On the irreversible dynamics emerging from quantum resonances

Könenberg, Martin; Merkli, Marco

doi:10.1063/1.4944614

Cited by 23 publications

(61 citation statements)

References 42 publications

(80 reference statements)

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“…• A different remainder estimate. The dynamical resonance theory of [11] which we use to prove the expansion (2.12) is designed to give a remainder that decays as t → ∞. Instead, one can modify this theory to yield a remainder which is O(V ) for all times, but may not vanish at t = ∞.…”

Section: Relaxation Of the Dimermentioning

confidence: 99%

“…Thus, for a rigorous analysis, we first perform the infinite volume limit and get results which hold for all times t ≥ 0. This approach has been fruitful in many situations recently [16,11,12,17,18,19,20].…”

Section: Dynamical Resonance Theory 41 the Mathematical Setupmentioning

confidence: 99%

“…where L is L col or L loc (see (4.17), (4.21)), depending on the model considered. (4.28) has the following resonance expansion, which follows from a general resonance expansion of propagators proven in [11]. Set, for ease of notation,…”

Section: Resonance Expansion Of the Propagatormentioning

confidence: 99%

“…Proposition 4.1), which is indispensable in order to deal with arbitrary values of λ 1 and λ 2 and which requires only the milder regularity p > −1/2. The other origin is that we use a 'dynamical resonance theory' developed in [11], which gives a proof of (4.30) under the assumptions that…”

Section: Mathematical Regularity Requirementsmentioning

confidence: 99%

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Dynamics of a chlorophyll dimer in collective and local thermal environments

et al. 2016

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We present a theoretical analysis of exciton transfer and decoherence effects in a photosynthetic dimer interacting with collective (correlated) and local (uncorrelated) protein-solvent environments. Our approach is based on the framework of the spin-boson model. We derive explicitly the thermal relaxation and decoherence rates of the exciton transfer process, valid for arbitrary temperatures and for arbitrary (in particular, large) interaction constants between the dimer and the environments. We establish a generalization of the Marcus formula, giving reaction rates for dimer levels possibly individually and asymmetrically coupled to environments. We identify rigorously parameter regimes for the validity of the generalized Marcus formula. The existence of long living quantum coherences at ambient temperatures emerges naturally from our approach.

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Section: Relaxation Of the Dimermentioning

confidence: 99%

Section: Dynamical Resonance Theory 41 the Mathematical Setupmentioning

confidence: 99%

Section: Resonance Expansion Of the Propagatormentioning

confidence: 99%

Section: Mathematical Regularity Requirementsmentioning

confidence: 99%

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Dynamics of a chlorophyll dimer in collective and local thermal environments

et al. 2016

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“…Combining (3.23) with Lemma 3.3, and invoking the isospectrality of the Feshbach map (see for instance Proposition B.2 in [14]), we obtain…”

Section: Proof Of Proposition 32 Letmentioning

confidence: 75%

Completely positive dynamical semigroups and quantum resonance theory

Könenberg

Merkli

2017

Lett Math Phys

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Abstract. Starting form a microscopic system-environment model, we construct a quantum dynamical semigroup for the reduced evolution of the open system. The difference between the true system dynamics and its approximation by the semigroup has the following two properties: It is (linearly) small in the system-environment coupling constant for all times, and it vanishes exponentially quickly in the large time limit. Our approach is based on the quantum dynamical resonance theory. The issueDue to the entanglement of an open system with its surroundings, its dynamics V (t) : ρ 0 → ρ t , mapping an initial system density matrix ρ 0 to its value at time t, is not a semigroup in time. For each fixed t, the mapping V (t), called a dynamical map, is a linear, completely positive, trace preserving transformation. 1 Under certain assumptions, one can approximate the dynamics of an open system by a continuous one-parameter semigroup of dynamical maps, called a quantum dynamical semigroup [5,11]. The dynamics given by such a semigroup has two important features: (i) is it markovian due to the semigroup property and (ii) it maps density matrices into density matrices due to its trace and positivity preserving quality. Complete positivity of the dynamical semigroup implies its positivity preservation, but not vice-versa. It is a crucial physical property which ensures that the dynamics of initially entangled systems interacting with an environment is well defined [1,3]. The semigroup property is particularly convenient since the spectral analysis of the generator L of the semigroup yields dynamical properties of the system, such as the final state(s) and convergence speeds. Controlling the remainder in the approximation V (t)ρ 0 ≈ e tL ρ 0 rigorously is difficult. Microscopic derivations, passing from a full (hamiltonian) model of system plus environment and tracing out the environment degrees of freedom, involve approximations (Born, Markov, rotating wave) that are hard to deal with mathematically. In some situations where the system-environment interaction is weak, measured by a small coupling constant λ, one can implement a (time-dependent) perturbation theory, λ = 0 giving the unperturbed (uncoupled) case. For certain systems it has been shown [7] that for all a > 0, lim

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