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Hidden Sound Velocity in Quantum Liquids: A Higher-Order Response Theory of Multi-Branch Collective Excitations

Jincheng Zhang

Published Aug 13, 2026• 0 citations
Publisher

Abstract

Quantum liquids, such as liquid helium and ultracold atomic gases, exhibit complex collective behaviors that traditional linear response theory fails to fully capture. In this work, we propose the theoretical framework of Hidden Sound Velocity in Quantum Liquids (HSVQL), hypothesizing the existence of multiple undiscovered collective velocities denoted as v_1, v_2, ..., v_n beyond standard propagation modes. By employing higher-order response theory, specifically analyzing the third-order susceptibility chi^(3) and nonlinear correlation functions, we demonstrate that nonlinear coupling channels reveal these hidden modes. We formulate a comprehensive hydrodynamic and microscopic theory to derive dispersion relations and quasiparticle characteristics, opening a new paradigm for uncovering novel excitations in strongly interacting many-body systems.

DOI
10.5281/zenodo.21916725

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Quantum liquids, such as liquid helium and ultracold atomic gases, exhibit complex collective behaviors that traditional linear response theory fails to fully capture. In this work, we propose the theoretical framework of Hidden Sound Velocity in Quantum Liquids (HSVQL), hypothesizing the existence of multiple undiscovered collective velocities denoted as v_1, v_2, ..., v_n beyond standard propagation modes. By employing higher-order response theory, specifically analyzing the third-order susceptibility chi^(3) and nonlinear correlation functions, we demonstrate that nonlinear coupling channels reveal these hidden modes. We formulate a comprehensive hydrodynamic and microscopic theory to derive dispersion relations and quasiparticle characteristics, opening a new paradigm for uncovering novel excitations in strongly interacting many-body systems.
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In many-body quantum systems, the elementary excitations that carry energy and momentum are usually understood as phonons, rotons, or other well‑studied quasi‑particles. In this work we propose a new class of collective excitations, termed information phonons, that exist in quantum liquids. Unlike conventional phonons, an information phonon is defined by a field operator φ_I that carries an additional degree of freedom encoding classical or quantum information. We construct a minimal model Hamiltonian that describes the coupling between the density fluctuations of the liquid and the information field, derive the dispersion relation for φ_I, and analyze its properties. Theoretical analysis shows that the information phonon can propagate with a velocity distinct from the sound velocity, possesses a non‑trivial topological structure, and can be manipulated by external fields. We discuss the implications of these excitations for quantum information processing, suggesting that IPQLs could provide a new platform for robust quantum memories and information transport in strongly correlated media. The discovery of such quasi‑particles opens a promising avenue toward realizing novel quantum technologies and deepening our understanding of emergent phenomena in quantum liquids.
The field of ultra-cold atomic physics allows probing of two-component quantum liquids with a hydrodynamic normal fluid accompanied by superfluid Bose-Einstein condensates (BEC’s), where the experimental results can be compared to theoretical predictions of the behavior of a weakly interacting two fluid system. Hydrodynamicity in quantum systems like BEC's can have influence on multiple aspects of the collective behavior of the system, such as on the oscillation frequency of quadrupole modes, multiple sound modes in the condensate, but also on high-order excitations which resemble standing sound waves. The hydrodynamicity and excitations of the ultra-cold atomic cloud are the main motivation for the experiments presented in this thesis. In the Utrecht experiment large BEC's up to a few hundred million atoms are produced, which are deeply in the hydrodynamic collisional regime. The macroscopic behavior of the cloud of atoms is dominated by inter-atomic collisions since the mean free path of the individual particles is much smaller than the size of the atomic sample and local equilibrium is established. The influence of the hydrodynamicity on the collective excitations can be investigated by measuring the quadrupole frequency of ultra-cold atomic clouds above the transition temperature Tc, where Bose-Einstein condensation occurs. This quadrupole frequency is determined by measuring the collective shape oscillations of the atomic cloud, where the oscillation frequency is influenced by inter-atomic collisions during the shape oscillations due to the hydrodynamicity of the atomic cloud. The hydrodynamic equations predict the existence of two sound modes in ultra-cold atomic gases below Tc. The speeds of sound are dependent on both the temperature and the chemical potential of the atomic cloud. For low enough temperatures or large enough chemical potential these two speeds of sound become comparable and reaching this regime experimentally allows measuring the speed of sound beyond this avoided crossing. An alternate method of measuring the speed of sound of ultra-cold atomic clouds is exploiting the analogy between a standing sound wave-pattern and high order excitations in BEC's, also referred to as Faraday waves. By exciting the wave-pattern with a frequency and measuring the wavenumber k of the wave-pattern, the speed of sound c can be extracted from the linear dispersion relation. In the process of exciting the standing wave-pattern, remarkable dynamics is discovered in the BECs. As a result of the excitation a large array of other modes are excited next to the wave-pattern. These modes are for example the dipole mode, the axial and radial quadrupole modes, and the scissor mode. This gives rise to complex dynamics in this hydrodynamic quantum mechanical system and although the ultra-cold sample is only excited with a very short pulsed excitation, these modes and the wave-pattern show a large degree of reproducibility during several seconds of time evolution.
In many-body quantum systems the conventional picture of energy transport assumes that excitations propagate through well‑defined quasiparticle channels governed by the system Hamiltonian. Recent theoretical investigations suggest that in strongly correlated materials there exist additional, hidden pathways for energy exchange that are not captured by standard quasiparticle descriptions. These hidden energy channels (HECs) arise from collective reconfigurations of the entanglement structure, mediated by emergent gauge fields and topological constraints. In this paper we formulate a unified framework to identify and characterize HECs in generic lattice models. We derive explicit expressions for the energy current operator that include both conventional and hidden contributions, and demonstrate how HECs modify the temperature dependence of thermal conductivity in prototypical models such as the two‑dimensional Hubbard model and the Kitaev honeycomb model. Our analysis predicts anomalous scaling laws and non‑monotonic temperature profiles that can serve as experimental signatures of HECs. The existence of these channels opens a new avenue for engineering efficient energy transport in quantum materials, with implications for quantum information processing and low‑temperature thermoelectric devices.