Can someone explain the phyics of flying a helicopter in such low density atmosphere? It must be less efficient than on earth, but evidently efficiency isn't proportional to density or else it could not fly at all.
No it mustn't. You'd expect efficiency to be higher, all else being equal, since there's less drag to overcome - aircraft can generally fly more efficiently at high altitude on Earth (up to a point). The limiting factor is that helicopter flight only works while the rotor tips are subsonic, so as the air gets thinner the "IAS" that a pitot tube on the rotor (that's going as fast as you safely can) would experience gets lower and lower, and so the flight dynamics will be like a helicopter with a slow rotor, but speeded up. But for a small helicopter the square-cube law is on your side and so a low "IAS" is quite doable.
Using actuator disc theory, accounting for 38% gravity and 1.2% air density, Ingenuity would need about 2.1x more power to hover on Mars.
But it's not that simple. The reynolds number which Ingenuity's blades are operating on Mars is extremely low, 10,000 to 20,000. This makes the airfoils less efficient compared to what you might design on Earth.
Compare to a Trex 450 (30% heavier weight equivalent) helicopter on Earth, it's got 10+ minutes of endurance and has a smaller diameter rotor, whereas Ingenuity has a 90 second stated endurance, although that is probably limited by navigation too.
No it mustn't. You'd expect efficiency to be higher, all else being equal, since there's less drag to overcome - aircraft can generally fly more efficiently at high altitude on Earth (up to a point). The limiting factor is that helicopter flight only works while the rotor tips are subsonic, so as the air gets thinner the "IAS" that a pitot tube on the rotor (that's going as fast as you safely can) would experience gets lower and lower, and so the flight dynamics will be like a helicopter with a slow rotor, but speeded up. But for a small helicopter the square-cube law is on your side and so a low "IAS" is quite doable.