The Effect of Time-Dependent Coupling on Non-Equilibrium Steady States

Cornean, Horia D.; Neidhardt, Hagen; Zagrebnov, Valentin A.

doi:10.1007/s00023-009-0400-5

Cited by 20 publications

(22 citation statements)

References 35 publications

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“…In that case, the NESS only depends on the initial states of the reservoirs and on the final one-particle Hamiltonian. It is, in particular, independent of the initial state of the sample and of the (possibly time-dependent) switching of the coupling/bias [CNZ,CMP2]. In fact, the presence of eigenvalues in the one-particle Hamiltonian of the fully coupled/biased system produces oscillations which prevent relaxation to a steady state [Ste, KKSG].…”

Section: Introductionmentioning

confidence: 99%

A geometric approach to the Landauer-Büttiker formula

Sâad

Pillet

2014

Journal of Mathematical Physics

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We consider an ideal Fermi gas confined to a geometric structure consisting of a central region -the sample -connected to several infinitely extended ends -the reservoirs. Under physically reasonable assumptions on the propagation properties of the one-particle dynamics within these reservoirs, we show that the state of the Fermi gas relaxes to a steady state. We compute the expected value of various current observables in this steady state and express the result in terms of scattering data, thus obtaining a geometric version of the celebrated Landauer-Büttiker formula.An operator on H is a linear map A : D → H , where D is a subspace of H . We say that D is the domain of A which we denote by Dom(A). A is densely defined if its domain is dense in H . The range and the kernel of A are the subspaces RanThe graph of an operator A on H is the the subspaceAn operator A is completely characterized by its graph. Moreover, a subspace G ⊂ H × H is the graph of an operator iff 〈0, v〉 ∈ G implies v = 0. If A and B are two operators such that Gr (A) ⊂ Gr (B ) we say that B is an extension of A and we write A ⊂ B . An operator A is closed if its graph is closed in H ×H , and this is the case iff Dom(A), equipped with the graph norm of A, is a Banach space. If A is both closed and bijective, then Gr (A −1 ) = KGr (A) and thus A −1 is also closed. If the closure Gr (A) cl of the graph of A in H × H is a graph we say that A is closable and we define its closure as the operator A cl such that Gr (A cl ) = Gr (A) cl . It is clear that A cl is the smallest closed extension of A, that is to say that if B is closed and A ⊂ B , then A cl ⊂ B . An operator A is densely defined iff J(Gr (A) ⊥ ) is a graph. In this case, the adjoint of A is the operator A * defined by Gr (A * ) = J(Gr (A) ⊥ ). A * is closed and its domain is given by(A * u, v) = (u, Av) holds for all 〈u, v〉 ∈ Dom(A * ) × Dom(A), in particular Ker (A * ) = Ran (A) ⊥ .A is closable iff A * is densely defined. In this case A cl = A * * and A cl * = A * . An operator A is bounded if there exists a constant C such that Gr (A) ⊂ {〈u, v〉 | v ≤ C u }. One easily verifies that A is continuous as a map from Dom(A) to H iff it is bounded. A bounded operator is obviously closable and its closure coincide with its unique continuous extension to the closure of Dom(A). In particular a bounded densely defined operator A has a unique continuous extension A cl with domain Dom(A cl ) = H . A cl is closed and bounded. The collection of all bounded operators with domain H is denoted by B(H ). It is a Banach algebra (actually a C * -algebra, see Section 2.2) with norm A ≡ sup u∈H , u =1Au .By the closed graph theorem, an operator A with domain H is bounded iff it is closed. If A is bounded and densely defined, then Dom(A * ) = H and A * is bounded. Furthermore, A * = A and A * A = A 2 .

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Section: Introductionmentioning

confidence: 99%

A geometric approach to the Landauer-Büttiker formula

Sâad

Pillet

2014

Journal of Mathematical Physics

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“…It was Landauer and Büttiker who found that this current is directly related to the transmission coefficients of some natural scattering system related to this particle transport problem. The phenomenological approach of Landauer and Büttiker later has been justified in several papers by deriving the formula from fundamental concepts of the Quantum Mechanics, see the series of papers [1,5,8,9,10,11,12,13,14] and [19].…”

Section: Introductionmentioning

confidence: 99%

“…(iii) If S = {H, H 0 } is time reversible and mirror symmetric we get from Lemma 2.14(ii) that σ ph nαm α ′ (λ) = σ ph n α ′ mα (λ), λ ∈ R, n, m ∈ N 0 , α, α ′ ∈ {l, r}, α = α ′ . Using that we get from (5.13) that (n)f (λ − µ − nω) − ρ ph (m)f (λ − µ − mω)) σ ph n α ′ mα (λ)dλ.Interchanging m and n we get(m)f (λ − µ − mω) − ρ ph (n)f (λ − µ − nω)) σ ph m α ′ nα (λ)dλ.Using that S is time reversible symmetric we get from Lemma 2 14. (i) that (m)f (λ − µ − mω) − ρ ph (n)f (λ − µ − nω)) σ ph nαm α ′ (λ)dλ.…”

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confidence: 99%

A New Model of Quantum Dot Light Emitting-Absorbing Devices

Neidhardt¹,

Wilhelm²,

Zagrebnov³

2014

Z. mat. fiz. anal. geom.

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Motivated by the Jaynes-Cummings (JC) model, we consider here a quantum dot coupled simultaneously to a reservoir of photons and two electric leads (free-fermion reservoirs). This new Jaynes-Cummings-leads (JCL)-type model makes it possible that the fermion current through the dot creates a photon flux, which describes a light-emitting device. The same model also describes a transformation of the photon flux into the current of fermions, i.e., a quantum dot light-absorbing device. The key tool to obtain these results is the abstract Landauer-Büttiker formula.

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“…Then one expects the joint system S + R 1 + · · · to relax towards a non-equilibrium steady states (NESS). Such states have been constructed in [Ru1,AH,JP2,APi,OM,MMS,CDNP,CNZ]. They carry currents, have non vanishing entropy production rate,.…”

Section: Introductionmentioning

confidence: 99%

Thermal Relaxation of a QED Cavity

Bruneau

Pillet

2008

J Stat Phys

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Abstract. We study repeated interactions of the quantized electromagnetic field in a cavity with single two-levels atoms. Using the Markovian nature of the resulting quantum evolution we study its large time asymptotics. We show that, whenever the atoms are distributed according to the canonical ensemble at temperature T > 0 and some generic non-degeneracy condition is satisfied, the cavity field relaxes towards some invariant state. Under some more stringent non-resonance condition, this invariant state is thermal equilibrium at some renormalized temperature T * . Our result is non-perturbative in the strength of the atom-field coupling. The relaxation process is slow (non-exponential) due to the presence of infinitely many metastable states of the cavity field.

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The Effect of Time-Dependent Coupling on Non-Equilibrium Steady States

Cited by 20 publications

References 35 publications

A geometric approach to the Landauer-Büttiker formula

A geometric approach to the Landauer-Büttiker formula

A New Model of Quantum Dot Light Emitting-Absorbing Devices

Thermal Relaxation of a QED Cavity

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