DOI: 10.1063/1.1331613. Quantum time correlation functions from complex time Monte Carlo simulations: A maximum entropy approach

Quantum time correlation functions from complex time Monte Carlo simulations: A maximum entropy approach

10.1063/1.1331613

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

We present a way of combining real-time path integral Monte Carlo simulations with a maximum entropy numerical analytic continuation scheme in a new approach for calculating time correlation functions for finite temperature many body quantum systems. The real-time dynamics is expressed in the form of the symmetrized time correlation function, which is suitable for Monte Carlo methods, and several simulation techniques are presented for evaluating this function accurately up to moderate values of time. The symmetrized time correlation function is then analytically continued in combination with imaginary time data to obtain the real-time correlation function. We test this approach on several exactly solvable problems, including two one-dimensional systems, as well two cases of vibrational relaxation of a system coupled to a dissipative environment. The computed time correlation functions are in good agreement with exact results over several multiples of the thermal time βℏ, and exhibit a significant improvement over analytic continuation of imaginary time correlation functions. Moreover, we show how the method can be systematically improved.

Bibliography

Krilov, G., Sim, E., & Berne, B. J. (2001). Quantum time correlation functions from complex time Monte Carlo simulations: A maximum entropy approach. The Journal of Chemical Physics, 114(3), 1075â1088.

Authors 3

Goran Krilov (first)
Eunji Sim (additional)
B. J. Berne (additional)

References 64 Referenced 47

10.1063/1.1699114 / J. Chem. Phys. (1953)
{'key': '2024020522082435600_r2'}
10.1103/PhysRev.136.A405 / Phys. Rev. A (1964)
{'key': '2024020522082435600_r4'}
10.1063/1.431514 / J. Chem. Phys. (1975)
10.1063/1.432868 / J. Chem. Phys. (1976)
10.1063/1.440575 / J. Chem. Phys. (1980)
{'key': '2024020522082435600_r8'}
10.1103/PhysRev.171.128 / Phys. Rev. (1968)
10.1063/1.446740 / J. Chem. Phys. (1984)
10.1007/BF02650179 / Int. J. Theor. Phys. (1982)
10.1016/S0550-3213(86)80034-7 / Nucl. Phys. B (1986)
10.1016/0009-2614(88)87380-9 / Chem. Phys. Lett. (1988)
10.1063/1.455551 / J. Chem. Phys. (1988)
10.1063/1.455061 / J. Chem. Phys. (1988)
10.1103/PhysRevA.41.5709 / Phys. Rev. A (1990)
10.1103/PhysRevA.44.2352 / Phys. Rev. A (1991)
