We develop a unified effective field theory framework for phonon dynamics in partially coherent quantum fluids, explicitly incorporating the role of a coherence parameter that encodes the fraction of the superfluid component. Starting from a microscopic description and systematically deriving the low-energy effective action, we show that coherence modifies the kinetic structure of the theory, leading to a renormalized sound speed and an emergent effective geometry governing phonon propagation. A key result of this work is the identification of a coherence dependent effective wave operator, from which the physically relevant metric is reconstructed. This resolves ambiguities associated with conformal rescalings and establishes a direct link between microscopic coherence and emergent spacetime structure. At the nonlinear level, we derive a temperature and coherence dependent effective mass for phonon excitations. Importantly, this mass does not correspond to a gap in the dispersion relation, but rather to an inertial response arising from thermodynamic gradients. We show that this effect is strongly enhanced near the superfluid transition and depends sensitively on the thermodynamic path. Order of magnitude estimates for ultracold atomic gases indicate that the effective mass can become comparable to the atomic mass in experimentally accessible regimes. This suggests that coherence-induced inertial effects may be observable through phonon dynamics in inhomogeneous or near critical systems. Our results establish a quantitative bridge between microscopic coherence, effective geometry, and emergent inertial phenomena, opening new avenues for probing collective excitations in quantum fluids.
We develop a unified effective field theory framework for phonon dynamics in partially coherent quantum fluids, explicitly incorporating the role of a coherence parameter that encodes the fraction of the superfluid component. Starting from a microscopic description and systematically deriving the low-energy effective action, we show that coherence modifies the kinetic structure of the theory, leading to a renormalized sound speed and an emergent effective geometry governing phonon propagation. A key result of this work is the identification of a coherence dependent effective wave operator, from which the physically relevant metric is reconstructed. This resolves ambiguities associated with conformal rescalings and establishes a direct link between microscopic coherence and emergent spacetime structure. At the nonlinear level, we derive a temperature and coherence dependent effective mass for phonon excitations. Importantly, this mass does not correspond to a gap in the dispersion relation, but rather to an inertial response arising from thermodynamic gradients. We show that this effect is strongly enhanced near the superfluid transition and depends sensitively on the thermodynamic path. Order of magnitude estimates for ultracold atomic gases indicate that the effective mass can become comparable to the atomic mass in experimentally accessible regimes. This suggests that coherence-induced inertial effects may be observable through phonon dynamics in inhomogeneous or near critical systems. Our results establish a quantitative bridge between microscopic coherence, effective geometry, and emergent inertial phenomena, opening new avenues for probing collective excitations in quantum fluids.
This work presents a unified, realistic, and mechanically grounded interpretation of fundamental physics across all scales, from quarks and elementary particles to atoms, macroscopic bodies, planetary motion, and black holes. The proposed framework provides a single coherent physical description capable of reproducing and explaining, within a common dynamical structure, the full range of phenomena traditionally treated separately by general relativity, quantum mechanics, and quantum electrodynamics. Within this approach, long-standing conceptual problems such as wave–particle duality, quantum interference, entanglement, and wavefunction collapse are not postulated as fundamental features of nature, but emerge naturally as dynamical properties of a physically real medium. The apparent dual behavior of matter and radiation, as well as nonlocal quantum correlations, arise from coherent and topologically constrained excitations of this medium, without invoking probabilistic ontologies or nonphysical abstractions. The theory is based on a revised physical concept of space, treated as a real superfluid medium endowed with density, elasticity, viscosity, permittivity, permeability, and a very small but non-zero electrical conductivity. In this model, space is no longer a passive geometric background, but an active physical system capable of storing, transmitting, and dissipating energy.Mass is interpreted as an isotropic compression of the superfluid, electric charge as an oriented torsional configuration, and fields as elastic stress and vorticity distributions of the medium itself. Electromagnetic and gravitational waves are described as propagating perturbations of the superfluid, while particles correspond to stable solitonic configurations sustained by the medium dynamics.At the microscopic level, starting from classical fluid equations (continuity and Euler equations) and applying the Madelung transformation, the Schrödinger equation is shown to emerge as a compact complex representation of the underlying real fluid dynamics, rather than as a fundamental postulate. Quantum phenomena such as quantization, tunneling, spin, and exclusion principles follow from stability, coherence, and topological constraints of solitonic wave structures. On cosmological scales, the same framework provides a unified interpretation of redshift, large-scale expansion phenomena, and the cosmic microwave background as cumulative dynamical and dissipative effects of wave propagation within the superfluid medium, rather than as consequences of metric expansion alone. Effects commonly attributed to dark matter and dark energy are reinterpreted as emergent manifestations of spatial density gradients, elastic stresses, and dissipative properties of the superfluid, without introducing additional unknown components. A wide range of experimentally verified phenomena—including the photoelectric effect, Compton scattering, Zeeman–Stark effects, the Aharonov–Bohm effect, Casimir effect, Unruh radiation, and cosmological attenuation effects—are consistently described within this unified framework. The proposed model offers an alternative foundational paradigm for physics, in which space, matter, and interactions emerge from a single physically intelligible dynamical system, restoring a continuous and causal description of nature from microscopic to cosmological scales.
