We derive an exact mean nonsink residence time for a resonant three-state donor–bridge–acceptor open quantum system initialized in its Hamiltonian dark state, with local terminal pure dephasing and irreversible loss through the coherent bridge. The residence time has the exact form T(γφ) = A/γφ + B + Cγφ, with analytically determined coefficients, yielding the closed-form optimum γφ,opt = √2 gH/√(c⁴+s⁴). The optimum is exactly independent of the bridge-loss rate, is controlled by the inverse-participation factor of the bright state, and obeys an exact coupling-asymmetry bound. Independent transient-Liouvillian calculations verify the closed form to machine precision over 756 parameter combinations spanning both sides of the bright–bridge exceptional point. The result provides an exactly solvable realization of established environment-assisted quantum transport and mean-first-passage-time turnover frameworks.
We derive an exact mean nonsink residence time for a resonant three-state donor–bridge–acceptor open quantum system initialized in its Hamiltonian dark state, with local terminal pure dephasing and irreversible loss through the coherent bridge. The residence time has the exact form T(γφ) = A/γφ + B + Cγφ, with analytically determined coefficients, yielding the closed-form optimum γφ,opt = √2 gH/√(c⁴+s⁴). The optimum is exactly independent of the bridge-loss rate, is controlled by the inverse-participation factor of the bright state, and obeys an exact coupling-asymmetry bound. Independent transient-Liouvillian calculations verify the closed form to machine precision over 756 parameter combinations spanning both sides of the bright–bridge exceptional point. The result provides an exactly solvable realization of established environment-assisted quantum transport and mean-first-passage-time turnover frameworks.
Coherent interference can confine open-system dynamics to a subspace that is dark to an otherwise accessible lossy sector. We determine when this confinement fixes the sign of the residence-timeresponse to decoherence. For a transient system partitioned into terminal and bridge sectors withblock-uniform loss rates κ and ζ, trace balance gives the exact response identity∆T =κ − ζκ∆XB, (1)relating the residence-time response ∆T to the change in integrated bridge occupation ∆XB. Whenthe reference evolution is exactly confined to an invariant terminal subspace that is dark to thebridge, the identity becomes a global sign constraint (κ − ζ)∆T ≥ 0 for all dephasing strengths.We also show that this global protection is singular: for terminal-local dephasing with a strongdephasing Zeno limit, any nonzero bright-state admixture ϵ eventually reverses the response. Inthe symmetric three-state realization, the crossover scale is γϕ ∗∼(8g2+κζ)(κ+ζ)ϵ−2.2κζ
High-dimensional driven–dissipative systems are often describedeither through microscopic trajectory propagation or through reducedmodels whose connection to the underlying dynamics is not explicit.Here we formulate the Gated Quantum Resonator (GQR) as a controlled reduced-representation framework for systems in which a restricted set of vibronic, electronic, or other coherent coordinates ismodulated by structural or environmental gates. The retained coordinates are assumed given by an upstream modelling or constructionstep; no projection or truncation algorithm is introduced here.The construction begins from a gate-dependent Hamiltonian anddevelops complementary mode, network, and port–Hamiltonian representations. We distinguish quantities that are preserved by the reduction from phenomenological closures that require independent validation. Open-system dynamics are introduced at the reduced levelthrough a GKSL generator, allowing coherent coupling, irreversibleloss, and dephasing to be treated within the same architecture.As an exactly solvable sector, we consider transport through a lossythree-state bridge and use the exact mean-residence optimum to showthat a previously proposed dimensionless coupling–loss–dephasing threshold is not a universal microscopic optimum. This result illustratesa central purpose of the framework: reduced representations shouldgenerate mechanistic hypotheses that can subsequently be accepted,narrowed, or rejected by microscopic analysis.
