Role of Dissipation in Resonance: A Variational Principle approach

  • Author / Creator
    Phani, Arindam
  • Resonance is at the heart of sensing and characterization tools in all fields of science. A nanoresonator has achieved the remarkable resolution of a proton mass. The coupling of a micromechanical oscillator to an optical field in a high finesse cavity has allowed sensitive probing even in the quantum regime. Such techniques rely on the frequency shift and or amplitude change of a very narrow-band resonator. The key to obtaining a narrow bandwidth of response lies in overcoming the damping effects, considered detrimental in the context. The primary aim in the design of resonators has been to minimize all dissipative effects thus. Unavoidably, dissipation is always introduced both from viscous friction with the fluid media and internal losses of the material, and is maximized at resonance. We take an alternative view of the role of dissipation in resonance and the information it conveys pertaining to a system. We explain the condition of maximization of dissipation at resonance as a variational problem dependent on phase, the phase appearing from an arbitrary path. We look at both mechanical and electrical resonance platforms and try to study the importance of dissipation in such systems in defining resonance altogether. The underlying phenomenon of standing waves is re-explored to explain the elusive resonance amplification from a radically alternate perspective using a path integral approach similar in form to Feynman’s quantum theory. Standing wave definition from the aspect of phase in time and space is considered. We comment on resonance amplification factor from a hypothesis-formulated in terms of measured in space. This time-phase evolution in space is explained as a continuous accumulated phase within the physical bounds of a resonator. The importance of the evolution of phase and its role in the origin of standing waves at resonance is highlighted. Comparison of theoretical results and experimental data show an excellent match. In addition, the fundamental treatment makes the formulation applicable to all resonating systems in a general way. We study a nanostructured mechanical resonator and show that when multiple coupled oscillators are involved, in the limits of continuum breakdown, inherent randomness in interactions with the media molecules can no longer be neglected leading to an additional non-continuum energy scale. The two energy scales compete in bringing long-range order over an inherent randomness and we show that such interplay can be explained by generalized Gibbs measure. The implication of such competing dynamic scales in the limits of continuum breakdown is profound revealing an extraordinary exponential amplification phenomenon. The work tries to highlight this in the context of an apparent dynamic range magnification of gas kinematic viscosity, making it a suitable parameter for gas characterization even in normal atmospheric conditions. We introduce photothermal electrical resonance spectroscopy of physisorbed molecules on a semiconductor nanowire resonator combined with infrared (IR) for molecular recognition of femtograms of adsorbed molecules exploiting dissipation signature at electrical resonance. The technique exploits the combination of very low thermal mass of the nanowire and high number of surfaces states on the nanowire for detection. We highlight that dissipation driven transition at play a crucial role in surface state population and de-population. We show that dissipation itself can be used as a measuring tool in the resonator-based devices. The new paradigm of dissipation-based sensing introduced in this work can be utilized in a broad range of fast, inexpensive, hand-held measuring devices.

  • Subjects / Keywords
  • Graduation date
  • Type of Item
  • Degree
    Doctor of Philosophy
  • DOI
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
  • Language
  • Institution
    University of Alberta
  • Degree level
  • Department
    • Department of Chemical and Materials Engineering
  • Specialization
    • Materials Engineering
  • Supervisor / co-supervisor and their department(s)
    • Thundat, Thomas (Chemical and Materials Engineering)
  • Examining committee members and their departments
    • Park, Simon (Mechanical and Manufacturing - University of Calgary)
    • Thundat, Thomas (Chemical and Materials Engineering)
    • Gupta, Manisha (Electrical and Computer Engineering)
    • Cadien, Ken (Chemical and Materials Engineering)
    • Wang, Xihua (Electrical and Computer Engineering)