Anomalous vacuum energy and stability of a quantum liquid

Abstract

We show that the vacuum (zero-point) energy of a low-temperature quantum liquid is a variable property which changes with the state of the system, in notable contrast to the static vacuum energy in solids commonly considered. We further show that this energy is inherently anomalous: it decreases with temperature and gives a negative contribution to a system's heat capacity. This effect operates in an equilibrium and macroscopic system, in marked contrast to small or out-of-equilibrium configurations discussed previously. We find that the negative contribution is over-compensated by the positive term from the excitation of longitudinal fluctuations and demonstrate how the overall positive heat capacity is related to the stability of a condensed phase at the microscopic level.

Stable equilibrium point and oscillatory motion of the Universe in a model with variable vacuum energy

“…and agrees with experimental specific heats of many liquids [12]. More relevant for this discussion, the zero-point energy of transverse modes in the liquid, E 0 , can be calculated using E(ω, T ) = hω 2 in (4) and gives [13]:…”

“…For now, we do not consider the contribution of matter to (13) and will return to its effect later. We consider an exact solution to an approximate version of the fuller problem in a simple model.…”

“…A non-perturbative approach to liquid thermodynamics [12] gives the important result that solid-like phonons in liquids evolve: the number of high-frequency solid-like transverse modes reduces with temperature. As a result, the liquid vacuum energy becomes a variable property that depends on the state of the system [13]. At some high temperature, transverse modes are lost at all available frequencies and the vacuum energy of liquid transverse modes becomes zero.…”