Weak, strong, and coherent regimes of Fröhlich condensation and their applications to terahertz medicine and quantum consciousness

Jeffrey R. Reimers, Laura K. McKemmish, Ross H. McKenzie, Alan E. Mark, and Noel S. Hush
PNAS March 17, 2009 106 (11) 4219-4224; https://doi.org/10.1073/pnas.0806273106

  1. Edited by Mark A. Ratner, Northwestern University, Evanston, IL, and approved January 22, 2009 (received for review June 30, 2008)

Article Figures & SI

Figures

  • Fig. 1.
    Fig. 1.

    Fröhlich's model for a driven system of Z = 3 oscillators connected to a thermal bath. Red- energy input into each system oscillator at rate s, blue- energy losses to the bath with a rate proportional to φ, and green- energy redistributions within the system at a rate proportional to χ.

  • Fig. 2.
    Fig. 2.

    Regions in which strong Fröhlich condensates can be observed. For linear dispersion and Z = 25 modes, the condensation index η is colored in plots as a function of the ratio of the energy input to the bath relaxation, s/φ, and the ratio of the rate of energy redistribution to bath relaxation, χ/φ. (A) single plot at a band-Center vibration frequency to temperature ratio of ℏω0/kT = 0.1 and band-narrowness parameter ω1/ω0 = 0.04 extracted from B. (B) All results. Superimposed on each plot is a hatched region indicating system temperature TS/T > 5/3 (500 K if the bath temperature is T = 300 K); such regions are certainly not accessible in a biological environment.

  • Fig. 3.
    Fig. 3.

    Regions in which at least weak Fröhlich condensates can be observed. For linear dispersion and Z = 25 modes, the condensation-induced enhancement factor n1/n1χ = 0, depicting the ratio of the number of quanta in the lowest-frequency mode to that expected if the source energy is evenly dispersed, is shown as a grid of plots akin to those in Fig. 2. For each plot, the abscissa is the ratio of the energy input to the bath relaxation, s/φ, whereas the ordinate is the ratio of the rate of energy redistribution to bath relaxation, χ/φ. White regions indicate regions with n1/n1χ = 0; much lower values should give experimentally observable effects. Superimposed on each plot is a hatched region indicating biologically inaccessible regions with system temperature TS/T > 5/3 (500 K if the bath temperature is T = 300 K).

  • Fig. 4.
    Fig. 4.

    Dynamics of the Wu–Austin Hamiltonian in the wide-band low-frequency limit (ω1/ω0 = 0.12, ℏω0/kT = 1/15), showing the change in the average kinetic energy in modes 1 (the mode undergoing Fröhlich condensation), 2, 3, 12, and 25 for Z = 25 system oscillators; the instantaneous kinetic energy in mode 1 is also shown (thin line). Other parameters are: linear frequency dispersion, ZB = 430 bath modes at T = 300 K (hence ω0 = 10.425 cm−1, ω1 = 1.251 cm−1), ZI = 200 source modes at TI = 96,000 K, α/k = 150 μK, β/k = 150 μK, γ/k = 750 μK.

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Weak, strong, and coherent regimes of Fröhlich condensation and their applications to terahertz medicine and quantum consciousness
Jeffrey R. Reimers, Laura K. McKemmish, Ross H. McKenzie, Alan E. Mark, Noel S. Hush
Proceedings of the National Academy of Sciences Mar 2009, 106 (11) 4219-4224; DOI: 10.1073/pnas.0806273106
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