10.1016/0009-2614(93)89135-5 / Chem. Phys. Lett. (1993)
10.1016/0009-2614(92)85654-S / Chem. Phys. Lett. (1992)
10.1021/j100112a050 / J. Chem. Phys. (1993)
10.1103/PhysRevLett.68.899 / Phys. Rev. Lett. (1992)
10.1103/PhysRevB.50.15210 / Phys. Rev. B (1994)
10.1063/1.478077 / J. Chem. Phys. (1999)
10.1103/PhysRevE.61.5961 / Phys. Rev. E (2000)
10.1063/1.1674535 / J. Chem. Phys. (1970)
10.1016/0301-0104(84)80039-7 / Chem. Phys. (1984)
10.1063/1.459848 / J. Chem. Phys. (1991)
10.1063/1.466320 / J. Chem. Phys. (1994)
10.1016/S0375-9601(98)00265-5 / Phys. Lett. A (1998)
10.1063/1.478571 / J. Chem. Phys. (1999)
10.1063/1.467175 / J. Chem. Phys. (1994)
10.1063/1.467176 / J. Chem. Phys. (1994)
10.1063/1.468503 / J. Chem. Phys. (1994)
{'key': '2024020522082435600_r34', 'first-page': '39', 'volume': '93', 'year': '1996', 'journal-title': 'Adv. Chem. Phys.'} / Adv. Chem. Phys. (1996)
10.1063/1.467892 / J. Chem. Phys. (1994)
10.1063/1.472508 / J. Chem. Phys. (1996)
10.1063/1.475227 / J. Chem. Phys. (1997)
10.1063/1.477420 / J. Chem. Phys. (1998)
10.1063/1.480834 / J. Chem. Phys. (2000)
10.1063/1.480028 / J. Chem. Phys. (1999)
10.1063/1.475790 / J. Chem. Phys. (1998)
10.1063/1.447913 / J. Chem. Phys. (1984)
10.1063/1.445601 / J. Chem. Phys. (1983)
10.1146/annurev.pc.37.100186.002153 / Annu. Rev. Phys. Chem. (1986)
10.1063/1.449861 / J. Chem. Phys. (1985)
{'key': '2024020522082435600_r46'}
{'key': '2024020522082435600_r47', 'first-page': '2796', 'volume': '99', 'year': '1983', 'journal-title': 'J. Chem. Phys.'} / J. Chem. Phys. (1983)
10.1007/BF01008729 / J. Stat. Phys. (1973)
10.1016/0003-4916(63)90068-X / Ann. Phys. (N.Y.) (1963)
{'key': '2024020522082435600_r50'}
10.1090/S0002-9939-1959-0108732-6 / Proc. Am. Math. Soc. (1959)
10.1103/PhysRevLett.63.1195 / Phys. Rev. Lett. (1989)
10.1016/0009-2614(74)80109-0 / Chem. Phys. Lett. (1974)
10.1016/S0009-2614(98)00736-2 / Chem. Phys. Lett. (1998)
10.1063/1.468244 / J. Chem. Phys. (1994)
10.1063/1.1703704 / J. Math. Phys. (1961)
10.1103/PhysRevB.44.6011 / Phys. Rev. B (1991)
{'key': '2024020522082435600_r58'}
10.1016/0370-1573(95)00074-7 / Phys. Rep. (1996)
{'key': '2024020522082435600_r60'}
{'key': '2024020522082435600_r61', 'first-page': '52', 'volume': '1', 'year': '1970', 'journal-title': 'SIAM (Soc. Ind. Appl. Math.) J. Math. Anal.'} / SIAM (Soc. Ind. Appl. Math.) J. Math. Anal. (1970)
10.1007/BF02427376 / Eur. Biophys. J. (1990)
10.1063/1.458647 / J. Chem. Phys. (1990)
10.1063/1.466780 / J. Chem. Phys. (1994)

