Using functional methods, we investigate in a low-temperature liquid, the
sound quanta defined by the quantized hydrodynamic fields, under the effects of
high-energy processes on the atomic/molecular scale. To obtain in the molecular
level the excitation spectra of liquids, we assume that the quantum fields are
coupled to an additive delta-correlated in space and time quantum noise field.
The hydrodynamic fields are defined in a fluctuating environment. After
defining the generating functional of connected correlation fuctions in the
presence of the noise field, we perform a functional integral over all noise
field configurations. This is done using a formal object inspired by the
distributional zeta-function method, named configurational zeta-function. Noi
obtain a new generating functional written in terms of an analytically
tractable functional series. Each term of the series describes in the liquid
the emergent non-interacting elementary excitations with the usual gapless
phonon-like dispersion relation and additional excitations with dispersion
relations with gaps in pseudo-momenta space, i.e., tachyonic-like excitations.
Furthermore, the Fourier representation of the two-point correlation functions
of the model with the contribution coming from all phononic and tachyonic-like
fields is presented. Finally, our analysis reveals that the emergent
tachyonic-like and phononic excitations yield a distinctive thermodynamic
signature – a quadratic temperature dependence of specific heat ($C_V \propto
T^2$) at low temperatures, providing a theoretical foundation for experiments
in confined and supercooled liquids.

Questo articolo esplora i giri e le loro implicazioni.

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