Amplification of coherent polar vibrations in biopolymers: Fröhlich condensate

We consider the nonequilibrium and dissipative evolution, and the steady state of the population of vibrational polar modes in a chain of biomolecules. These polar modes are excited through a coupling with a metabolic pumping source and are in anharmonic interaction with an elastic continuum. Groups of polar modes are coupled in this way through nonlinear terms in the kinetic equations. This nonlinearity is shown to be the source of an unexpected phenomenon characterizing complex behavior in this kind of system: after a threshold of intensity of the pumping source is achieved, polar modes with the lowest frequencies increase enormously their population in a way reminiscent of a Bose-Einstein condensation (Fr\"ohlich effect). The transient time for the steady-state condensate to follow is very short (picosecond time scale) and the condensation appears even for weak values of the anharmonic coupling strength responsible for its occurrence. Further, it seemingly requires accessible levels of metabolic pumping power in order to be produced and sustained.