueous Paul trap is its stability characteristics, i.e., range of the system parameters for which a targeted charged particle stays a sufficiently long time in a confinement region to provide the desired functions and manipulations. Understanding the functions of the Paul trap filled with water (or more general, with a high viscous medium) requires, in addition to the stability analysis based on the mean motion of particle, a detailed understanding of its response to the thermal fluctuations. Theoretical analysis the explicit closed-form analytical expressions for thermal fluctuations of position and velocity, and the cross-covariance of position and velocity are derived in terms of integrals of Mathieu functions by solving the equation of motion in Langevin form for a charge particle in an aqueous quadrupole Paul trap. The influence of the covariance to the fluctuations will be discussed
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