Quantum dynamics for a system coupled to slow baths: On-the-fly filtered propagator method

Sim, Eunji

doi:10.1063/1.1394208

Cited by 84 publications

(106 citation statements)

References 12 publications

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“…(6) are done using the augmented density matrix algorithm [11], supplemented with the method of "on-fly screening" [12]. This algorithm utilizes the fact that for the LA pho- …”

Section: Numerical Calculation Methodsmentioning

confidence: 99%

“…In this case the path integral can be reformulated as a pseudo-Markovian evolution of the so-called augmented density matrix. Here we apply a modification of this formalism combined with the "on-fly" path selection algorithm [12] to study the dynamics of Rabi oscillations in quantum dots. We obtain numerically accurate the dynamics of the system and study the previously inaccessible regime of long evolution times and high temperatures.…”

Section: Introductionmentioning

confidence: 99%

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High pulse area undamping of Rabi oscillations in quantum dots coupled to phonons

Vagov

Croitoru

Axt

et al. 2006

Physica Status Solidi (b)

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We study the dynamics of strongly confined semiconductor quantum dots, coupled to acoustic phonons and driven by external laser pulses, by a numerical path integral method. Our method fully explores the relevant memory of the system thus accounting for all non-Markovian features of the dynamics. The decay time and the frequency of Rabi oscillations are found to depend notably on the temperature and the applied field. The field dependence is non-monotonic leading to an undamping of Rabi oscillations at high pulse areas.

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“…(6) are done using the augmented density matrix algorithm [11], supplemented with the method of "on-fly screening" [12]. This algorithm utilizes the fact that for the LA pho- …”

Section: Numerical Calculation Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

High pulse area undamping of Rabi oscillations in quantum dots coupled to phonons

Vagov

Croitoru

Axt

et al. 2006

Physica Status Solidi (b)

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“…[52][53][54] Much effort has been made to overcome these problems and extend the applicability of this method. [55][56][57][58][59][60][61][62][63][64] Because this approach can easily incorporate the semi-classical approximation for the bath, it may be advantageous in the study of polyatomic systems treated in multi-dimensional coordinates, but applications to this point incorporating full quantum mechanical dynamics have been limited to relatively small systems without time-dependent external force.…”

Section: Introductionmentioning

confidence: 99%

Real-time and imaginary-time quantum hierarchal Fokker-Planck equations

Tanimura

2015

The Journal of Chemical Physics

128

237

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We consider a quantum mechanical system represented in phase space (referred to hereafter as "Wigner space"), coupled to a harmonic oscillator bath. We derive quantum hierarchal Fokker-Planck (QHFP) equations not only in real time but also in imaginary time, which represents an inverse temperature. This is an extension of a previous work, in which we studied a spin-boson system, to a Brownian system. It is shown that the QHFP in real time obtained from a correlated thermal equilibrium state of the total system possesses the same form as those obtained from a factorized initial state. A modified terminator for the hierarchal equations of motion is introduced to treat the non-Markovian case more efficiently. Using the imaginary-time QHFP, numerous thermodynamic quantities, including the free energy, entropy, internal energy, heat capacity, and susceptibility, can be evaluated for any potential. These equations allow us to treat non-Markovian, non-perturbative system-bath interactions at finite temperature. Through numerical integration of the real-time QHFP for a harmonic system, we obtain the equilibrium distributions, the auto-correlation function, and the first-and second-order response functions. These results are compared with analytically exact results for the same quantities. This provides a critical test of the formalism for a non-factorized thermal state and elucidates the roles of fluctuation, dissipation, non-Markovian effects, and systembath coherence. Employing numerical solutions of the imaginary-time QHFP, we demonstrate the capability of this method to obtain thermodynamic quantities for any potential surface. It is shown that both types of QHFP equations can produce numerical results of any desired accuracy. The FORTRAN source codes that we developed, which allow for the treatment of Wigner space dynamics with any potential form (TanimuranFP15 and ImTanimuranFP15), are provided as the supplementary material. C 2015 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License. [http://dx

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“…(1) the path integral method is able to deliver a full solution for the dynamics of the electronic subsystem with a controlled accuracy [7][8][9][10]. The method directly evaluates the time evolution operator b UðtÞ at discrete times.…”

Section: Modelmentioning

confidence: 99%

Dynamics of quantum dots with strong electron phonon coupling: Correlation expansion vs. path integrals

Vagov¹,

Croitoru²,

Axt³

et al. 2011

Physica Status Solidi (b)

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We have simulated coherent control signals from quantum dots for carrier phonon interactions covering the low as well as the strong coupling limit. Calculations using the correlation expansion for phonon assisted density matrices are compared with numerically exact results obtained from a time dependent path-integral approach. Even at elevated coupling strengths both calculations agree well for not too high temperatures. For pulse lengths and delay times shorter than the phonon induced memory time the correlation expansion gives good results in almost all cases. For strong coupling and/or high temperatures drastic discrepancies emerge. Interestingly, the correlation expansion works better at high pulse areas, which is related to a dynamic decoupling of electron and phonon dynamics in strongly confined systems. 1 Introduction For theoretical studies of the combined dynamics of carriers and phonons in optically excited semiconductor nanostructures, the correlation expansion for the elements of the density matrix is one of the most widely used tools that has been applied to quantum dots [1-3] as well as to higher dimensional structures [4,5]. Within this approach, the infinite hierarchy of phonon assisted density matrices is truncated by factorizing higher order correlation functions on a chosen level. Although the solution of the corresponding dynamical equations contains contributions of any order in the carrier phonon coupling, higher orders are treated only approximately. While for small couplings the truncation scheme is generally expected to yield reliable results, it is an open question where its limits of validity are for increased interaction strength. Moreover, these limits may depend on temperature and on the excitation conditions.For strongly confined quantum dots coupled to acoustic phonons, numerically exact results for the dynamics of the elements of the carrier density matrix are available by means of the time dependent path integral method and can be used to test the range of validity of the correlation expansion on a given level of truncation. It is known that in the linear

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Quantum dynamics for a system coupled to slow baths: On-the-fly filtered propagator method

Cited by 84 publications

References 12 publications

High pulse area undamping of Rabi oscillations in quantum dots coupled to phonons

High pulse area undamping of Rabi oscillations in quantum dots coupled to phonons

Real-time and imaginary-time quantum hierarchal Fokker-Planck equations

Dynamics of quantum dots with strong electron phonon coupling: Correlation expansion vs. path integrals

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