Time-local master equation connecting the Born and Markov approximations

Karlewski, Christian; Marthaler, Michael

doi:10.1103/physrevb.90.104302

Cited by 22 publications

(32 citation statements)

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“…38) are consistent with the numerical results shown in figure 3(b) (dashed-dotted-line) for asymmetrical coupling G = G as an example.We further consider the single level in the dot with spin-dependence as described by the Hamiltonian, The involved states in the dot are ñ |0 ,  ñ | ,  ñ | , and ñ º   ñ | | 2 denoting the empty, two single-occupation spin states, and the double-occupation spin-pair state, respectively. In this state-basis, we have = ñá  +  ñá  demonstrate the Coulomb interaction effect more transparently, we fix the dot level with spin-degeneracy, spin-independent coupling strength, G = G = G (a = L R , ).…”

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confidence: 91%

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Non-Markovian correlation functions for open quantum systems

2016

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Beyond the conventional quantum regression theorem, a general formula for non-Markovian correlation functions of arbitrary system operators both in the time-and frequency-domain is given. We approach the problem by transforming the conventional time-non-local master equation into dispersed time-local equations-of-motion. The validity of our approximations is discussed and we find that the non-Markovian terms have to be included for short times. While calculations of the density matrix at short times suffer from the initial value problem, a correlation function has a well defined initial state. The resulting formula for the non-Markovian correlation function has a simple structure and is as convenient in its application as the conventional quantum regression theorem for the Markovian case. For illustrations, we apply our method to investigate the spectrum of the current fluctuations of interacting quantum dots contacted with two electrodes. The corresponding non-Markovian characteristics are demonstrated.

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confidence: 91%

“…Following the estimation of the order of magnitude of the self-energy in[38], we roughly get (see appendix C.2 for the detail) )ˆ¯(ˆ¯)]} {ˆ[ ( )ˆ¯(ˆ¯)]} ( )…”

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confidence: 99%

Non-Markovian correlation functions for open quantum systems

2016

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“…To obtain

ρ false(t false)

in practice, one commonly first derives a kinetic or generalized master equation . Modeling the leads as reservoirs that are initially each in a grand‐canonical equilibrium state contained in

ρ_{0}^{lead}

, and furthermore assuming no initial system‐environment correlations,

ρ_{0}^{tot} = ρ_{0} \cdot ρ_{0}^{lead}

, the relaxation dynamics for any time

t > 0

is described by the quantum kinetic equation

\partial_{t} ρ (t) = - italiciL ρ (t) + \int_{0}^{t} {dt}^{'} scriptW false(t - t^{'} false) ρ (t^{'})

.…”

Section: Duality Relation For Open Electronic Systemsmentioning

confidence: 99%

Relaxation of quantum dots in a magnetic field at finite bias – Charge, spin, and heat currents

Vanherck

Schulenborg

Saptsov

et al. 2017

Physica Status Solidi (b)

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We perform a detailed study of the effect of finite bias and magnetic field on the tunneling‐induced decay of the state of a quantum dot by applying a recently discovered general duality [Phys. Rev. B 93, 81411 (2016)]. This duality provides deep physical insight into the decay dynamics of electronic open quantum systems with strong Coulomb interaction. It associates the amplitudes of decay eigenmodes of the actual system to the eigenmodes of a so‐called dual system with attractive interaction. Thereby, it predicts many surprising features in the transient transport and its dependence on experimental control parameters: the attractive interaction of the dual model shows up as sharp features in the amplitudes of measurable time‐dependent currents through the actual repulsive system. In particular, for interacting quantum dots, the time‐dependent heat current exhibits a decay mode that dissipates the interaction energy and that is tied to the fermion parity of the system. We show that its decay amplitude has an unexpected gate‐voltage dependence that is robust up to sizable bias voltages and then bifurcates, reflecting that the Coulomb blockade is lifted in the dual system. Furthermore, combining our duality relation with the known Iche‐duality, we derive new symmetry properties of the decay rates as a function of magnetic field and gate voltage. Finally, we quantify charge‐ and spin‐mode mixing due to the magnetic field using a single mixing parameter.

