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Efficient choice of colored noise in the stochastic dynamics of open quantum systems

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Efficient choice of colored noise in the stochastic dynamics of open quantum systems. / Matos, D.; Lane, M. A.; Ford, I. J.; Kantorovich, L.

In: Physical Review E, Vol. 102, No. 6, 062134, 16.12.2020.

Research output: Contribution to journalArticlepeer-review

Harvard

Matos, D, Lane, MA, Ford, IJ & Kantorovich, L 2020, 'Efficient choice of colored noise in the stochastic dynamics of open quantum systems', Physical Review E, vol. 102, no. 6, 062134. https://doi.org/10.1103/PhysRevE.102.062134

APA

Matos, D., Lane, M. A., Ford, I. J., & Kantorovich, L. (2020). Efficient choice of colored noise in the stochastic dynamics of open quantum systems. Physical Review E, 102(6), [062134]. https://doi.org/10.1103/PhysRevE.102.062134

Vancouver

Matos D, Lane MA, Ford IJ, Kantorovich L. Efficient choice of colored noise in the stochastic dynamics of open quantum systems. Physical Review E. 2020 Dec 16;102(6). 062134. https://doi.org/10.1103/PhysRevE.102.062134

Author

Matos, D. ; Lane, M. A. ; Ford, I. J. ; Kantorovich, L. / Efficient choice of colored noise in the stochastic dynamics of open quantum systems. In: Physical Review E. 2020 ; Vol. 102, No. 6.

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@article{8897d63f1516462798a1cf278ae9a3ca,
title = "Efficient choice of colored noise in the stochastic dynamics of open quantum systems",
abstract = "The stochastic Liouville-von Neumann (SLN) equation describes the dynamics of an open quantum system reduced density matrix coupled to a non-Markovian harmonic environment. The interaction with the environment is represented by complex colored noises which drive the system, and whose correlation functions are set by the properties of the environment. We present a number of schemes capable of generating colored noises of this kind that are built on a noise amplitude reduction procedure [Imai et al., Chem. Phys. 446, 134 (2015)CMPHC20301-010410.1016/j.chemphys.2014.11.014], including two analytically optimized schemes. In doing so, we pay close attention to the properties of the correlation functions in Fourier space, which we derive in full. For some schemes the method of Wiener filtering for deconvolutions leads to the realization that weakening causality in one of the noise correlation functions improves numerical convergence considerably, allowing us to introduce a well-controlled method for doing so. We compare the ability of these schemes, along with an alternative optimized scheme [Schmitz and Stockburger, Eur. Phys. J.: Spec. Top. 227, 1929 (2019)1951-635510.1140/epjst/e2018-800094-y], to reduce the growth in the mean and variance of the trace of the reduced density matrix, and their ability to extend the region in which the dynamics is stable and well converged for a range of temperatures. By numerically optimizing an additional noise scaling freedom, we identify the scheme which performs best for the parameters used, improving convergence by orders of magnitude and increasing the time accessible by simulation.",
author = "D. Matos and Lane, {M. A.} and Ford, {I. J.} and L. Kantorovich",
year = "2020",
month = dec,
day = "16",
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language = "English",
volume = "102",
journal = "Physical review. E",
issn = "2470-0045",
publisher = "American Physical Society",
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}

RIS (suitable for import to EndNote) Download

TY - JOUR

T1 - Efficient choice of colored noise in the stochastic dynamics of open quantum systems

AU - Matos, D.

AU - Lane, M. A.

AU - Ford, I. J.

AU - Kantorovich, L.

PY - 2020/12/16

Y1 - 2020/12/16

N2 - The stochastic Liouville-von Neumann (SLN) equation describes the dynamics of an open quantum system reduced density matrix coupled to a non-Markovian harmonic environment. The interaction with the environment is represented by complex colored noises which drive the system, and whose correlation functions are set by the properties of the environment. We present a number of schemes capable of generating colored noises of this kind that are built on a noise amplitude reduction procedure [Imai et al., Chem. Phys. 446, 134 (2015)CMPHC20301-010410.1016/j.chemphys.2014.11.014], including two analytically optimized schemes. In doing so, we pay close attention to the properties of the correlation functions in Fourier space, which we derive in full. For some schemes the method of Wiener filtering for deconvolutions leads to the realization that weakening causality in one of the noise correlation functions improves numerical convergence considerably, allowing us to introduce a well-controlled method for doing so. We compare the ability of these schemes, along with an alternative optimized scheme [Schmitz and Stockburger, Eur. Phys. J.: Spec. Top. 227, 1929 (2019)1951-635510.1140/epjst/e2018-800094-y], to reduce the growth in the mean and variance of the trace of the reduced density matrix, and their ability to extend the region in which the dynamics is stable and well converged for a range of temperatures. By numerically optimizing an additional noise scaling freedom, we identify the scheme which performs best for the parameters used, improving convergence by orders of magnitude and increasing the time accessible by simulation.

AB - The stochastic Liouville-von Neumann (SLN) equation describes the dynamics of an open quantum system reduced density matrix coupled to a non-Markovian harmonic environment. The interaction with the environment is represented by complex colored noises which drive the system, and whose correlation functions are set by the properties of the environment. We present a number of schemes capable of generating colored noises of this kind that are built on a noise amplitude reduction procedure [Imai et al., Chem. Phys. 446, 134 (2015)CMPHC20301-010410.1016/j.chemphys.2014.11.014], including two analytically optimized schemes. In doing so, we pay close attention to the properties of the correlation functions in Fourier space, which we derive in full. For some schemes the method of Wiener filtering for deconvolutions leads to the realization that weakening causality in one of the noise correlation functions improves numerical convergence considerably, allowing us to introduce a well-controlled method for doing so. We compare the ability of these schemes, along with an alternative optimized scheme [Schmitz and Stockburger, Eur. Phys. J.: Spec. Top. 227, 1929 (2019)1951-635510.1140/epjst/e2018-800094-y], to reduce the growth in the mean and variance of the trace of the reduced density matrix, and their ability to extend the region in which the dynamics is stable and well converged for a range of temperatures. By numerically optimizing an additional noise scaling freedom, we identify the scheme which performs best for the parameters used, improving convergence by orders of magnitude and increasing the time accessible by simulation.

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DO - 10.1103/PhysRevE.102.062134

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JO - Physical review. E

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SN - 2470-0045

IS - 6

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ER -

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