Accelerating the computation of bath spectral densities with super-resolution


Quantum transport and other phenomena are typically modeled by coupling the system of interest to an environment, or bath, held at thermal equilibrium. Realistic bath models are at least as challenging to construct as models for the quantum systems themselves, since they must incorporate many degrees of freedom that interact with the system on a wide range of timescales. Owing to computational limitations, the environment is often modeled with simple functional forms, with a few parameters fit to experiment to yield semi-quantitative results. Growing computational resources have enabled the construction of more realistic bath models from molecular dynamics (MD) simulations. In this paper, we develop a numerical technique to construct these atomistic bath models with better accuracy and decreased cost. We apply a novel signal processing technique, known as super-resolution, combined with a dictionary of physically motivated bath modes to derive spectral densities from MD simulations. Our approach reduces the required simulation time and provides a more accurate spectral density than can be obtained via standard Fourier transform methods. Moreover, the spectral density is provided as a convenient closed-form expression which yields an analytic time-dependent bath kernel. Exciton dynamics of the Fenna–Matthews–Olson light-harvesting complex are simulated with a second-order time-convolutionless master equation, and spectral densities constructed via super-resolution are shown to reproduce the dynamics using only a quarter of the amount of MD data.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3


  1. 1.

    Breuer H-P, Petruccione F (2007) The theory of open quantum systems. Oxford University Press, Oxford

    Google Scholar 

  2. 2.

    Shenvi N, Schmidt JR, Edwards ST, Tully JC (2008) Phys Rev A 78:022502

    Article  Google Scholar 

  3. 3.

    Berkelbach TC, Hybertsen MS, Reichman DR (2013) J Chem Phys 138:4102

    Google Scholar 

  4. 4.

    Berkelbach TC, Hybertsen MS, Reichman DR (2013) J Chem Phys 138:114103

    Article  Google Scholar 

  5. 5.

    Singh N, Brumer P (2011) Faraday Discuss 153:41

    CAS  Article  Google Scholar 

  6. 6.

    Jang S, Newton MD, Silbey RJ (2007) J Phys Chem B 111:6807

    CAS  Article  Google Scholar 

  7. 7.

    Mohseni M, Rebentrost P, Lloyd S, Aspuru-Guzik A (2008) J Chem Phys 129:174106

    Article  Google Scholar 

  8. 8.

    Plenio MB, Huelga SF (2008) New J Phys 10:113019

    Article  Google Scholar 

  9. 9.

    Rebentrost P, Mohseni M, Kassal I, Lloyd S, Aspuru-Guzik A (2009) New J Phys 11:033003

    Article  Google Scholar 

  10. 10.

    Cao J, Silbey RJ (2009) J Phys Chem A 113:13825

    CAS  Article  Google Scholar 

  11. 11.

    Ishizaki A, Fleming GR (2009) Proc Natl Acad Sci 106:17255

    Article  Google Scholar 

  12. 12.

    Ishizaki A, Fleming GR (2011) J Phys Chem B 115:6227

    CAS  Article  Google Scholar 

  13. 13.

    Sarovar M, Ishizaki A, Fleming GR, Whaley KB (2010) Nat Phys 6:462

    CAS  Article  Google Scholar 

  14. 14.

    Abramavicius D, Mukamel S (2010) J Chem Phys 133:064510

    Article  Google Scholar 

  15. 15.

    Wu J, Liu F, Shen Y, Cao J, Silbey RJ (2010) New J Phys 12:105012

    Article  Google Scholar 

  16. 16.

    Moix J, Wu J, Huo P, Coker D, Cao J (2011) J Phys Chem Lett 2:3045

    CAS  Article  Google Scholar 

  17. 17.

    Kreisbeck C, Kramer T, Rodríguez M, Hein B (2011) J Chem Theory Comput 7:2166

    CAS  Article  Google Scholar 

  18. 18.

    Skochdopole N, Mazziotti DA (2011) J Phys Chem Lett 2:2989

    CAS  Article  Google Scholar 

  19. 19.

    Ritschel G, Roden J, Strunz WT, Aspuru-Guzik A, Eisfeld A (2011) J Phys Chem Lett 2:2912

    CAS  Article  Google Scholar 

  20. 20.