Dates

Type	When
Created	23 years, 1 month ago (July 26, 2002, 10:13 a.m.)
Deposited	1 year, 6 months ago (Feb. 5, 2024, 6:17 p.m.)
Indexed	1 year, 6 months ago (Feb. 11, 2024, 7:59 a.m.)
Issued	24 years, 7 months ago (Jan. 15, 2001)
Published	24 years, 7 months ago (Jan. 15, 2001)
Published Print	24 years, 7 months ago (Jan. 15, 2001)

Funders 0

None

BibTeX

@article{Krilov_2001, title={Quantum time correlation functions from complex time Monte Carlo simulations: A maximum entropy approach}, volume={114}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.1331613}, DOI={10.1063/1.1331613}, number={3}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Krilov, Goran and Sim, Eunji and Berne, B. J.}, year={2001}, month=jan, pages={1075–1088} }

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      "first-page": "3897",
      "DOI": "10.1063/1.440575",
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      "year": "1980",
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      "first-page": "128",
      "DOI": "10.1103/PhysRev.171.128",
      "volume": "171",
      "year": "1968",
      "journal-title": "Phys. Rev."
    },
    {
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      "doi-asserted-by": "crossref",
      "first-page": "860",
      "DOI": "10.1063/1.446740",
      "volume": "80",
      "year": "1984",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020522082435600_r11",
      "doi-asserted-by": "crossref",
      "first-page": "467",
      "DOI": "10.1007/BF02650179",
      "volume": "21",
      "year": "1982",
      "journal-title": "Int. J. Theor. Phys."
    },
    {
      "key": "2024020522082435600_r12",
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      "first-page": "717",
      "DOI": "10.1016/S0550-3213(86)80034-7",
      "volume": "271",
      "year": "1986",
      "journal-title": "Nucl. Phys. B"
    },
    {
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      "first-page": "277",
      "DOI": "10.1016/0009-2614(88)87380-9",
      "volume": "143",
      "year": "1988",
      "journal-title": "Chem. Phys. Lett."
    },
    {
      "key": "2024020522082435600_r14",
      "doi-asserted-by": "crossref",
      "first-page": "5753",
      "DOI": "10.1063/1.455551",
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      "year": "1988",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020522082435600_r15",
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      "first-page": "2170",
      "DOI": "10.1063/1.455061",
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      "year": "1988",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020522082435600_r16",
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      "first-page": "5709",
      "DOI": "10.1103/PhysRevA.41.5709",
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      "first-page": "2352",
      "DOI": "10.1103/PhysRevA.44.2352",
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    {
      "key": "2024020522082435600_r18",
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      "first-page": "285",
      "DOI": "10.1016/0009-2614(93)89135-5",
      "volume": "210",
      "year": "1993",
      "journal-title": "Chem. Phys. Lett."
    },
    {
      "key": "2024020522082435600_r19",
      "doi-asserted-by": "crossref",
      "first-page": "435",
      "DOI": "10.1016/0009-2614(92)85654-S",
      "volume": "193",
      "year": "1992",
      "journal-title": "Chem. Phys. Lett."
    },
    {
      "key": "2024020522082435600_r20",
      "doi-asserted-by": "crossref",
      "first-page": "2417",
      "DOI": "10.1021/j100112a050",
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    },
    {
      "key": "2024020522082435600_r21",
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      "first-page": "899",
      "DOI": "10.1103/PhysRevLett.68.899",
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      "year": "1992",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "2024020522082435600_r22",
      "doi-asserted-by": "crossref",
      "first-page": "15210",
      "DOI": "10.1103/PhysRevB.50.15210",
      "volume": "50",
      "year": "1994",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024020522082435600_r23",
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      "first-page": "12",
      "DOI": "10.1063/1.478077",
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      "year": "1999",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020522082435600_r24",
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      "first-page": "5961",
      "DOI": "10.1103/PhysRevE.61.5961",
      "volume": "61",
      "year": "2000",
      "journal-title": "Phys. Rev. E"
    },
    {
      "key": "2024020522082435600_r25",
      "doi-asserted-by": "crossref",
      "first-page": "3578",
      "DOI": "10.1063/1.1674535",
      "volume": "53",
      "year": "1970",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020522082435600_r26",
      "doi-asserted-by": "crossref",
      "first-page": "27",
      "DOI": "10.1016/0301-0104(84)80039-7",
      "volume": "91",
      "year": "1984",
      "journal-title": "Chem. Phys."
    },
    {
      "key": "2024020522082435600_r27",
      "doi-asserted-by": "crossref",
      "first-page": "2723",
      "DOI": "10.1063/1.459848",
