W. Kohn, Z.B. Zabinsky, Y. Shen
University of Washington,
Keywords: quantization, NEMS, nano-laser controlled diode, optimal gauge meta-control, dynamic programming ensemble, laser sensors, light squeezing, Noether invariance
Summary:A proposed innovative heating and cooling system synthesizes a nano-particle ensemble that is embedded in paint for heating or cooling of a room. The nano-particles implement a synchronized laser heating and cooling system, which tracks a heat flow signal generated by an intelligent sensor. The control of each nano-particle in the ensemble is mediated by its Josephson junction laser diode that responds to the intelligent sensor in the room and photon sensors in the nano-particles. Each nano-particle includes a cavity resonator with a controllable mirror that responds to the Josephson junction laser command and either releases a photon stream if the energy is below a threshold set in the intelligent sensor or absorbs a photon stream if the energy is above the threshold. We propose a meta-control methodology to design a feedback mechanism in the nano-particle. The meta-control generates the energy target sent by the Josephson junction laser. The design approach is based on establishing a quantized invariant condition between the Lagrangian describing the macroscopic operation of the heat pump that will be realized by a cavity resonator system, and an ideal non-dissipative Lagrangian. A gauge control minimizes the difference between the Lagrangian of the system and the ideal Lagrangian. Our approach consists of quantizing the macroscopic dynamics of a heat pump to describe the dynamics of each nano-particle. At the quantum level, each nano-particle is characterized by the appropriate probability density operator and dynamics. The design approach of the meta-control is based on the Rund-Trautman invariance condition. The optimization of the operation of the nano-particle is established by applying Noether’s invariance theorem to the Rund-Trautman condition. The ensemble of nano-particles designed by the meta-control approach exhibits a distribution of heat that is close to the target distribution generated by the intelligent sensor. The Noether invariance variational optimization provides a feedback control law at the macroscopic level. The gauge control is established by finding coefficients that minimize the distance between an ideal non-dissipative Lagrangian, and a physical Lagrangian. The resulting macroscopic Hamiltonian is quantized providing a probability density operator propagator. The probability density operator propagator establishes the dynamics of the nano-particle, realizing an implementation of the meta-controlled heating and cooling system. At the mesoscopic level, we consider a range of temperature control between 50 – 75 degrees F. We discuss some material properties using GA-AL-AZ implementing the cavity resonator with a silicon-doped Josephson junction laser. The room has specific properties such as size. The proposed meta-control technology at the nanoscopic level is based on the principles of laser-cooling and trapping energy. The manufacturing of this heating and cooling system will be carried out by self-assembly.