Vacuum energy gets flexible

Kostya Trachenko at the School of Physics and Astronomy in Queen Mary University of London and Vadim Brazhkin from the Institute for High Pressure Physics in Troitsk, Russia explain the new implications for vacuum energy in quantum liquids based on their recently published JPCM letter. 

Solving the Schrodinger equation for a harmonic oscillator results in the system always having a finite non-zero energy, called zero-point energy. The sum over all normal frequencies gives the zero-point energy of a quantum solid. Zero-point energy does not feature in thermodynamic properties of solids. Indeed, observables such as heat capacity involve derivatives whereas zero-point energy is assumed to be a constant property. It is believed to form a constant, static, energy background.

Zero-point energy also emerges in quantum field theory where it is called vacuum energy, the sum of energies of the field modes. Important open questions in the area are related to the amount of vacuum energy, its divergence and its upper energy cutoff: how large is vacuum energy? Is the largest term in the sum related to Planck energy and what kind of physics operates above Planck energy?

Cosmology is yet another field where vacuum energy plays a prominent role. The observed accelerating expansion of the Universe is linked to the cosmological constant related to the vacuum energy of some cosmological scalar fields. Theoretical calculations are in striking disagreement with observations, calling for an understanding of the fundamental mechanism by which vacuum energy can vary.

Illustration of a particle jump between two quasi-equilibrium positions in a liquid.

Illustration of a particle jump between two quasi-equilibrium positions in a liquid. © 2016 IOP Publishing Ltd.

Recent new findings reported in J. Phys.: Condens. Matter have two implications for vacuum energy. Firstly, vacuum energy is not static as once previously thought but can vary as displayed in liquids. The key to the variability is that collective modes in liquids evolve. In particular, transverse modes in liquids propagate above the inverse of liquid relaxation time (LRT), the time between particle jumps as shown in the figure. Therefore, the vacuum energy of transverse modes changes with LRT. Consequently, liquid’s vacuum energy varies with the state of the system (temperature and pressure) because LRT does.

Secondly, the liquid vacuum energy is anomalous: it decreases with temperature because LRT decreases, giving a negative contribution to heat capacity. It turns out that this weird behavior is not inconsistent with thermodynamics: temperature excitations of the longitudinal mode come to the rescue and ensure that the total heat capacity is positive. The reason this works can be traced to the right combination of system parameters that ensure the stability of the liquid phase at the microscopic level.

CC-BY logoThis work is licensed under a Creative Commons Attribution 3.0 Unported License. Image taken from K Trachenko and V V Brazhkin 2016 J. Phys.: Condens. Matter 28 12LT01. Copyright 2016 IOP Publishing Ltd.

Categories: Journal of Physics: Condensed Matter

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