Linear-algebraic bath transformation for simulating complex open quantum systems

Huh, Joonsuk; Mostame, Sarah; Fujita, Takatoshi; Yung, Man‐Hong; Aspuru‐Guzik, Alán

doi:10.1088/1367-2630/16/12/123008

Cited by 22 publications

(17 citation statements)

References 77 publications

(132 reference statements)

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“…Though we have seen in section 2 that the overall coupling strength of the original system to the environment can be captured by using only one RC, the resulting final SD in general depends on the shape of the initial SD (but not on its 'absolute value') and might be still large compared to parameters of the system, which has to be checked in each case separately. Still, the RC method allows us to go beyond the standard perturbative approach in a reasonable way and furthermore, by applying a conceptually similar yet technically different mapping, one can show that also the resulting SD becomes small [81].…”

Section: Final Remarksmentioning

confidence: 99%

Nonequilibrium thermodynamics in the strong coupling and non-Markovian regime based on a reaction coordinate mapping

et al. 2016

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We propose a method to study the thermodynamic behaviour of small systems beyond the weak coupling and Markovian approximation, which is different in spirit from conventional approaches. The idea is to redefine the system and environment such that the effective, redefined system is again coupled weakly to Markovian residual baths and thus, allows to derive a consistent thermodynamic framework for this new system-environment partition. To achieve this goal we make use of the reaction coordinate (RC) mapping, which is a general method in the sense that it can be applied to an arbitrary (quantum or classical and even time-dependent) system coupled linearly to an arbitrary number of harmonic oscillator reservoirs. The core of the method relies on an appropriate identification of a part of the environment (the RC), which is subsequently included as a part of the system. We demonstrate the power of this concept by showing that non-Markovian effects can significantly enhance the steady state efficiency of a three-level-maser heat engine, even in the regime of weak system-bath coupling. Furthermore, we show for a single electron transistor coupled to vibrations that our method allows one to justify master equations derived in a polaron transformed reference frame.can then be shown to have a transparent thermodynamic interpretation [3-5] and they provide the work horse for the field of quantum and stochastic thermodynamics, see [6][7][8][9][10] for recent reviews.However, many interesting physical effects cannot be captured with such a ME approach and thus, quantum and stochastic thermodynamics is still restricted to a small regime of applicability. Consequently, many groups have started to look at thermodynamics in the strong coupling and non-Markovian regime . Though these works present important theoretical cornerstones, they are still far away from providing a satisfactory extension of thermodynamics beyond the weak coupling limit. In particular, if one wishes to address the performance of a steadily working heat engine, the general results derived in [11][12][13][14][15][16][17][18][19][20][21] are not of great help because they either focus on integrated changes of thermodynamic values (e.g., the total heat exchanged in a finite time instead of the rate of heat exchange) and additionally rely on an initially decorrelated system-environment state [11][12][13] and/or coupling only to a single thermal reservoir [11,[13][14][15][16][17];or they remain very formal [18][19][20][21]. Furthermore, model-specific studies are either based on simple or exactly solvable models from the field of quantum transport [22][23][24][25] and quantum Brownian motion [26][27][28][29], or spin-boson models [30][31][32] often in combination with specific transformations applicable only to special Hamiltonians (polaron transformations) [31,[33][34][35][36]; or the investigations are restricted to numerical studies [37].The goal of this paper is to close the gap between the general results, which are often hard to apply in practice, and studi...

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Section: Final Remarksmentioning

confidence: 99%

Nonequilibrium thermodynamics in the strong coupling and non-Markovian regime based on a reaction coordinate mapping

et al. 2016

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“…Similar mappings are frequently used in the literature to treat strong-coupling limits. When they only involve position operators, the collective mode is then called reaction-coordinate [36][37][38], but also mappings to different lattice topologies exist [39].…”

