We study Andreev-mediated transport and current fluctuations in interacting normal-superconducting quantum-dot systems. Using a generalized master equation based on real-time diagrammatics and full counting statistics, we compute the steady-state current, zero-frequency noise, and rate of entropy production in the large superconducting-gap limit. We show how Coulomb interactions modify Andreev-mediated transport by renormalizing resonant conditions and suppressing superconducting coherence, leading to a pronounced reduction of current precision even when average currents are only weakly affected. These effects are particularly evident at high temperatures, where conventional Coulomb-blockade features are thermally smeared while fluctuation properties remain highly sensitive. By analyzing thermodynamic uncertainty relations, we demonstrate that violations of the quantum bound present in the noninteracting regime are progressively reduced and eventually suppressed as interactions increase, whereas the recently proposed hybrid bound remains satisfied. Our results clarify how Coulomb interactions, and nonequilibrium fluctuations jointly determine transport properties in hybrid superconducting devices, and establish current precision as a robust benchmark for interacting Andreev transport beyond the noninteracting limit.
Cavity magnonics is moving beyond the conventional paradigm of coherent spin--photon hybridization toward the controlled engineering of dissipative and coherent interactions, Floquet dynamics, and quantum fluctuations. This Perspective examines how these ingredients reshape collective dynamics and open new avenues for quantum state engineering, transport, and sensing. We discuss the role of dissipative coupling and anti-
PT symmetry in enabling long-lived collective modes and enhanced spectral response, and highlight Floquet engineering as a means of engineering nonreciprocal transport and phase-controlled interactions. We then review recent progress in quantum magnonics, ranging from squeezed and entangled magnon states, including the squeezing of thermal magnons, to prospective schemes for preparing magnonic Schrödinger-cat states. We also discuss how parametric driving and active gain strongly modify hybrid susceptibilities and amplify magnon--photon response. These advances expand the scope of cavity magnonics beyond conventional polariton physics, establishing it as a versatile platform for sensing, transduction, spin transport, and hybrid quantum technologies.
Abstract The unraveling of open quantum system dynamics in terms of stochastic quantum trajectories offers a picture of open system dynamics that consistently considers memory effects stemming from the finite correlation time of environment fluctuations. These fluctuations significantly influence the coherence and energy transport properties of excitonic systems. When their correlation time is comparable to the timescale of the Hamiltonian evolution, it leads to the departure of open system dynamics from the Markovian limit. In this work, we leverage the unraveling of exciton dynamics through stochastic Hamiltonian propagators to design quantum circuits that simulate exciton transport, capturing finite memory effects. In addition to enabling the synthesis of parametrizable quantum circuits, stochastic unitary propagators provide a transparent framework for investigating non-Markovian effects on exciton transport. Our analysis reveals a nuanced relationship between environment correlation time and transport efficiency, identifying a regime of ‘memory-assisted’ quantum transport where time-correlated fluctuations allow the system to reach higher efficiency. However, this property is not universal and can only be realized in conjunction with specific features of the system Hamiltonian.