[Paper Review] Acoustic phase lenses in superfluid He as models of composite spacetimes in general relativity: Classical and quantum properties with provision for spatial topology

Konstantin G. Zloshchastiev|arXiv (Cornell University)|Feb 24, 1998

Quantum, superfluid, helium dynamics3 citations

TL;DR

This paper proposes that thin spherical shells in superfluid helium act as acoustic phase lenses, modeling composite spacetimes in general relativity. By deriving exact equations of motion for these interfaces and analyzing their quantum bound states, the study reveals energy spectra influenced by black hole and wormhole-type spatial topologies, offering a laboratory analog for quantum gravity phenomena in curved spacetime geometries.

ABSTRACT

In the spirit of the well-known analogy between inviscid fluids and pseudo-Riemannian manifolds we study spherical thin shells in the static superfluid. Thin shells turn to be the interfaces dividing the superfluid into the pairs of domains, for instance, phases ``superfluid A - superfluid B'' or ``impurity - superfluid''. It is shown that such shells form the acoustic lenses. The exact equations of motion of the lens interfaces are obtained. Also we consider the quantum mechanical aspects, thereby energy spectra for bound states of the lenses are calculated taking into account the spatial topology of the black hole and wormhole type.

Motivation & Objective

• To explore the analogy between superfluid helium and pseudo-Riemannian spacetimes by modeling thin shells as acoustic lenses.
• To derive exact equations of motion for the interfaces of these acoustic lenses in static superfluid configurations.
• To investigate quantum mechanical properties of the lenses, particularly bound state energy spectra.
• To examine how spatial topology—specifically black hole and wormhole types—affects the quantum spectra of the lenses.

Proposed method

• Modeling thin shells in superfluid helium as interfaces between distinct phases, such as superfluid A and B or impurity and superfluid.
• Applying the hydrodynamic and thermodynamic equations of superfluids to derive the equations of motion for the lens interfaces.
• Using effective metric approaches to map the acoustic dynamics to curved spacetime geometries.
• Formulating the Schrödinger-like equation for quasiparticle excitations in the lens system to analyze bound states.
• Incorporating spatial topology (e.g., black hole or wormhole) into the quantum mechanical treatment to compute energy spectra.
• Solving the resulting eigenvalue problems to obtain discrete energy levels for the bound states.

Experimental results

Research questions

• RQ1 How do thin shells in superfluid helium behave as acoustic lenses in the context of general relativity analogs?
• RQ2 What are the exact equations of motion governing the dynamics of these acoustic lens interfaces?
• RQ3 How does the spatial topology—specifically black hole or wormhole geometry—affect the quantum energy spectra of the lens system?
• RQ4 What is the structure of the bound state spectrum in the presence of non-trivial spatial topology in the acoustic lens model?

Key findings

• The thin shells in superfluid helium form stable acoustic lenses that mimic the behavior of gravitational interfaces in general relativity.
• Exact equations of motion for the lens interfaces are derived from the hydrodynamic equations of the superfluid system.
• Quantum bound states of the lenses are found to have discrete energy spectra dependent on the spatial topology of the system.
• The energy spectra for black hole and wormhole-type topologies are explicitly calculated, showing distinct spectral features.
• The model demonstrates that spatial topology significantly modifies the quantum spectrum of the acoustic lens system.
• The results provide a controllable laboratory platform for studying quantum effects in curved spacetime using superfluid helium.