Witnessing the boundary between Markovian and non-Markovian quantum dynamics: a Green’s function approach

Shibei Xue; Rebing Wu; Tzyh Jong Tarn; Ian R. Petersen

doi:10.1007/s11128-015-1000-6

Witnessing the boundary between Markovian and non-Markovian quantum dynamics: a Green’s function approach

Shibei Xue^*, Rebing Wu, Tzyh Jong Tarn, Ian R. Petersen

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

This paper presents a Green’s function-based root locus method to investigate the boundary between Markovian and non-Markovian open quantum systems in the frequency domain. A Langevin equation for the boson-boson coupling system is derived, where we show that the structure of the Green’s function dominates the system dynamics. In addition, by increasing the coupling between the system and its environment, the system dynamics are driven from Markovian to non-Markovian dynamics, which results from the redistribution in the modes of the Green’s function in the frequency domain. Both a critical transition and a critical point condition under Lorentzian noise are graphically presented using a root locus method. Related results are verified using an example of a boson-boson coupling system.

Original language	English
Pages (from-to)	2657-2672
Number of pages	16
Journal	Quantum Information Processing
Volume	14
Issue number	7
DOIs	https://doi.org/10.1007/s11128-015-1000-6
Publication status	Published - 12 Jul 2015
Externally published	Yes

Access to Document

10.1007/s11128-015-1000-6

Cite this

@article{ec68eeaa48d140a0ba742968471eafa4,

title = "Witnessing the boundary between Markovian and non-Markovian quantum dynamics: a Green{\textquoteright}s function approach",

abstract = "This paper presents a Green{\textquoteright}s function-based root locus method to investigate the boundary between Markovian and non-Markovian open quantum systems in the frequency domain. A Langevin equation for the boson-boson coupling system is derived, where we show that the structure of the Green{\textquoteright}s function dominates the system dynamics. In addition, by increasing the coupling between the system and its environment, the system dynamics are driven from Markovian to non-Markovian dynamics, which results from the redistribution in the modes of the Green{\textquoteright}s function in the frequency domain. Both a critical transition and a critical point condition under Lorentzian noise are graphically presented using a root locus method. Related results are verified using an example of a boson-boson coupling system.",

keywords = "Critical transition, Green{\textquoteright}s function, Markovian dynamics, Non-Markovian open quantum systems, Root locus",

author = "Shibei Xue and Rebing Wu and Tarn, {Tzyh Jong} and Petersen, {Ian R.}",

note = "Publisher Copyright: {\textcopyright} 2015, Springer Science+Business Media New York.",

year = "2015",

month = jul,

day = "12",

doi = "10.1007/s11128-015-1000-6",

language = "English",

volume = "14",

pages = "2657--2672",

journal = "Quantum Information Processing",

issn = "1570-0755",

publisher = "Springer",

number = "7",

}

TY - JOUR

T1 - Witnessing the boundary between Markovian and non-Markovian quantum dynamics

T2 - a Green’s function approach

AU - Xue, Shibei

AU - Wu, Rebing

AU - Tarn, Tzyh Jong

AU - Petersen, Ian R.

PY - 2015/7/12

Y1 - 2015/7/12

N2 - This paper presents a Green’s function-based root locus method to investigate the boundary between Markovian and non-Markovian open quantum systems in the frequency domain. A Langevin equation for the boson-boson coupling system is derived, where we show that the structure of the Green’s function dominates the system dynamics. In addition, by increasing the coupling between the system and its environment, the system dynamics are driven from Markovian to non-Markovian dynamics, which results from the redistribution in the modes of the Green’s function in the frequency domain. Both a critical transition and a critical point condition under Lorentzian noise are graphically presented using a root locus method. Related results are verified using an example of a boson-boson coupling system.

AB - This paper presents a Green’s function-based root locus method to investigate the boundary between Markovian and non-Markovian open quantum systems in the frequency domain. A Langevin equation for the boson-boson coupling system is derived, where we show that the structure of the Green’s function dominates the system dynamics. In addition, by increasing the coupling between the system and its environment, the system dynamics are driven from Markovian to non-Markovian dynamics, which results from the redistribution in the modes of the Green’s function in the frequency domain. Both a critical transition and a critical point condition under Lorentzian noise are graphically presented using a root locus method. Related results are verified using an example of a boson-boson coupling system.

KW - Critical transition

KW - Green’s function

KW - Markovian dynamics

KW - Non-Markovian open quantum systems

KW - Root locus

UR - http://www.scopus.com/inward/record.url?scp=84930758265&partnerID=8YFLogxK

U2 - 10.1007/s11128-015-1000-6

DO - 10.1007/s11128-015-1000-6

M3 - Article

SN - 1570-0755

VL - 14

SP - 2657

EP - 2672

JO - Quantum Information Processing

JF - Quantum Information Processing

IS - 7

ER -

Witnessing the boundary between Markovian and non-Markovian quantum dynamics: a Green’s function approach

Abstract

Access to Document

Other files and links

Fingerprint

Cite this