Scattering-Assisted Reservoirs

• Scattering-assisted reservoirs are systems that use intrinsic or engineered scattering to redirect energy and information, creating pathways for dynamics that exceed conventional coherent systems.
• They enable enhanced cooling, entanglement generation, and nonlinear wave-mixing, with applications spanning quantum networks, optical computing, and magnonic pattern recognition.
• Engineered control of scattering processes, such as disorder tuning and wavefront shaping, provides flexible tuning of memory and computational capacity in advanced physical reservoirs.

A scattering-assisted reservoir is any system in which the intrinsic or engineered scattering processes within a material or structure fundamentally enable, mediate, or enhance the storage, transformation, or transmission of energy, information, or computational states. Such systems appear across condensed matter, quantum optics, reservoir computing, and spintronics, with diverse realizations ranging from impurity-mediated phonon processes in graphene to nonlinear photon interactions in optical fibers, and from quantum spin networks coupled via bosonic reservoirs to physical implementations of reservoir computing leveraging optical or magnonic scattering. The key unifying principle is that scattering—either disorder-induced, nonlinear, or quantum in origin—creates new pathways for dynamics, memory, and information processing that would be inaccessible or inefficient in idealized, non-scattering (i.e., clean or perfectly coherent) systems.

1. Fundamental Mechanisms of Scattering-Assisted Reservoirs

Scattering-assisted reservoirs rely on the modification of energy and information flow via processes that break or relax ideal conservation laws, produce nonlinear mixing, or introduce new dynamical timescales. Several archetypal mechanisms are documented:

• Disorder-assisted phonon scattering (“supercollisions” in graphene): The presence of disorder in the lattice allows electrons to relax their momentum non-conservatively, dramatically enhancing electron-phonon energy exchange and thus the cooling rate of hot carriers. The cooling power is given by

$$\mathcal{J} = A(T_\mathrm{el}^3 - T_\mathrm{ph}^3), \qquad A = \frac{9.62 g^2 \nu^2(\mu) k_B^3}{\hbar k_F \ell}$$

with $A$ tunable via the disorder parameter $k_F \ell$, predicting an energy-loss rate that strongly departs from the linear-in-$\Delta T$ dependence of pure systems (Song et al., 2011).

• Reservoir-mediated quantum dynamics: In open quantum systems, collective coupling of spin ensembles or qubits to a shared bosonic reservoir results in phenomena such as superradiance, negative-temperature steady states, or entanglement between non-interacting subsystems. The dynamics are governed by master equations where the Lindblad dissipator includes cross-terms (e.g., $L[J^-_A + J^-_B]$), enabling energy/information transfer, entanglement, and nonlocal relaxation (Hama et al., 2018, Dias et al., 2021).
• Nonlinear wave-mixing and spectral broadening: In photonic and magnonic systems, scattering-induced nonlinear interactions—such as stimulated Brillouin scattering in fibers or three-magnon splitting in thin ferromagnets—provide the required memory and nonlinearity for reservoir computing. For example, the coupled-mode equations for stimulated Brillouin scattering are

$$\begin{cases} \partial_T a_p + \partial_Z a_p = -a_s a_a \ \partial_T a_s - \partial_Z a_s = a_p a_a^* \ \partial_T a_a + (1 + j\Delta) a_a = a_p a_s^* \end{cases}$$

where $a_p$, $a_s$, and $a_a$ are normalized pump, Stokes, and acoustic amplitudes, respectively (Phang, 2023).

2. Realizations in Optical, Magnonic, and Quantum Platforms

The practical realization of scattering-assisted reservoirs spans a variety of architectures:

System Type	Scattering Mechanism	Functional Role
Graphene	Disorder-assisted e-ph supercollisions	Dramatically boosted electron-lattice cooling for hot carriers
Optical RC	Multiple light scattering (Rayleigh/Brillouin)	High-dimensional nonlinear mapping for AI tasks
Magnonic RC	Three-magnon mode mixing in vortex-state disks	Nonlinear pattern recognition and memory via spectral features
Quantum Net	Shared bosonic reservoir for spins or qubits	Entanglement, negative-temperature, energy transport
Quantum Well	Exciton and carrier scattering in nonradiative reservoir	Nonlinear broadening and recombination for optical control

In optical reservoir computing architectures, random projections essential for high-dimensional state representation are physically implemented using multiple light scattering in disordered media; for example, speckle patterns generated after modulating light with a DMD and passage through a diffusive medium, described mathematically as $s = |H d|^2$ where $H$ encodes the system's scattering matrix (Dong et al., 2016, Dong et al., 2019).

Magnon-based reservoirs use microwave-driven excitation of quantized spin-wave modes, with nonlinear three-magnon processes redistributing energy among secondary (split) modes in response to input sequences. These interactions follow conservation laws such as $f_A = f_A^+ + f_A^-$ and $m_A^+ = -m_A^-$, creating a natural high-dimensional, nonlinear computational substrate (Heins et al., 4 Feb 2025, Körber et al., 2022).

In quantum settings, repeated scattering of a system mode with a sequence of reservoir modes via beam splitters relaxes the system toward a stationary (typically thermal) state defined by the reservoir statistics, with asymptotic entanglement and a reduction of system nonclassicality (Bievre et al., 2023).

