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arXiv:2609.08910

On spatial decoherence in many-body systems

Stefano Marcantoni, Marco Merkli

math-phquant-phSubmitted Sep 8, 2026• Announced Sep 9, 2026• 0 citations

Abstract

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 $λ$ and short times scaling as $t\propto λ^{-α}$, with $α\ge0$, in the limit $λ\rightarrow\infty$. On short time scales $α>1$ the dynamics is trivial while on longer ones $0\leα<1$ the decoherence is instantaneous. We show that the decoherence process is resolved exactly for $α=1$, defining the fine-grained time scale $τ=λt$. 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.

Comments: 39 pages

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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

λ

and short times scaling as

t\propto λ^{-α}

, with

α\ge0

, in the limit

λ\rightarrow\infty

. On short time scales

α>1

the dynamics is trivial while on longer ones

0\leα<1

the decoherence is instantaneous. We show that the decoherence process is resolved exactly for

0\leα<1

, defining the fine-grained time scale

τ=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.

Markovian regime decoherence effects in quantum computers are studied in terms of the fidelity for the situation where the number of qubits N becomes large. A general expression giving the decoherence time scale in terms of Markovian relaxation elements and expectation values of products of system fluctuation operators is obtained, which could also be applied to study decoherence in other macroscopic systems such as Bose condensates and superconductors. A standard circuit model quantum computer involving three-state lambda system ionic qubits is considered, with qubits localized around well-separated positions via trapping potentials. The centre of mass vibrations of the qubits act as a reservoir. Coherent one and two qubit gating processes are controlled by time-dependent localized classical electromagnetic fields that address specific qubits, the two qubit gating processes being facilitated by a cavity mode ancilla, which permits state interchange between qubits. With a suitable choice of parameters, it is found that the decoherence time can be made essentially independent of N.

Although coupling to a super-Ohmic bosonic reservoir leads only to partial dephasing on short time scales, exponential decay of coherence appears in the Markovian limit (for long times) if anharmonicity of the reservoir is taken into account. This effect not only qualitatively changes the decoherence scenario but also leads to localization processes in which superpositions of spatially separated states dephase with a rate that depends on the distance between the localized states. As an example of the latter process, we study the decay of coherence of an electron state delocalized over two semiconductor quantum dots due to anharmonicity of phonon modes.

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 consider environment induced decoherence of quantum superpositions to mixtures in the limit in which that process is much faster than any competing one generated by the Hamiltonian

{H}_{\mathrm{sys}}

of the isolated system. This interaction-dominated decoherence limit is of importance for the emergence of classical behavior in the macroscopic domain, since it will always be the relevant regime for large enough separations between the superposed wave packets. The usual golden-rule treatment then does not apply, but we can employ a short-time expansion for the free motion while keeping the interaction

{H}_{\mathrm{int}}

in full. We thus reveal decoherence as a universal short-time phenomenon largely independent of the character of the system as well as the bath and of the basis the superimposed states are taken from. Simple analytical expressions for the decoherence time scales are obtained in the limit in which decoherence is even faster than any time scale emerging from the reservoir Hamiltonian

{H}_{\mathrm{res}}.

We present a rigorous analysis of the phenomenon of decoherence for general N -level quantum systems coupled a reservoir modelled by a thermal bosonic quantum environment. We present an explicit form of the dominant reduced dynamics of open systems. We give explicit results for a spin 1/2 (qubit), including decoherence and thermalization times. Our approach is based on a dynamical theory of quantum resonances. It yields the exact reduced dynamics of the small system and does not involve master equation or van Hove limit approximations. This approach is suitable for a wide variety of systems which are not explicitly solvable, including systems of interacting spins (registers of interacting qubits), for which the coupling between the system and the environment is fixed but small.