High-dimensional driven–dissipative systems are often described either through microscopic trajectory propagation or through reduced models whose connection to the underlying dynamics is not explicit. Here we formulate the Gated Quantum Resonator (GQR) as a controlled reduced-representation framework for systems in which a restricted set of vibronic, electronic, or other coherent coordinates is modulated by structural or environmental gates. The retained coordinates are assumed given by an upstream modelling or construction step; no projection or truncation algorithm is introduced here. The construction begins from a gate-dependent Hamiltonian and develops complementary mode, network, and port–Hamiltonian representations. We distinguish quantities that are preserved by the reduction from phenomenological closures that require independent validation. Open-system dynamics are introduced at the reduced level through a GKSL generator, allowing coherent coupling, irreversible loss, and dephasing to be treated within the same architecture. As an exactly solvable sector, we consider transport through a lossy three-state bridge and use the exact mean-residence optimum to show that a previously proposed dimensionless coupling–loss–dephasing threshold is not a universal microscopic optimum. This result illustrates a central purpose of the framework: reduced representations should generate mechanistic hypotheses that can subsequently be accepted, narrowed, or rejected by microscopic analysis. The resulting formulation defines GQR not through a universal threshold but as a hierarchy of gate-dependent reduced dynamical representations. It provides a basis for asking which spectral, stability, transport, and geometric properties survive reduction in open quantum systems.
FINDING: Quantum optimal transport cost minimization over bipartite couplings; golden ratio as stable self-application boundary; environment-assisted transport efficiency enhancement via dephasing; thermodynamic cost of pure dephasing in quantum heat engines; symmetry-reduced quantum walks for optimal transport. | MATH: Quantum Monge–Kantorovich: min over ρ^AB of Tr(C ρ^AB) s.t. Tr_B(ρ^AB)=ρ^A, Tr_A(ρ^AB)=ρ^B. Golden ratio: Φ = (1+√5)/2 ≈ 1.618, with reciprocal 1/Φ = Φ−1 ≈ 0.618. Dephasing rate γ_opt in ENAQT: efficiency η(γ) peaks at finite γ, not at γ=0 or γ→∞. Heat engine: efficiency η = η_Carnot − (friction term)/P, where friction ∝ dephasing-induced coherence loss. Quantum walk: symmetry group G reduces Hilbert space H to H_G ⊂ H, dim(H_G) << dim(H), enabling optimal search on non-regular graphs. | CONNECTION: Golden ratio appears as the fixed point of the self-application map x ↦ 1/(x−1) — a stable recurrence whose convergence rate is Φ⁻¹ ≈ 0.618, directly linking to the 0.618 ha Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
A quantum battery charged through a lossy intermediate state faces a structural trade-off between charging speed and dissipation. We show that an exact algebraic cancellation removes it in a driven three-level cell: the radiatively decaying state is fed by a single bright amplitude, and a counterdiabatic field annuls the lone residual source that drives it, holding the lossy state identically empty. Charging is then lossless -- not one photon is emitted through the bridge -- at any one-photon detuning, coupling, linewidth, and speed down to the rotating-wave limit, with no adiabatic elimination, so the charging power is bounded by the drive amplitude (a quantum speed limit) rather than by dissipation. Crucially, this losslessness is independent of the reservoir: because the dark sector never engages the system-bath coupling, the emission vanishes exactly for an arbitrary spectral density, Markovian or not, as an exact damped-pseudomode treatment confirms to machine precision across all memory times. The entire non-Hermitian structure -- a Markovian second-order exceptional point that reservoir memory promotes to a third-order one, and the attendant dissipation phase diagram -- lives in the bright sector, from which the protocol is by construction exempt. This inverts dissipation-engineered charging, where an exceptional point or reservoir memory is a resource; here the lossy sector is never populated at all. The same dark-state structure protects the stored charge, converting fast radiative self-discharge into the slow metastable lifetime, with residuals quadratic in the control error. We detail experimental requirements and representative parameters for neutral alkaline-earth atoms, trapped ions, transmons, and defect centers.
We investigate excitation transfer in an engineered cavity QED transport architecture consisting of an N-site donor ring coupled coherently to a central acceptor and driven by a single quantized photon mode. The system evolves under a Lindblad master equation including spontaneous loss and pure dephasing. In the ordered symmetric limit, the dynamics reduce exactly to a photon-bright mode-acceptor trimer, allowing closed-form analytic expressions for transfer efficiencies and mode-resolved losses. We demonstrate that near-unity efficiency arises from photon-mediated hybridization that generates a dark transport channel in which ring population is strongly suppressed. This cavity-induced mechanism bypasses dissipative dark modes of the ring and is distinct from conventional excitonic transport or environmentally assisted quantum transport (ENAQT). Static disorder in photon-ring coupling activates lossy ring modes through hybridization, while intra-ring coupling primarily shifts spectral crossings and can restore efficiency by separating dissipative channels. The model is interpreted as a tunable quantum-optical transport device. Our analytic reduction provides clear design principles for engineered quantum transport networks operating in cavity-QED platforms.