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<p>We analyze the quantum dynamics of a relativistic homogeneous superfluid in a complex scalar field theory. Unlike zero-charge condensates, which undergo quantum evaporation due to internal number-changing processes, we show that <i>U</i> (1) superfluids preserve their internal coherence indefinitely in this theory. In particular, although not Hamiltonian eigenstates, these configurations are stable in the full quantum theory to all orders in perturbation theory. This is demonstrated by explicitly constructing the corresponding quantum state and studying its dynamics. Crucially, maintaining stability requires the quantum state to go beyond a naive coherent-state construction: specific non-Gaussian corrections are essential for having a stationary state. The resulting state is identified as the interacting vacuum of the superfluid fluctuations, which also serves as the ground state of the modified Hamiltonian <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <mover accent="true"> <mi>H</mi> <mo stretchy="true">̂</mo> </mover> <mo>–</mo> <mi>μ</mi> <mover accent="true"> <mi>Q</mi> <mo stretchy="true">̂</mo> </mover> </math></EquationSource> <EquationSource Format="TEX">\( \hat{H}\hbox{--} \mu \hat{Q} \)</EquationSource> </InlineEquation>, with <i>μ</i> the full-fledged quantum chemical potential and <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math display="inline"> <mover accent="true"> <mi>Q</mi> <mo stretchy="true">̂</mo> </mover> </math></EquationSource> <EquationSource Format="TEX">\( \hat{Q} \)</EquationSource> </InlineEquation> the <i>U</i> (1) charge. Finally, we check that the phonon mode remains gapless once one-loop corrections are included, confirming the robustness of the Goldstone theorem beyond the semiclassical regime, even in systems with a spontaneously broken Lorentz symmetry.</p>

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Coherence and quantum stability of relativistic superfluid states

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月8日

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  • Lasha Berezhiani,
  • Giordano Cintia,
  • Giacomo Contri

摘要

We analyze the quantum dynamics of a relativistic homogeneous superfluid in a complex scalar field theory. Unlike zero-charge condensates, which undergo quantum evaporation due to internal number-changing processes, we show that U (1) superfluids preserve their internal coherence indefinitely in this theory. In particular, although not Hamiltonian eigenstates, these configurations are stable in the full quantum theory to all orders in perturbation theory. This is demonstrated by explicitly constructing the corresponding quantum state and studying its dynamics. Crucially, maintaining stability requires the quantum state to go beyond a naive coherent-state construction: specific non-Gaussian corrections are essential for having a stationary state. The resulting state is identified as the interacting vacuum of the superfluid fluctuations, which also serves as the ground state of the modified Hamiltonian H ̂ – μ Q ̂ \( \hat{H}\hbox{--} \mu \hat{Q} \) , with μ the full-fledged quantum chemical potential and Q ̂ \( \hat{Q} \) the U (1) charge. Finally, we check that the phonon mode remains gapless once one-loop corrections are included, confirming the robustness of the Goldstone theorem beyond the semiclassical regime, even in systems with a spontaneously broken Lorentz symmetry.