      "volume": "94",
      "year": "1991",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020522082435600_r28",
      "doi-asserted-by": "crossref",
      "first-page": "4377",
      "DOI": "10.1063/1.466320",
      "volume": "100",
      "year": "1994",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020522082435600_r29",
      "doi-asserted-by": "crossref",
      "first-page": "243",
      "DOI": "10.1016/S0375-9601(98)00265-5",
      "volume": "243",
      "year": "1998",
      "journal-title": "Phys. Lett. A"
    },
    {
      "key": "2024020522082435600_r30",
      "doi-asserted-by": "crossref",
      "first-page": "6635",
      "DOI": "10.1063/1.478571",
      "volume": "110",
      "year": "1999",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020522082435600_r31",
      "doi-asserted-by": "crossref",
      "first-page": "5093",
      "DOI": "10.1063/1.467175",
      "volume": "100",
      "year": "1994",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020522082435600_r32",
      "doi-asserted-by": "crossref",
      "first-page": "5106",
      "DOI": "10.1063/1.467176",
      "volume": "100",
      "year": "1994",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020522082435600_r33",
      "doi-asserted-by": "crossref",
      "first-page": "6157",
      "DOI": "10.1063/1.468503",
      "volume": "101",
      "year": "1994",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020522082435600_r34",
      "first-page": "39",
      "volume": "93",
      "year": "1996",
      "journal-title": "Adv. Chem. Phys."
    },
    {
      "key": "2024020522082435600_r35",
      "doi-asserted-by": "crossref",
      "first-page": "9909",
      "DOI": "10.1063/1.467892",
      "volume": "101",
      "year": "1994",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020522082435600_r36",
      "doi-asserted-by": "crossref",
      "first-page": "7064",
      "DOI": "10.1063/1.472508",
      "volume": "105",
      "year": "1996",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020522082435600_r37",
      "doi-asserted-by": "crossref",
      "first-page": "9312",
      "DOI": "10.1063/1.475227",
      "volume": "107",
      "year": "1997",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020522082435600_r38",
      "doi-asserted-by": "crossref",
      "first-page": "7745",
      "DOI": "10.1063/1.477420",
      "volume": "109",
      "year": "1998",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020522082435600_r39",
      "doi-asserted-by": "crossref",
      "first-page": "2605",
      "DOI": "10.1063/1.480834",
      "volume": "112",
      "year": "2000",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020522082435600_r40",
      "doi-asserted-by": "crossref",
      "first-page": "9147",
      "DOI": "10.1063/1.480028",
      "volume": "111",
      "year": "1999",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020522082435600_r41",
      "doi-asserted-by": "crossref",
      "first-page": "3871",
      "DOI": "10.1063/1.475790",
      "volume": "108",
      "year": "1998",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020522082435600_r42",
      "doi-asserted-by": "crossref",
      "first-page": "2512",
      "DOI": "10.1063/1.447913",
      "volume": "81",
      "year": "1984",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020522082435600_r43",
      "doi-asserted-by": "crossref",
      "first-page": "5063",
      "DOI": "10.1063/1.445601",
      "volume": "79",
      "year": "1983",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020522082435600_r44",
      "doi-asserted-by": "crossref",
      "first-page": "401",
      "DOI": "10.1146/annurev.pc.37.100186.002153",
      "volume": "37",
      "year": "1986",
      "journal-title": "Annu. Rev. Phys. Chem."
    },
    {
      "key": "2024020522082435600_r45",
      "doi-asserted-by": "crossref",
      "first-page": "5863",
      "DOI": "10.1063/1.449861",
      "volume": "83",
      "year": "1985",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020522082435600_r46"
    },
    {
      "key": "2024020522082435600_r47",
      "first-page": "2796",
      "volume": "99",
      "year": "1983",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020522082435600_r48",
      "doi-asserted-by": "crossref",
      "first-page": "215",
      "DOI": "10.1007/BF01008729",
      "volume": "9",
      "year": "1973",
      "journal-title": "J. Stat. Phys."
    },
    {
      "key": "2024020522082435600_r49",
      "doi-asserted-by": "crossref",
      "first-page": "118",
      "DOI": "10.1016/0003-4916(63)90068-X",
      "volume": "24",
      "year": "1963",
      "journal-title": "Ann. Phys. (N.Y.)"
    },
    {
      "key": "2024020522082435600_r50"
    },
    {
      "key": "2024020522082435600_r51",
      "doi-asserted-by": "crossref",
      "first-page": "545",
      "DOI": "10.1090/S0002-9939-1959-0108732-6",
      "volume": "10",
      "year": "1959",
      "journal-title": "Proc. Am. Math. Soc."
    },
    {
      "key": "2024020522082435600_r52",
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      "DOI": "10.1016/0009-2614(74)80109-0",
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      "DOI": "10.1016/S0009-2614(98)00736-2",
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