Many-Body Floquet Theory for Radiative Heat Transfer in Time-Modulated Systems

TL;DR

This work develops a general Floquet-based framework to describe radiative heat transfer among time-modulated dipoles, extending fluctuational electrodynamics to nonstationary, far-from-equilibrium regimes with memory effects. By formulating a perturbative expansion in modulation, a generalized fluctuation–dissipation theorem, and a Floquet-driven Landauer-like transmission, it captures all inelastic frequency-conversion channels across multiple scattering paths. Near-resonant modulation acts as a parametric amplifier, redistributing thermal fluctuations into Floquet sidebands and enabling active, spectral control of nanoscale heat transfer. The approach provides a powerful, unified toolkit for designing tunable, potentially nonreciprocal radiative exchange in complex many-body systems, with practical routes to ultrafast dielectric modulation via phase transitions, carrier dynamics, or nonlinear phononics.

Abstract

We develop a general theory of radiative heat exchange between dipoles with time-modulated optical properties. This framework extends fluctuational electrodynamics beyond equilibrium by incorporating nonstationary correlations and memory effects induced by temporal modulation. Closed-form expressions for the heat currents in modulated many-body systems are obtained, together with a generalized Landauer-like formulation of the pairwise exchanges, where the transmission coefficient accounts for all inelastic frequency-conversion channels. Near-resonant modulation redistributes and amplifies thermal fluctuations across Floquet sidebands, acting as a parametric amplifier of thermal radiation and enabling active, frequency-selective control of nanoscale heat transfer.

Figures (3)

• Figure 1: Dipolar corrections of order $n$ in the scalar approximation with (a) a sinusoidal variation of $\delta\alpha$ of period $\tau=2\pi/\Omega$ and with (b) a rectangular variation $\delta\alpha(\omega,t)$ with the same period ($\delta\alpha(\omega,t)$ is equal to one when $\tau\in[0,\tau/2]$ and zero elsewhere and it is decomposed in 20 Fourier modes). Here we take $\omega_0=10^{15}\,\mathrm{rad}\cdot\mathrm{s}^{-1}$, $\gamma=5\cdot10^{13}\,\mathrm{s}^{-1}$, $\alpha_0=0.001$, $\tilde{p}=0.01$ and the temperature is $T=300\,$K. Here, the modulation frequency coincides with the resonance frequency of the Lorentzian (i.e. $\Omega=\omega_0$). Inset: temporal variation of $\delta\alpha$.
• Figure 2: Power spectrum of thermal emission at $T=300\,K$ of a static and modulated dipole associated to a SiC nanoparticle Palik$100\;nm$ radius under a sinusoidal variation (a)-(c) of $\delta\alpha$ of period $\tau=\frac{2\pi}{\Omega}$ and with a rectangular variation (d)-(f) of $\delta\alpha(\omega,t)$ (20 Fourier components are considered). Here we choose an oscillation amplitude of $\delta\alpha_0=0.3 \mathrm{Im}[\alpha]$. Inset: temporal variation of $\delta\alpha$.
• Figure 3: Power spectrum at $T=300\,$K of a modulated dipole (same as in Fig. \ref{['Fig:power_spectrum']}) under a rectangular modulation at frequency $\Omega=10^{14}\,\mathrm{rad}\cdot\mathrm{s}^{-1}$ (20 Fourier components ) with various modulation amplitude $\delta\alpha$.