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“…An open quantum system is most naturally described in terms of its reduced density matrix ρ(t), whose equation of motion is ∂ t ρ(t) = −i[H, ρ(t)] + t 0 dt W(t − t )ρ(t ) [with = k B = e = 1]. The kernel W takes into account the coupling to the external reservoirs [43][44][45][46] that causes ρ(t) to decay. Introducing the Laplace transform of W, W (ω) = ∞ 0 dte iωt W(t), the decay dynamics can be expressed in terms of the frequency(ω)-dependent right eigenvectors of W (ω), the decay modes.…”

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confidence: 99%

“…The kernel W takes into account the coupling to the external reservoirs [43][44][45][46] that causes ρ(t) to decay. Introducing the Laplace transform of…”

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Fermion-parity duality and energy relaxation in interacting open systems

et al. 2016

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We study the transient heat current out of a confined electron system into a weakly coupled electrode in response to a voltage switch. We show that the decay of the Coulomb interaction energy for this repulsive system exhibits signatures of electron-electron attraction, and is governed by an interaction-independent rate. This can only be understood from a general duality that relates the non-unitary evolution of a quantum system to that of a dual model with inverted energies. Deriving from the fermion-parity superselection postulate, this duality applies to a large class of open systems.PACS numbers: 73.63.Kv, Energy decay due to heat currents is of key importance in the continued downscaling of electronic devices [1]. The quantum [2][3][4][5][6] and interaction effects [7][8][9] that arise on the nanoscale give rise to new possibilities [10][11][12][13] and motivate both fundamental [14] and application oriented [3, 4, 8, 13, 15] studies on quantum heatengines, possibly realized in, e.g., cold atoms, trapped ions, or quantum dots. The successful control and exploitation of heat in nanodevices requires both a fundamental understanding and the practical ability to detect and manipulate few-electron heat currents. Under stationary conditions, progress has been achieved using various approaches [16][17][18], including heat transfer through molecular-scale devices [19] with electrostatic gating [20]. However, any device is eventually adjusted by some external agent that provokes a time-dependent response. In the context of electronic heat currents, this raises a very basic question that, despite recent promising theoretical [21][22][23][24][25][26][27] and experimental [28][29][30] studies, has not been answered so far: how does a small electron system, typically governed by a strong level-quantization and Coulomb interaction, dissipate in time its stored energy into a coupled electronic bath?The essence of time-dependent transport in such systems is already captured by the simple model sketched in Figs. 1(a,b). Here, an instant energy shift of a single electronic orbital in a quantum dot leads to a timedependent charge current I N (t) [31,32] and heat current I Q (t) into a tunnel-coupled electrode. In the weak coupling regime, expressions for these currents can be calculated straightforwardly, and in the case of the transient charge current I N (t) also allow for an intuitive physical understanding [33]. This is, however, not the case for the heat current I Q (t) = a c e −γct +a p e −γpt . Compared to the charge current I N (t) ∝ e −γct , the heat current contains a second decay mode. The mere presence of this mode can be expected: it originates from the dissipation of the Coulomb energy. However, what is quite remarkable is that its rate γ p turns out to be completely independent of the interaction strength U [34-37] -despite entering the heat current only as a consequence of the interaction. Even more surprisingly, as indicated by the blue dashed line in Fig. 1(e 2 dealing with a system governed by repulsive i...

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Time-local master equation connecting the Born and Markov approximations

Cited by 22 publications

References 47 publications

Non-Markovian correlation functions for open quantum systems

Non-Markovian correlation functions for open quantum systems

Relaxation of quantum dots in a magnetic field at finite bias – Charge, spin, and heat currents

Fermion-parity duality and energy relaxation in interacting open systems

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