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arXiv:2606.16634 · Open Systems & Information Dynamics

Ultrastrongly coupled open systems and fine grained time

Stefano Marcantoni, Marco Merkli

quant-phmath-phSubmitted Jun 15, 2026• Announced Jun 16, 2026• 0 citations
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Abstract

We study the dynamics of a d-level quantum system coupled to a bosonic reservoir when the coupling constant is large. It is known that in the limit of infinite coupling strength, the system undergoes an instantaneous nonselective measurement, resulting in the immediate decoherence in the measurement basis, followed by a unitary Zeno dynamics. Here we resolve this dynamical process by introducing a fine grained scaling regime of short times proportional to the inverse coupling. We provide a rigorous derivation of the open system dynamics in this regime of ultrastrong coupling and demonstrate how decoherence unfolds continuously in the new time scale. We show that Markovian dynamics which are not given by semigroups arise naturally, in contrast to what happens in the weak coupling theory.

Comments
21 pages, 1 figure; accepted in OSID

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We study the dynamics of a d-level quantum system coupled to a bosonic reservoir when the coupling constant is large. It is known that in the limit of infinite coupling strength, the system undergoes an instantaneous nonselective measurement, resulting in the immediate decoherence in the measurement basis, followed by a unitary Zeno dynamics. Here we resolve this dynamical process by introducing a fine grained scaling regime of short times proportional to the inverse coupling. We provide a rigorous derivation of the open system dynamics in this regime of ultrastrong coupling and demonstrate how decoherence unfolds continuously in the new time scale. We show that Markovian dynamics which are not given by semigroups arise naturally, in contrast to what happens in the weak coupling theory.
We study the dynamics of a many-body quantum system strongly interacting with a bosonic reservoir. The coupling is given by a potential operator for the system and it is linear in the field. We show that in the limit of infinite coupling strength the system undergoes instantaneous spatial decoherence. To resolve the decoherence process in time we consider large coupling strengths λλλ and short times scaling as t∝λ−αt\propto λ^{-α}t∝λ−α, with α≥0α\ge0α≥0, in the limit λ→∞λ\rightarrow\inftyλ→∞. On short time scales α>1α>1α>1 the dynamics is trivial while on longer ones 0≤α<10\leα<10≤α<1 the decoherence is instantaneous. We show that the decoherence process is resolved exactly for α=1α=1α=1, defining the fine-grained time scale τ=λtτ=λtτ=λt. We construct an approximate effective evolution map of the many-body system with controlled error estimates. Generically, the effective dynamics is markovian, but not given by a dynamical semigroup. As a physical application we give a rigorous description of the phenomenon of localization of macroscopic quantum objects in position space.
We study the dynamics of an open quantum system linearly coupled to a bosonic reservoir. We show that, in the ultrastrong coupling limit, the system undergoes a nonselective measurement and then evolves unitarily according to an effective Zeno Hamiltonian. This dynamical process is largely independent of the reservoir state. We examine the entanglement breaking effect of the ultrastrong coupling on the system. We also derive the evolution equation for systems in contact with several reservoirs when one coupling is ultrastrong. The effective system dynamics displays a rich structure and, contrarily to the single reservoir case, it is generally non-Markovian. Our approach is based on a Dyson series expansion, in which we can take the ultrastrong limit termwise, and a subsequent resummation of the series. Our derivation is mathematically rigorous and uncomplicated.
We consider a quantum system dynamics caused by successive selective and nonselective measurements of the probe coupled to the system. For the finite measurement rate ${\ensuremath{\tau}}^{\ensuremath{-}1}$ and the system-probe interaction strength $\ensuremath{\gamma}$ we derive analytical evolution equations in the stroboscopic limit $\ensuremath{\tau}\ensuremath{\rightarrow}0$ and ${\ensuremath{\gamma}}^{2}\ensuremath{\tau}=\mathrm{const}$, which can be considered as a deviation from the Zeno subspace dynamics on a longer time scale $T\ensuremath{\sim}{({\ensuremath{\gamma}}^{2}\ensuremath{\tau})}^{\ensuremath{-}1}\ensuremath{\gg}{\ensuremath{\gamma}}^{\ensuremath{-}1}$. Nonlinear quantum dynamics is analyzed for selective stroboscopic projective measurements of an arbitrary rank. Nonselective measurements are shown to induce the semigroup dynamics of the system-probe aggregate. Both nonlinear and decoherent effects become significant at the time scale $T\ensuremath{\sim}{({\ensuremath{\gamma}}^{2}\ensuremath{\tau})}^{\ensuremath{-}1}$, which is illustrated by a number of examples.
We study non-Markovian dynamics of an open quantum system system interacting with a nonstationary squeezed bosonic reservoir. We derive exact and approximate descriptions for the open system dynamics. Focusing on the spin boson model, we compare exact dynamics with Redfield theory and a quantum optical master equation for both short and long time dynamics and in non-Markovian and Markov regimes. The squeezing of the bath results in asymptotic oscillations in the stationary state, which are captured faithfully by the Redfield master equation in the case of weak coupling. Furthermore, we find that the bath squeezing direction modifies the effective system-environment coupling strength and, thus, the strength of the dissipation.
In the framework of the theory of open quantum systems, we derive quantum master equations for the ultrastrong system-bath coupling regime and, more generally, the strong-decoherence regime. In this regime, the strong decoherence is complemented by slow relaxation processes. We use a generalization of the F\"orster and modified Redfield perturbation theories known in the theory of excitation-energy transfer. Also, we show that the mean-force Gibbs state in the corresponding limits is stationary for the derived master equations.
In this work we investigate the late-time steady states of open quantum systems coupled to a thermal reservoir in the strong coupling regime. In general such systems do not necessarily relax to a Boltzmann distribution if the coupling to the thermal reservoir is nonvanishing or equivalently if the relaxation time scales are finite. Using a variety of nonequilibrium formalisms valid for non-Markovian processes, we show that starting from a product state of the closed system = system+environment, with the environment in its thermal state, the open system which results from coarse graining the environment will evolve towards an equilibrium state at late times. This state can be expressed as the reduced state of the closed system thermal state at the temperature of the environment. For a linear (harmonic) system and environment, which is exactly solvable, we are able to show in a rigorous way that all multitime correlations of the open system evolve towards those of the closed system thermal state. Multitime correlations are especially relevant in the non-Markovian regime, since they cannot be generated by the dynamics of the single-time correlations. For more general systems, which cannot be exactly solved, we are able to provide a general proof that all single-time correlations of the open system evolve to those of the closed system thermal state, to first order in the relaxation rates. For the special case of a zero-temperature reservoir, we are able to explicitly construct the reduced closed system thermal state in terms of the environmental correlations.