Effective operator formalism for open quantum systems

Reiter, Florentin; Sørensen, Anders S.

doi:10.1103/physreva.85.032111

Cited by 275 publications

(331 citation statements)

References 19 publications

(53 reference statements)

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“…A first general book on the topic has appeared [6]; applications of nonHermitian quantum mechanics involve the study of scattering by complex potentials and quantum transport [7][8][9][10][11][12][13][14][15][16][17], description of metastable states [18][19][20][21][22][23], optical waveguides [24][25][26], multi-photon ionization [27][28][29], and nano-photonic and plasmonic waveguides [30]. The theoretical investigations are also undergoing rapid developments: non-Hermitian quantum mechanics has been investigated within a relativistic framework [31] and it has been adopted by various researchers as a means to describe open quantum systems [32][33][34][35][36][37][38][39][40][41][42]. Moreover, it seems that a few theoretical studies have been dedicated to the statistical mechanics and dynamics of systems with non-Hermitian Hamiltonians [43][44][45][46][47][48][49]...…”

Section: Introductionmentioning

confidence: 99%

Embedding quantum systems with a non-conserved probability in classical environments

Sergi

2015

Theor Chem Acc

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Quantum systems with a non-conserved probability can be described by means of non-HermitianHamiltonians and non-unitary dynamics. In this paper, the case in which the degrees of freedom can be partitioned in two subsets with light and heavy masses is treated. A classical limit over the heavy coordinates is taken in order to embed the non-unitary dynamics of the subsystem in a classical environment. Such a classical environment, in turn, acts as an additional source of dissipation (or noise), beyond that represented by the non-unitary evolution. The non-Hermitian dynamics of a Heisenberg two-spin chain, with the spins independently coupled to harmonic oscillators, is considered in order to illustrate the formalism.

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Section: Introductionmentioning

confidence: 99%

Embedding quantum systems with a non-conserved probability in classical environments

Sergi

2015

Theor Chem Acc

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“…Kubo formulas, for example, describe the response to time-dependent Hamiltonian perturbations. Also for open systems described by Lindblad operators similar formulations of perturbation theory can be developed [1][2][3][4][5][6][7][8][9]. If the density matrix of the unperturbed system is not unique (as is the case for all Hamiltonian systems) one has to use degenerate Liouville perturbation theory [1,7].…”

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confidence: 99%

Perturbative approach to weakly driven many-particle systems in the presence of approximate conservation laws

2018

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We develop a Liouville perturbation theory for weakly driven and weakly open quantum systems in situations when the unperturbed system has a number of conservations laws. If the perturbation violates the conservation laws, it drives the system to a new steady state which can be approximately but efficiently described by a (generalized) Gibbs ensemble characterized by one Lagrange parameter for each conservation law. The value of those has to be determined from rate equations for conserved quantities. Remarkably, even weak perturbations can lead to large responses of conserved quantities. We present a perturbative expansion of the steady state density matrix; first we give the condition that fixes the zeroth order expression (Lagrange parameters) and then determine the higher order corrections via projections of the Liouvillian. The formalism can be applied to a wide range of problems including two-temperature models for electron-phonon systems, Bose condensates of excitons or photons or weakly perturbed integrable models. We test our formalism by studying interacting fermions coupled to non-thermal reservoirs, approximately described by a Boltzmann equation. In equilibrium many particle systems can be efficiently described by Gibbs ensembles, characterized by one Lagrange parameter (inverse temperature, chemical potential) for each exactly conserved quantity (energy, particle number). Such a simple but powerful description is, in general, absent for driven non-equilibrium systems. As long as weak perturbations, which drive the system out of equilibrium, have small effects one can resort to perturbation theory. Kubo formulas, for example, describe the response to time-dependent Hamiltonian perturbations. Also for open systems described by Lindblad operators similar formulations of perturbation theory can be developed [1-9]. If the density matrix of the unperturbed system is not unique (as is the case for all Hamiltonian systems) one has to use degenerate Liouville perturbation theory [1,7].There are many situations where even weak perturbations of interacting many-particle systems can have large effects. A famous example is the Bose-Einstein condensation of excitons and polaritons [10][11][12]: irradiation by light creates more and more excitons which equilibrate approximately and form a Bose-Einstein condensate. Importantly, the exciton number is approximately conserved thus even weak pumping can compensate for exciton losses and leads to large densities of these excitations. Similarly, condensations of photons or magnons have been observed [13][14][15][16][17]. This is a general phenomenon: whenever approximate conservation laws exist, small perturbations which weakly break those conservation laws can drive the system out of equilibrium, to a steady state completely different from the initial one. In the example given above, the approximately conserved quantity is the exciton number. Other examples use the approximate conservation of spin to induce large nuclear spin polarization [18] for medical applications o...

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“…If there are disparate-fast and slow-time scales in the dynamics of a system, AE provides an efficient procedure to adiabatically eliminate quantized levels that give rise to fast oscillations. This method is, however, rather difficult to use and often requires tedious steps; accordingly, an easier and more practical version sharing the same spirit has recently been proposed [10]. Most AE methods, though, require definite knowledge of high-and low-energy manifolds, i.e., those to be removed and retained, respectively.…”

Section: Introductionmentioning

confidence: 99%

Effective formalism for open-quantum-system dynamics: Time-coarse-graining approach

2018

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We formulate an effective-description framework for the dynamics of open quantum systems by extending the time-coarse-graining formalism to open systems. Our coarse-graining procedure efficiently removes highfrequency processes which are responsible for coherences between lower-and upper-manifold states and are irrelevant when considering only low-energy dynamics. We investigate the regime of validity of the resulting coarse-grained master equation by applying it to multi-level atoms driven by far-detuned lasers. Except for such high-frequency coherences, we find good agreement between the exact and coarse-grained dynamics unless the driving lasers are too strong or the initial high-frequency coherences are sizable.

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Effective operator formalism for open quantum systems

Cited by 275 publications

References 19 publications

Embedding quantum systems with a non-conserved probability in classical environments

Embedding quantum systems with a non-conserved probability in classical environments

Perturbative approach to weakly driven many-particle systems in the presence of approximate conservation laws

Effective formalism for open-quantum-system dynamics: Time-coarse-graining approach

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