    Rebentrost P, Aspuru-Guzik A (2011) J Chem Phys 134:101103

    Article  Google Scholar 

  21. 21.

    Pachón LA, Brumer P (2012) Phys Chem Chem Phys 14:10094

    Article  Google Scholar 

  22. 22.

    Vlaming SM, Silbey RJ (2012) J Chem Phys 136:055102

    Article  Google Scholar 

  23. 23.

    Caruso F, Saikin SK, Solano E, Huelga SF, Aspuru-Guzik A, Plenio MB (2012) Phys Rev B 85:125424

    Article  Google Scholar 

  24. 24.

    Zhu J, Kais S, Rebentrost P, Aspuru-Guzik A (2011) J Phys Chem B 115:1531

    CAS  Article  Google Scholar 

  25. 25.

    Roden J, Eisfeld A, Wolff W, Strunz W (2009) Phys Rev Lett 103:058301

    Article  Google Scholar 

  26. 26.

    Olbrich C, Kleinekathöfer U (2010) J Phys Chem B 114:12427

    CAS  Article  Google Scholar 

  27. 27.

    Olbrich C, Jansen TLC, Liebers J, Aghtar M, Strümpfer J, Schulten K, Knoester J, Kleinekathöfer U (2011) J Phys Chem B 115:8609

    CAS  Article  Google Scholar 

  28. 28.

    Hein B, Kreisbeck C, Kramer T, Rodríguez M (2012) New J Phys 14:023018

    Article  Google Scholar 

  29. 29.

    Christensson N, Kauffmann HF, Pullerits T, Mančal T (2012) J Phys Chem B 116:7449

    CAS  Article  Google Scholar 

  30. 30.

    Chin AW, Prior J, Rosenbach R, Caycedo-Soler F, Huelga SF, Plenio MB (2013) Nat Phys 9:113

    CAS  Article  Google Scholar 

  31. 31.

    Kreisbeck C, Kramer T (2012) J Phys Chem Lett 3:2828

    CAS  Article  Google Scholar 

  32. 32.

    Valleau S, Eisfeld A, Aspuru-Guzik A (2012) J Chem Phys 137:224103

    Article  Google Scholar 

  33. 33.

    Tuckerman M (2010) Statistical mechanics: theory and molecular simulation. OUP, Oxford

    Google Scholar 

  34. 34.

    Runge E, Gross EK (1984) Phys Rev Lett 52:997

    CAS  Article  Google Scholar 

  35. 35.

    Mallat S (2008) A wavelet tour of signal processing, 3rd edn: the sparse way. Academic Press, London

    Google Scholar 

  36. 36.

    Hu H, Van QN, Mandelshtam VA, Shaka AJ (1998) Reference deconvolution, phase correction, and line listing of NMR spectra by the 1D filter diagonalization method. J Magn Reson 134(1):76–87

    CAS  Article  Google Scholar 

  37. 37.

    Hoch JC, Maciejewski MW, Mobli M, Schuyler AD, Stern AS (2014) Nonuniform sampling and maximum entropy reconstruction in multidimensional NMR. Acc Chem Res 47(2):708–717

    CAS  Article  Google Scholar 

  38. 38.

    Freeman WT, Jones TR, Pasztor EC (2002) IEEE Comput Graph Appl 22:56

    Article  Google Scholar 

  39. 39.

    Patti AJ, Sezan MI, Murat Tekalp A (1997) IEEE Trans Image Process 6:1064

    CAS  Article  Google Scholar 

  40. 40.

    Elad M, Feuer A (1997) IEEE Trans Image Process 6:1646

    CAS  Article  Google Scholar 

  41. 41.

    Puschmann KG, Kneer F (2005) Astron Astrophys 436:373

    Article  Google Scholar 

  42. 42.

    Mccutchen CW (1967) J Opt Soc Am 57:1190

    CAS  Article  Google Scholar 

  43. 43.

    Kouame D, Ploquin M (2009) Super-resolution in medical imaging: an illustrative approach through ultrasound. In: IEEE international symposium on biomedical imaging: from nano to macro, 2009. ISBI ’09, pp 249–252

  44. 44.