3. Information Processing and Memory in Scattering-Assisted Physical Reservoirs

Scattering-assisted reservoirs demonstrate computational capacity—specifically, short-term memory, nonlinear transformation, and pattern recognition—by leveraging the high-dimensional projections and temporal mixing provided by scattering. Physical implementations of reservoirs (e.g., in optical fibers or magnetic disks) natively produce a reservoir map $$x(t+1) = f(W_\mathrm{in} g(i(t)) + W_\mathrm{res} g(x(t)) + b)$$ via the physical evolution of the scattered field or excitations. The mapping properties are determined by:

• The statistical structure of the transmission/scattering matrix (for optics)
• The nonlinear interaction kernel (Brillouin gain, magnon splitting)
• The energy or momentum conservation rules imposed by the scattering dynamics

Robustness to noise and input variability typically arises because the nonlinear mixing inherent to the scattering process distributes input information over many measurable "reservoir nodes" (modes, frequencies, or virtual spatial channels). Such multiplexing allows high performance on tasks including temporal pattern recognition (e.g., $\geq 95$\% sequence classification accuracy with magnonic reservoirs), chaotic time series prediction, and cross-variable observer tasks for complex dynamical systems (Körber et al., 2022, Heins et al., 4 Feb 2025, Cox et al., 10 Apr 2024).

4. Reservoir Engineering and Control via Scattering Properties

Engineered control over scattering processes enables flexible tuning of reservoir characteristics:

• Disorder tuning in electronic systems: By changing the mean free path $\ell$ (e.g., through substrate engineering, annealing, or impurity doping), one alters the parameter $k_F \ell$ and thereby the energy transfer rate $A$; more disorder (smaller $\ell$) produces faster electron-phonon energy relaxation (Song et al., 2011).
• Wavefront shaping for energy storage: The Wigner–Smith time-delay operator $Q(\omega)$ allows identifying incident wavefronts that maximize energy storage inside a resonator within a disordered environment. The optimal input is the eigenvector corresponding to the largest proper delay time, providing enhanced light–matter interaction or energy harvesting (Hougne et al., 2020).
• Spin-bath coupling configurations: In spin networks, varying the symmetry or connectivity of domains coupled to a shared reservoir changes the dynamical outcomes (e.g., enabling negative-temperature steady states or controlling entanglement growth) (Hama et al., 2018, Dias et al., 2021).

In quantum battery charging, the type of reservoir (bosonic vs. fermionic) and feedback protocol profoundly influence charging efficiency and ergotropy. For fermionic reservoirs, increased environmental temperature enhances extracted work, unlike the bosonic case where higher temperature impedes efficient energy storage (Yao et al., 18 Feb 2025).

5. Distinctive Dynamical and Statistical Signatures

Scattering-assisted reservoirs exhibit several distinctive fingerprints:

• Non-exponential, power-law relaxation: Disorder-assisted electron-phonon scattering in graphene yields $$T_\mathrm{el}(t) = T_{\mathrm{el},0}/[1 + (A/\alpha)T_{\mathrm{el},0}(t-t_0)]$$ (a $1/t$ law) deviating from naive exponential decay (Song et al., 2011).
• Dimension-dependent resonance statistics: In models of quantum random Lorentz gases, resonance density distributions in the complex frequency plane provide fingerprints for the background scattering-induced "memory" spectrum; in 1D, Anderson localization creates long-lived resonances scaling as $|\mathrm{Im}\,k|^{-1}$, with implications for slow memory effects (Gaspard et al., 2021).
• Entanglement and nonclassicality transfer: Repeated scattering via beam splitters asymptotically entangles the system and reservoir while reducing the system's nonclassicality, especially when the reservoir is prepared in non-Gaussian states (Bievre et al., 2023).

6. Applications and Prospects

Scattering-assisted reservoirs are relevant for:

• Hot-carrier device engineering: Cooling rates controlled via disorder enable variable hot-carrier lifetime in bolometric and photodetector technologies (Song et al., 2011).
• Photonic and magnonic physical reservoir computing: Optical/magnonic scattering enables highly parallel, scalable, energy-efficient computation for AI tasks, including time-series prediction, pattern recognition, and high-dimensional signal transformation (Dong et al., 2016, Dong et al., 2019, Körber et al., 2022, Phang, 2023, Cox et al., 10 Apr 2024, Heins et al., 4 Feb 2025).
• Quantum information transfer: Reservoir-mediated energy migration and entanglement generation provide architectures for quantum networks and batteries, where engineered coupling to collective environments can both distribute and concentrate excitations, and enable robust state transfer (Hama et al., 2018, Dias et al., 2021, Yao et al., 18 Feb 2025).
• Molecular neuromorphic hardware: SERS-based few-molecule reservoirs demonstrate that high-dimensional, nonlinear dynamical systems are feasible at the molecular scale for practical computational tasks (Nishioka et al., 2023).

These approaches collectively demonstrate the wide applicability of scattering-assisted reservoir concepts and point toward increasingly integrated, high-dimensional, and controllable platforms for energy, information storage, and computation based fundamentally on the physical mechanisms of scattering and dissipation.