Emergent energy scales in magnonic systems with relative motion

Abstract: Relative motion between interacting systems can generate emergent energy scales that are absent in isolated systems. While uniform motion can be eliminated by a Galilean transformation, relative motion between interacting systems generally cannot. In the presence of characteristic spatial structures, relative motion gives rise to a Doppler frequency scale determined by the characteristic wavevector of the excitation and the relative velocity of the system. This emergent scale provides a fundamental mechanism for driving nonequilibrium phenomena in moving systems. In particular, the emergent energy scale is determined by how the relative motion probes the spatial structure of the relevant excitation. In this tutorial, we illustrate these ideas using magnonic systems as a concrete platform. We first discuss motion-induced magnon transport between relatively moving ferromagnets, in which the Doppler frequency serves as an effective nonequilibrium bias in the perturbative regime. This mechanism produces magnon currents even in the absence of conventional driving forces such as temperature gradients or chemical potential differences. We then introduce motion-induced parametric instabilities. When the emergent scale becomes sufficiently large to resonantly create magnon pairs, the perturbative description breaks down, and the magnonic vacuum becomes unstable. Above a critical velocity threshold, spontaneous magnon-pair creation emerges, resulting in strongly enhanced transport and nonequilibrium dynamics. Connections to related phenomena, including quantum friction, Cherenkov emission, and Zeldovich superradiance, are also highlighted. The concept of an emergent energy scale provides a unifying framework for understanding transport phenomena and instabilities in quantum systems with relative motion.

• The paper demonstrates that relative motion introduces a Doppler-driven energy scale that fundamentally alters magnon transport between ferromagnetic systems.
• It employs perturbation theory and dimensional analysis to quantify magnon current scaling with velocity while identifying a threshold for PT-symmetry breaking and dynamical instability.
• The study connects emergent magnonic instabilities to broader nonequilibrium phenomena, offering insights applicable to quantum friction, Cherenkov emission, and superradiance.

Emergent Energy Scales in Magnonic Systems with Relative Motion

Conceptual Framework of Motion-Induced Energy Scales

The paper "Emergent energy scales in magnonic systems with relative motion" (2606.29316) systematically addresses how relative motion between interacting quantum systems, specifically ferromagnets, can induce nontrivial energy scales otherwise absent in isolated systems. Through rigorous application of Galilean transformations and dimensional analysis, the study establishes that emergent frequency scales arise when the relative velocity is combined with a characteristic wavevector intrinsic to the excitations—principally manifesting as a Doppler shift for finite-wavenumber modes. Critically, this emergent scale is not eliminated by changing reference frames; instead, it underpins unique nonequilibrium phenomena and directly probes the spatial structure of collective excitations in the interacting system.

Magnonic Transport via Doppler-Driven Nonequilibrium Bias

The transport regime is analytically developed using perturbation theory, with motion-induced magnon transport between relatively moving ferromagnets as the prototypical example. Relative motion introduces an effective nonequilibrium bias via the Doppler frequency, driving magnon currents despite the absence of classical drivers like temperature gradients or chemical potential differences. The analytic evaluation reveals that:

• The emergent energy scale enters the transport process through spectral overlap and population imbalance of magnons across the interface.
• Spin transfer between magnets is proportional to the second order of the relative velocity ($v^2$), as first-order terms vanish upon integration due to their symmetry.
• The approach provides a formal basis for motion-induced transport, generalizing conventional thermodynamic bias to dynamic, spatially structured interactions.

This framework extends transport theory by explicitly incorporating the Doppler shift as a controllable parameter for nonequilibrium magnon tunneling and offers predictive relations for the scaling of magnon currents with velocity.

Dynamical Instabilities and Parametric Magnon Pair Creation

A qualitatively distinct regime arises when the emergent frequency scale becomes sufficient to drive resonant magnon pair creation. Here, the excitation-nonconserving channel dominates, and the emergent Doppler scale acts as an effective parametric drive:

• Instability threshold is determined through sum-frequency resonance conditions, resulting in spontaneous magnon-pair creation above a critical velocity, $v_c \sim 4D\omega_0$.
• The system transitions from perturbative transport to exponential amplification of collective excitations, signifying breakdown of the linear response regime.
• Explicit stability analysis is conducted via the eigenvalues of a Liouvillian governing magnon creation and annihilation operators. The eigenvalue structure leads to PT-symmetry breaking, with real eigenvalues below threshold and complex conjugate pairs (indicating instability) above threshold.
• The growth rate of unstable modes is quantified as $$\Gamma_k = 4g_{nc} - ( \omega_a + \omega_b - k v )^2$$, linking the creation rate directly to velocity and interaction strength.

This treatment connects magnonic instabilities to broader paradigms in non-Hermitian physics and identifies the conditions for spontaneous amplification and nonequilibrium steady-state formation in moving quantum systems.

Connections with Quantum Friction, Cherenkov Emission, and Superradiance

The theoretical framework extends beyond magnonics to other interacting bosonic systems, elucidating deep parallels with quantum friction, Cherenkov radiation, and superradiant amplification:

• Quantum friction is interpreted as momentum transfer via correlated photon pair generation across moving interfaces, analogous to magnon pair creation in the discussed system.
• The emergent scale and resonance conditions provide a unifying lens for understanding transport and instability phenomena in phononic, plasmonic, and photonic contexts.
• The dynamical Casimir effect, wherein parametric driving generates photon pairs from vacuum fluctuations, is conceptually linked to motion-induced magnon instabilities.

By characterizing the role of emergent scales, the paper offers a universal framework for quantifying nonequilibrium quantum phenomena induced by relative motion.

Implications and Speculative Outlook

The findings have significant theoretical and practical implications:

• The explicit dependence of energy scales on velocity and wavevector enables engineering of transport and instability regimes in magnonic devices, potentially facilitating nonequilibrium spintronic applications and robust quantum information transfer.
• The identification of PT symmetry breaking fosters new directions in non-Hermitian magnonics and collective gain/loss mechanisms.
• The unifying approach suggests future research could exploit emergent scales for active control over quantum friction, superradiant amplification, and correlated pair dynamics in hybrid quantum systems.

Integrating these concepts into device architectures and experimental platforms could unlock dynamic manipulation of quantum transport and instabilities, with cross-disciplinary relevance to condensed matter, photonics, and quantum technologies.

Conclusion

This paper provides a comprehensive theoretical construct for emergent energy scales in magnonic systems with relative motion, elucidating transport phenomena and dynamical instabilities as manifestations of Doppler-driven nonequilibrium quantum dynamics. The analytic foundation and resonance-based criteria unify diverse motion-induced effects across quantum platforms, offering predictive tools for both fundamental physics and practical device engineering. The research invites further exploration into controllable nonequilibrium quantum processes, non-Hermitian dynamics, and their applications within and beyond magnonic systems.