    Ma J (2010) IEEE Trans Instrum Meas 59:1600

    Article  Google Scholar 

  45. 45.

    Donoho DL (2006) IEEE Trans Inf Theory 52:1289

    Article  Google Scholar 

  46. 46.

    Oka A, Lampe L (2009) A compressed sensing receiver for bursty communication with UWB impulse radio. In: IEEE international conference on ultra-wideband, 2009. ICUWB 2009, pp 279–284

  47. 47.

    Herman MA, Strohmer T (2009) IEEE Trans Signal Process 57:2275

    Article  Google Scholar 

  48. 48.

    Qiu C, Lu W, Vaswani N (2009) Real-time dynamic MR image reconstruction using Kalman filtered compressed sensing. In: IEEE international conference on acoustics, speech and signal processing, 2009. ICASSP 2009, pp 393–396

  49. 49.

    Lustig M, Donoho D, Pauly JM (2007) Magn Reson Med 58:1182

    Article  Google Scholar 

  50. 50.

    Nagahara M, Quevedo DE, Ostergaard J (2012) Sparse representations for packetized predictive networked control. In: 2012 IEEE 51st annual conference on decision and control (CDC), pp 1362–1367

  51. 51.

    Tuma T, Rooney S, Hurley P (2009) On the applicability of compressive sampling in fine grained processor performance monitoring. In: 2009 14th IEEE international conference on engineering of complex computer systems. IEEE, pp 210–219

  52. 52.

    Shabani A, Kosut RL, Mohseni M, Rabitz H, Broome MA, Almeida MP, Fedrizzi A, White AG (2011) Efficient measurement of quantum dynamics via compressive sensing. Phys Rev Lett 106(10):100401

    CAS  Article  Google Scholar 

  53. 53.

    Mishali M, Eldar YC (2010) IEEE J Sel Top Signal Process 4:375

    Article  Google Scholar 

  54. 54.

    Duarte MF, Davenport MA, Takhar D, Laska JN, Sun T, Kelly KF, Baraniuk RG (2008) IEEE Signal Process Mag 25:83

    Article  Google Scholar 

  55. 55.

    Coulter WK, Hillar CJ, Isley G, Sommer FT (2010) Adaptive compressed sensing — A new class of self-organizing coding models for neuroscience. 2010 IEEE International conference on acoustics, speech and signal processing, Dallas, TX, p 5494–5497

  56. 56.

    Candès EJ, Fernandez-Granda C (2014) Commun Pure Appl Math 67:906–956

    Article  Google Scholar 

  57. 57.

    Bioucas-Dias JM, Figueiredo MA (2007) IEEE Trans Image Process 16:2992

    Article  Google Scholar 

  58. 58.

    Bioucas-Dias JM, Figueiredo MAT (2007) Two-step algorithms for linear inverse problems with non-quadratic regularization. In: IEEE international conference on image processing, 2007. ICIP 2007, pp I–105–I–108

  59. 59.

    Vulto SIE, de Baat MA, Louwe RJW, Permentier HP, Neef T, Miller M, van Amerongen H, Aartsma TJ (1998) J Phys Chem B 102:9577

    CAS  Article  Google Scholar 

  60. 60.

    Adolphs J, Renger T (2006) Biophys J 91:2778

    CAS  Article  Google Scholar 

  61. 61.

    Chen X, Cao J, Silbey RJ (2013) J Chem Phys 138:224104

    Article  Google Scholar 

  62. 62.

    Yuen-Zhou J, Krich JJ, Aspuru-Guzik A (2012) J Chem Phys 136:234501

    Article  Google Scholar 

  63. 63.

    Shim S, Rebentrost P, Valleau SP, Aspuru-Guzik AN (2012) Biophys J 102:649

    CAS  Article  Google Scholar 

  64. 64.

    Kolli A, Nazir A, Olaya-Castro A (2011) J Chem Phys 135:154112

    Article  Google Scholar 

  65. 65.

    Jang S (2011) J Chem Phys 135:034105

    Article  Google Scholar 

  66. 66.

    Ishizaki A, Fleming GR (2009) J Chem Phys 130:234111

    Article  Google Scholar 

  67. 67.

