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VOLUME 90 | ISSUE 9 | PAGE 659
Osmotic pressure of matter and vacuum energy
G. E. Volovik

Low Temperature Laboratory, Helsinki University of Technology, FIN-02015 HUT, Finland
Landau Institute for Theoretical Physics RAS, 119334 Moscow, Russia

PACS: 05.70.-a, 12.60.-i, 67.60.-g
The walls of the box which contains matter represent a membrane that allows the relativistic quantum vacuum to pass but not matter. That is why the pressure of matter in the box may be considered as the analog of the osmotic pressure. However, we demonstrate that the osmotic pressure of matter is modified due to interaction of matter with vacuum. This interaction induces the nonzero negative vacuum pressure inside the box, as a result the measured osmotic pressure becomes smaller than the matter pressure. As distinct from the Casimir effect, this induced vacuum pressure is the bulk effect and does not depend on the size of the box. This effect dominates in the thermodynamic limit of the infinite volume of the box. Analog of this effect has been observed in the dilute solution of 3He in liquid 4He, where the superfluid 4He plays the role of the non-relativistic quantum vacuum, and 3He atoms play the role of matter.

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