Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

On a model for quantum friction. I. Fermi's Golden Rule and dynamics at zero temperature

Claude‐Alain Pillet, Vojkan Jakšić

Published Jan 1, 1995• 17 citations
OpenAlex

Abstract

We investigate the dynamics of a quantum particle in a confining potential linearly coupled to a bosonic field at temperature zero. For a massive field we show, by employing complex deformation techniques, that Markovian semigroup which approximates the particles dynamics on the time scale $\tau=\lambda^2t$ ($\lambda$ strength of the coupling) is determined by the resonances of the full energy operator. We also show that Markovian master equation technique leads to the right prediction for the life-time of resonances. We discuss the dissipation of the particle into its ground state both in the time mean and on the above time scale.

Related papers

Quantum markovian master equations: Resonance theory overcomes the weak coupling regime

Marco Merkli

Quantum systems coupled to environments exhibit intricate dynamics. The master equation gives a Markov approximation of the dynamics, allowing for analytic and numerical treatments. It is ubiquitous in theoretical and applied quantum sciences. The accuracy of the master equation approximation was so far proven in the regime where time must not exceed an upper bound depending on the system-environment interaction strength (weak coupling regime). Here, we show that the Markov approximation is valid for fixed coupling strength and for all times. We also construct a new approximate markovian dynamics -- a completely positive, trace preserving semigroup -- which is asymptotically in time exact, to all orders in the coupling.

•Aug 6, 2019•1 citation

Breakdown of Fermi's Golden Rule in 1d systems at non-zero temperature

Young, Thomas, Jerome Lloyd, Curt W. von Keyserlingk

In interacting quantum systems, the single-particle Green's function is expected to decay in time due to the interaction induced decoherence of quasiparticles. In the limit of weak interaction strengths ($Δ$), a naive application of Fermi's Golden Rule (FGR) predicts an $\mathcal{O}(Δ^{2})$ quasiparticle decay rate. However, for 1d fermions on the lattice at $T>0$, this calculation gives a divergent result and the scaling of the quasiparticle lifetime with interaction strength remains an open question. In this work we propose a solution to this question: combining numerical simulations using the recently introduced dissipation-assisted operator evolution (DAOE) method, with non-perturbative diagrammatic re-summations, we predict a logarithmic enhancement of the quasiparticle decay rate $τ^{-1} \sim Δ^{2} \log Δ^{-2}$. We argue that this effect is present in a wide variety of well-known weakly interacting quantum fermionic and bosonic systems, and even in some classical systems, provided the non-interacting limit has quasiparticles with a generic dispersion.

arXiv:2508.00254•Aug 1, 2025•0 citations

A STOCHASTIC GOLDEN RULE AND QUANTUM LANGEVIN EQUATION FOR THE LOW DENSITY LIMIT

Luigi Accardi, Alexander Nikolaevich Pechen, Igor Vasil'evich Volovich

A rigorous derivation of quantum Langevin equation from microscopic dynamics in the low density limit is given. We consider a quantum model of a microscopic system (test particle) coupled with a reservoir (gas of light Bose particles) via interaction of scattering type. We formulate a mathematical procedure (the so-called stochastic golden rule) which allows us to determine the quantum Langevin equation in the limit of large time and small density of particles of the reservoir. The quantum Langevin equation describes not only dynamics of the system but also the reservoir. We show that the generator of the corresponding master equation has the Lindblad form of most general generators of completely positive semigroups.

arXiv:math-ph/0206032•Infinite Dimensional Analysis Quantum Probability and Related Topics•Sep 1, 2003•18 citations

Friction as a consistent quantum-mechanical concept

Dmitry V. Zhdanov, Denys I. Bondar, Tamar Seideman

A quantum analog of friction (understood as a completely positive, Markovian, translation-invariant, phenomenological model of dissipation) is known to be at odds with detailed balance in the thermodynamic limit. We show that this is not the case for quantum systems with internal (e.g., spin) states nonadiabatically coupled to translational dynamics. For such systems, a quantum master equation is derived which phenomenologically accounts for the frictional effect of a uniform zero-temperature environment. A simple analytical example is provided. Conjectures regarding the finite-temperature case are also formulated. The results are important for efficient simulations of complex molecular dynamics and quantum reservoir engineering applications.

arXiv:1810.00614•Physical Review A•Oct 29, 2018•2 citations

On spatial decoherence in many-body systems

Stefano Marcantoni, Marco Merkli

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.