    Tanimura Y, Kubo R (1989) J Phys Soc Jpn 58:101

    Article  Google Scholar 

  68. 68.

    Kreisbeck C, Kramer T, Rodríguez TM, Hein B (2011) J Chem Theory Comput 7(7):2166–2174

    CAS  Article  Google Scholar 

  69. 69.

    Pereverzev A, Bittner ER (2006) J Chem Phys 125:4906

    Article  Google Scholar 

  70. 70.

    Timm C (2011) Phys Rev B 83:115416

    Article  Google Scholar 

  71. 71.

    Ahn D (1994) Phys Rev B 50:8310

    Article  Google Scholar 

  72. 72.

    Heinz-Peter B, Kappler B, Petruccione F (2000) Decoherence: theoretical, experimental, and conceptual problems. 233

  73. 73.

    Shabani A, Lidar DA (2005) Phys Rev A 71:020101

    Article  Google Scholar 

  74. 74.

    Smirne A, Vacchini B (2010) Phys Rev A 82:022110

    Article  Google Scholar 

  75. 75.

    Kleinekathöfer U (2004) J Chem Phys 121:2505

    Article  Google Scholar 

  76. 76.

    Berens PH, White SR, Wilson KR (1981) J Chem Phys 75:515

    CAS  Article  Google Scholar 

  77. 77.

    Candes EJ, Romberg J, Tao T (2006) IEEE Trans Inf Theory 52:489

    Article  Google Scholar 

  78. 78.

    Andrade X, Sanders JN, Aspuru-Guzik A (2012) Proc Natl Acad Sci 109:13928

    CAS  Article  Google Scholar 

  79. 79.

    Sanders JN, Saikin SK, Mostame S, Andrade X, Widom JR, Marcus AH, Aspuru-Guzik A (2012) J Phys Chem Lett 3:2697

    CAS  Article  Google Scholar 

  80. 80.

    Cornell WD, Cieplak P, Bayly CI, Gould IR, Merz KM, Ferguson DM, Spellmeyer DC, Fox T, Caldwell JW, Kollman PA (1995) J Am Chem Soc 117:5179

    CAS  Article  Google Scholar 

  81. 81.

    Ceccarelli M, Procacci P, Marchi M (2003) J Comput Chem 24:129

    CAS  Article  Google Scholar 

  82. 82.

    Becke AD (1988) Phys Rev A 38:3098

    CAS  Article  Google Scholar 

  83. 83.

    Miehlich B, Savin A, Stoll H, Preuss H (1989) Chem Phys Lett 157:200

    CAS  Article  Google Scholar 

  84. 84.

    Lee C, Yang W, Parr RG (1988) Phys Rev B 37:785

    CAS  Article  Google Scholar 

  85. 85.

    Shao Y, Molnar LF, Jung Y, Kussmann J, Ochsenfeld C, Brown ST, Gilbert AT, Slipchenko LV, Levchenko SV, O’Neill DP (2006) Phys Chem Chem Phys 8:3172

    CAS  Article  Google Scholar 

Download references


We acknowledge S. Valleau for useful discussions and computer code. We acknowledge the financial support of Defense Advanced Research Projects Agency Grant N66001-10-1-4063 and the Defense Threat Reduction Agency under Contract No. HDTRA1-10-1-0046. T.M. acknowledges support from the National Science Foundation (NSF) through the Graduate Research Fellowship Program (GRFP). S.B. acknowledges support from the Department of Energy (DoE) through the Computational Sciences Graduate Fellowship (CSGF). J.N.S. acknowledges support from the Department of Defense (DoD) through the National Defense Science & Engineering Graduate Fellowship (NDSEG) Program. A.A.G. thanks the Corning Foundation.

Author information



Corresponding author

Correspondence to Alán Aspuru-Guzik.

Additional information

Published as part of the special collection of articles “Festschrift in honour of A. Vela”.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Markovich, T., Blau, S.M., Parkhill, J. et al. Accelerating the computation of bath spectral densities with super-resolution. Theor Chem Acc 135, 215 (2016).

Download citation


  • Spectral densities
  • Super-resolution
  • Hierarchical equations of motion