We study the recently proposed effective-field theory for the phonon of an arbitrary nonrelativistic superfluid. After computing the one-loop phonon self-energy, we obtain the low-temperature T contributions to the phonon dispersion law at low momentum and see that the real part of those can be parametrized as a thermal correction to the phonon velocity. Because the phonons are the quanta of the sound waves, at low momentum their velocity should agree with the speed of sound. We find that our results match at order T4lnT with those predicted by Andreev and Khalatnikov for the speed of sound, derived from the superfluid hydrodynamical equations and the phonon kinetic theory. We get also higher-order corrections of order T4, which are not reproduced pushing naively the kinetic theory computation. Finally, as an application, we consider the cold Fermi gas in the unitarity limit and find a universal expression for the low-T relative correction to the speed of sound for these systems.
Fermionic many-body systems provide an unrivaled arena to investigate how interactions drive the emergence of collective quantum behavior, such as macroscopic coherence and superfluidity. Central to these phenomena is the formation of Cooper pairs, correlated states of two fermions that behave as composite bosons and condense below a critical temperature. However, unlike elementary bosons, these pairs retain their internal structure set by underlying fermionic correlations, essential for understanding superfluid properties throughout the so-called Bose-Einstein condensate (BEC) to Bardeen-Cooper-Schrieffer (BCS) crossover -- a cornerstone of strongly correlated fermionic matter. Here, we harness a sonic analog of the optical Sagnac effect to disclose the composite nature of fermionic condensates across the BEC-BCS crossover. We realize an in-situ loop interferometer by coherently exciting two counter-propagating long-wavelength phonons of an annular fermionic superfluid with tuneable interparticle interactions. The frequency degeneracy between clock- and anticlock-wise sound modes is lifted upon controllably injecting a quantized supercurrent in the superfluid ring, resulting in a measurable Doppler shift that enables us to probe the elementary quantum of circulation and the angular momentum carried by each particle in the fermionic fluid. Our observations directly reveal that the superflow circulation is quantized in terms of h/2m, where m is the mass of the constituents, in striking contrast to bosonic condensates where h/m is the relevant circulation quantum. Further, by operating our interferometer at tunable temperature, we measure the thermal depletion of the superfluid in the unitary Fermi gas, demonstrating phonon interferometry as a powerful technique for probing fundamental properties of strongly-correlated quantum systems.
In this work, we generalize the two-fluid theory to a superfluid system with anisotropic effective masses along different principal axis directions. As a specific example, such a theory can be applied to spin-orbit coupled Bose-Einstein condensate at low temperature. The normal density from phonon excitations and the second sound velocity are obtained analytically. Near the phase transition from the plane wave to zero-momentum phases, due to the effective mass divergence, the normal density from phonon excitation increases greatly, while the second sound velocity is suppressed significantly. With quantum hydrodynamic formalism, we give a unified derivation for suppressed superfluid density and Josephson relation. At last, the momentum distribution function and fluctuation of phase for the long wavelength are also discussed.
Abstract Understanding the universal behavior of strongly-interacting systems of particles has been a major goal in multiple fields of physics from atomic physics to cosmology. Using a recently introduced manybody perturbation formalism for fermions which uses group theoretic and graphical techniques to solve the N -body problem, I study the thermodynamic behavior of the unitary regime for a trapped Fermi gas and investigate the role of the Pauli principle in the emergence of collective behavior, specifically superfluidity at ultralow temperatures. The method, which is called symmetry invariant perturbation theory, has no adjustable parameters and currently offers a solution to the manybody Schrodinger equation through first order in inverse dimensionality exactly. The solution at first order defines collective coordinates in terms of five types of N -body normal modes, identified as symmetric stretch, symmetric bend, single particle angular excitation, single particle radial excitation and phonon. A correspondence is established ‘on paper’ that enforces the Pauli principle through the assignment of specific normal mode quantum numbers. Applied at ultracold temperatures, this normal mode assignment yields occupation only in an extremely low frequency N -body phonon mode. A single particle radial excitation mode at a much higher frequency creates a gap that stabilizes the superfluidity at low temperatures. This radial excitation involves excitation of a single particle out of the synced motion of the phonon mode, rather than the breaking of a fermion pair. Coupled with the corresponding values for the energies at unitarity obtained by this manybody calculation, I obtain good agreement with experimental thermodynamic results. In particular, the lambda transition in the specific heat is clearly seen. Based on these findings, I propose a mechanism for the emergence of superfluidity at ultralow temperatures in this unitary regime that is driven by quantum statistics and the enforcement of the Pauli principle through the selection of normal modes. My results for the calculated thermodynamic quantities suggest that the emergence of some collective behaviors in macroscopic systems is due to the Pauli principle producing manybody pairing and the resulting macroscopic occupation of an N -body phonon mode.
We develop a unified field-theoretical description of the Bose-Hubbard model that captures low-energy dynamics across the insulator-to-superfluid transition. We show that commonly used cumulant expansions about the Mott ground state fail in the superfluid phase not only quantitatively but also fundamentally, because they impose an incorrect canonical structure. Expanding instead about the appropriate mean-field saddle point, we derive an effective action in which the dynamics of fluctuations are governed by a Berry-phase term, giving rise to an emergent magnetic field in the associated oscillator description. This field encodes particle-hole symmetry breaking in both the Mott-insulator phase and the superfluid, and vanishes at the point where a pure Goldstone mode emerges. The resulting effective hydrodynamic theory admits a speed of sound that approaches the Bogoliubov limit in the weakly interacting regime, demonstrating consistency across the entire phase diagram, from the Mott-insulator to the deep superfluid regime. While the total density remains continuous within mean-field theory, we find that quantum fluctuations generate a discontinuous contribution at the quantum phase transition, which vanishes at the tip of the Mott lobe.