math-phCross-listedarXiv:2609.08910•Sep 9, 2026•0 citations

Dynamics of Open Quantum Systems II, Markovian Approximation

Marco Merkli

A finite-dimensional quantum system is coupled to a bath of oscillators in thermal equilibrium at temperature T>0 . We show that for fixed, small values of the coupling constant λ , the true reduced dynamics of the system is approximated by the completely positive, trace preserving Markovian semigroup generated by the Davies-Lindblad generator. The difference between the true and the Markovian dynamics is O(|λ|1/4) for all times, meaning that the solution of the Gorini-Kossakowski-Sudarshan-Lindblad master equation is approximating the true dynamics to accuracy O(|λ|1/4) for all times. Our method is based on a recently obtained expansion of the full system-bath propagator. It applies to reservoirs with correlation functions decaying in time as 1/t4 or faster, which is a significant improvement relative to the previously required exponential decay.

arXiv:2105.00023•Quantum•Jan 3, 2022•24 citations
We investigate the dynamics of a quantum particle in a confining potential linearly coupled to a bosonic field at temperature zero. For a massive field we show, by employing complex deformation techniques, that Markovian semigroup which approximates the particles dynamics on the time scale τ=λ2t\tau=\lambda^2tτ=λ2t (λ\lambdaλ strength of the coupling) is determined by the resonances of the full energy operator. We also show that Markovian master equation technique leads to the right prediction for the life-time of resonances. We discuss the dissipation of the particle into its ground state both in the time mean and on the above time scale.
Quantum systems coupled to environments exhibit intricate dynamics. The master equation gives a Markov approximation of the dynamics, allowing for analytic and numerical treatments. It is ubiquitous in theoretical and applied quantum sciences. The accuracy of the master equation approximation was so far proven in the regime where time must not exceed an upper bound depending on the system-environment interaction strength (weak coupling regime). Here, we show that the Markov approximation is valid for fixed coupling strength and for all times. We also construct a new approximate markovian dynamics -- a completely positive, trace preserving semigroup -- which is asymptotically in time exact, to all orders in the coupling.
In interacting quantum systems, the single-particle Green's function is expected to decay in time due to the interaction induced decoherence of quasiparticles. In the limit of weak interaction strengths (ΔΔΔ), a naive application of Fermi's Golden Rule (FGR) predicts an O(Δ2)\mathcal{O}(Δ^{2})O(Δ2) quasiparticle decay rate. However, for 1d fermions on the lattice at T>0T>0T>0, this calculation gives a divergent result and the scaling of the quasiparticle lifetime with interaction strength remains an open question. In this work we propose a solution to this question: combining numerical simulations using the recently introduced dissipation-assisted operator evolution (DAOE) method, with non-perturbative diagrammatic re-summations, we predict a logarithmic enhancement of the quasiparticle decay rate τ−1∼Δ2log⁡Δ−2τ^{-1} \sim Δ^{2} \log Δ^{-2}τ−1∼Δ2logΔ−2. We argue that this effect is present in a wide variety of well-known weakly interacting quantum fermionic and bosonic systems, and even in some classical systems, provided the non-interacting limit has quasiparticles with a generic dispersion.
A rigorous derivation of quantum Langevin equation from microscopic dynamics in the low density limit is given. We consider a quantum model of a microscopic system (test particle) coupled with a reservoir (gas of light Bose particles) via interaction of scattering type. We formulate a mathematical procedure (the so-called stochastic golden rule) which allows us to determine the quantum Langevin equation in the limit of large time and small density of particles of the reservoir. The quantum Langevin equation describes not only dynamics of the system but also the reservoir. We show that the generator of the corresponding master equation has the Lindblad form of most general generators of completely positive semigroups.
A quantum analog of friction (understood as a completely positive, Markovian, translation-invariant, phenomenological model of dissipation) is known to be at odds with detailed balance in the thermodynamic limit. We show that this is not the case for quantum systems with internal (e.g., spin) states nonadiabatically coupled to translational dynamics. For such systems, a quantum master equation is derived which phenomenologically accounts for the frictional effect of a uniform zero-temperature environment. A simple analytical example is provided. Conjectures regarding the finite-temperature case are also formulated. The results are important for efficient simulations of complex molecular dynamics and quantum reservoir engineering applications.
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.
A finite-dimensional quantum system is coupled to a bath of oscillators in thermal equilibrium at temperature T>0 . We show that for fixed, small values of the coupling constant λ , the true reduced dynamics of the system is approximated by the completely positive, trace preserving Markovian semigroup generated by the Davies-Lindblad generator. The difference between the true and the Markovian dynamics is O(|λ|1/4) for all times, meaning that the solution of the Gorini-Kossakowski-Sudarshan-Lindblad master equation is approximating the true dynamics to accuracy O(|λ|1/4) for all times. Our method is based on a recently obtained expansion of the full system-bath propagator. It applies to reservoirs with correlation functions decaying in time as 1/t4 or faster, which is a significant improvement relative to the previously required exponential decay.