Section: B Explicit Bogoliubov Mappingmentioning

confidence: 99%

Collective couplings: Rectification and supertransmittance

2016

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We investigate heat transport between two thermal reservoirs that are coupled via a large spin composed of N identical two level systems. One coupling implements the dissipative Dicke superradiance. The other coupling is locally of the pure-dephasing type and requires to go beyond the standard weak-coupling limit by employing a Bogoliubov mapping in the corresponding reservoir. After the mapping, the large spin is coupled to a collective mode with the original pure-dephasing interaction, but the collective mode is dissipatively coupled to the residual oscillators. Treating the large spin and the collective mode as the system, a standard master equation approach is now able to capture the energy transfer between the two reservoirs. Assuming fast relaxation of the collective mode, we derive a coarse-grained rate equation for the large spin only and discuss how the original Dicke superradiance is affected by the presence of the additional reservoir. Our main finding is a cooperatively enhanced rectification effect due to the interplay of supertransmittant heat currents (scaling quadratically with N ) and the asymmetric coupling to both reservoirs. For large N , the system can thus significantly amplify current asymmetries under bias reversal, functioning as a heat diode. We also briefly discuss the case when the couplings of the collective spin are locally dissipative, showing that the heat-diode effect is still present. I. MOTIVATIONThe study of radiative effects in two-level systems has a long history. Here, the spin-boson model [1] takes a very prominent role. Originating from the interaction of a two-level atom with the electromagnetic field [2], it is often used as a toy model in many other contexts. Not surprisingly, it has become a canonical model to explore fundamental methods of open systems [3][4][5] and effectively arises in a rather large number of physical systems and effects, including e.g. the dynamics of light-harvesting complexes [6], detectors [7], and the interaction of quantum dots with generalized environments [8].Ideally, one aims at a reduced description taking only the finite-dimensional spin dynamics into account. However, when the number of spins is increased, the curse of dimensionality -the exponential growth of the system Hilbert space with its size -usually inhibits investigations of large spin-boson models. When additional symmetries come into play -e.g. when the spins have the same splitting and couple collectively to all other componentssimplified descriptions are applicable. Collective effects may for example dramatically influence the dephasing behavior of the environment, leading to phenomena such as super-and sub-decoherence [9,10]. Furthermore, they play a significant role in the modelling of light-harvesting complexes [11][12][13][14]. Perhaps one of the clearest manifesta- * gernot.schaller@tu-berlin.de tions of collective behaviour is Dicke superradiance [15]. Here, the collectivity of the coupling between N two-level atoms and a low-temperature bosonic reservoir induces an...

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“…In the context of linear bosonic reservoirs (Caldeira-Leggett or Brownian motion models), this technique has a longer tradition 6 . It has found various applications in the theory of open quantum systems [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] and it is also closely related to the "time evolving density matrix using orthogonal polynomials algorithm" (TEDOPA) [23][24][25][26][27][28] . We remark that, although it shares many similarities with the bosonic case, the RC mapping was not studied for fermionic reservoirs before.…”

Section: Introductionmentioning

confidence: 99%

Fermionic reaction coordinates and their application to an autonomous Maxwell demon in the strong-coupling regime

et al. 2018

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We establish a theoretical method which goes beyond the weak-coupling and Markovian approximations while remaining intuitive, using a quantum master equation in a larger Hilbert space. The method is applicable to all impurity Hamiltonians tunnel coupled to one (or multiple) baths of free fermions. The accuracy of the method is in principle not limited by the system-bath coupling strength, but rather by the shape of the spectral density and it is especially suited to study situations far away from the wide-band limit. In analogy to the bosonic case, we call it the fermionic reaction coordinate mapping. As an application, we consider a thermoelectric device made of two Coulomb-coupled quantum dots. We pay particular attention to the regime where this device operates as an autonomous Maxwell demon shoveling electrons against the voltage bias thanks to information. Contrary to previous studies, we do not rely on a Markovian weak-coupling description. Our numerical findings reveal that in the regime of strong coupling and non-Markovianity, the Maxwell demon is often doomed to disappear except in a narrow parameter regime of small power output.

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Linear-algebraic bath transformation for simulating complex open quantum systems

Cited by 22 publications

References 77 publications

Nonequilibrium thermodynamics in the strong coupling and non-Markovian regime based on a reaction coordinate mapping

Nonequilibrium thermodynamics in the strong coupling and non-Markovian regime based on a reaction coordinate mapping

Collective couplings: Rectification and supertransmittance

Fermionic reaction coordinates and their application to an autonomous Maxwell demon in the strong-coupling regime

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