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Quantum fluctuations can promote or inhibit glass formation

Abstract

Glasses are dynamically arrested states of matter that do not exhibit the long-range periodic structure of crystals1,2,3,4. Here we develop new insights from theory and simulation into the impact of quantum fluctuations on glass formation. As intuition may suggest, we observe that large quantum fluctuations serve to inhibit glass formation as tunnelling and zero-point energy allow particles to traverse barriers facilitating movement. However, as the classical limit is approached a regime is observed in which quantum effects slow down relaxation making the quantum system more glassy than the classical system. This dynamical ‘reentrance’ occurs in the absence of obvious structural changes and has no counterpart in the phenomenology of classical glass-forming systems.

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Figure 1: Dynamic phase diagram calculated from the QMCT for a hard-sphere fluid.
Figure 2: Diffusion as a function of quantumness from RPMD simulations.
Figure 3: Snapshots from the RPMD simulations.

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References

  1. Debenedetti, P. G. & Stillinger, F. H. Supercooled liquids and the glass transition. Nature 410, 259–267 (2001).

    Article  ADS  Google Scholar 

  2. Berthier, L. et al. Direct experimental evidence of a growing length scale accompanying the glass transition. Science 310, 1797–1800 (2005).

    Article  ADS  Google Scholar 

  3. Biroli, G. et al. Thermodynamic signature of growing amorphous order in glass-forming liquids. Nature Phys. 4, 771–775 (2008).

    Article  ADS  Google Scholar 

  4. Hedges, L. O., Jack, R. L., Garrahan, J. P. & Chandler, D. E. Dynamic order–disorder in atomistic models of structural glass formers. Science 323, 1309–1313 (2009).

    Article  ADS  Google Scholar 

  5. Amir, A., Oreg, Y. & Imry, Y. Slow relaxations and aging in the electron glass. Phys. Rev. Lett. 103, 126403 (2009).

    Article  ADS  Google Scholar 

  6. Wu, W. H. et al. From classical to quantum glass. Phys. Rev. Lett. 67, 2076–2079 (1991).

    Article  ADS  Google Scholar 

  7. Boninsegni, M., Prokof’ev, N. & Svistunov, B. Superglass phase of 4He. Phys. Rev. Lett. 96, 105301 (2006).

    Article  ADS  Google Scholar 

  8. Biroli, G., Chamon, C. & Zamponi, F. Theory of the superglass phase. Phys. Rev. B 78, 224306 (2008).

    Article  ADS  Google Scholar 

  9. Hunt, B. et al. Evidence for a superglass state in solid 4He. Science 324, 632–636 (2009).

    Article  ADS  Google Scholar 

  10. Götze, W. Complex Dynamics of Glass-Forming Liquids: A Mode-Coupling Theory (Oxford Univ. Press, 2009).

    MATH  Google Scholar 

  11. Biroli, G., Bouchard, J., Miyazaki, K. & Reichman, D. R. Inhomogeneous mode-coupling theory and growing dynamic length in supercooled liquids. Phys. Rev. Lett. 97, 195701 (2006).

    Article  ADS  Google Scholar 

  12. Dawson, K. et al. Higher-order glass-transition singularities in colloidal systems with attractive interactions. Phys. Rev. Lett. 63, 011401 (2001).

    Google Scholar 

  13. Götze, W. & Voightmann, Th. Effect of composition changes on the structural relaxation of a binary mixture. Phys. Rev. E 67, 021502 (2003).

    Article  ADS  Google Scholar 

  14. Zaccarelli, E. et al. Confirmation of anomalous dynamical arrest in attractive colloids: A molecular dynamics study. Phys. Rev. E 66, 041402 (2002).

    Article  ADS  Google Scholar 

  15. Foffi, G. et al. Mixing effects for the structural relaxation in binary hard-sphere liquids. Phys. Rev. Lett. 91, 085701 (2003).

    Article  ADS  Google Scholar 

  16. Pham, K. N. et al. Multiple glassy states in a simple model system. Science 296, 104–106 (2002).

    Article  ADS  Google Scholar 

  17. Götze, W. & Lücke, M. Dynamical structure factor S(q,ω) of liquid helium II at zero temperature. Phys. Rev. B 13, 3825–3842 (1976).

    Article  ADS  Google Scholar 

  18. Pusey, P. N. & van Megen, W. Observation of a glass transition in suspensions of spherical colloidal particles. Phys. Rev. Lett. 59, 2083–2086 (1987).

    Article  ADS  Google Scholar 

  19. Foffi, G. et al. α-relaxation processes in binary hard-sphere mixtures. Phys. Rev. E 69, 011505 (2004).

    ADS  Google Scholar 

  20. Craig, I. R. & Manolopoulos, D. E. Quantum statistics and classical mechanics: Real time correlation functions from ring polymer molecular dynamics. J. Chem. Phys. 121, 3368–3373 (2004).

    Article  ADS  Google Scholar 

  21. Miller, T. F. & Manolopoulos, D. E. Quantum diffusion in liquid water from ring polymer molecular dynamic. J. Chem. Phys. 123, 154504 (2005).

    Article  ADS  Google Scholar 

  22. Richardson, J. O. & Althorpe, S. C. Ring-polymer molecular dynamics rate-theory in the deep-tunneling regime: Connection with semiclassical instanton theory. J. Chem. Phys. 131, 214106 (2009).

    Article  ADS  Google Scholar 

  23. Kob, W. & Andersen, H. C. Testing mode-coupling theory for a supercooled binary Lennard-Jones mixture I: The van Hove correlation function. Phys. Rev. E 51, 4626–4641 (1995).

    Article  ADS  Google Scholar 

  24. Rounder, E. Hydrophobic solvation, quantum nature, and diffusion of atomic hydrogen in liquid water. Radiat. Phys. Chem. 72, 201–206 (2005).

    Article  ADS  Google Scholar 

  25. Wipf, H. Hydrogen in Metals III: Properties and Applications (Springer, 1997).

    Book  Google Scholar 

  26. Markland, T. E., Habershon, S. & Manolopoulos, D. E. Quantum diffusion of hydrogen and muonium atoms in liquid water and hexagonal ice. J. Chem. Phys. 128, 194506 (2008).

    Article  ADS  Google Scholar 

  27. Westfahl, H., Schmalian, J. & Wolynes, P. G. Dynamical mean-field theory of quantum stripe glass. Phys. Rev. B 68, 134203 (2003).

    Article  ADS  Google Scholar 

  28. Lee, Y. & Berne, B. J. Global optimization: Quantum thermal annealing with path integral Monte Carlo. J. Phys. Chem. A 104, 86–95 (2000).

    Article  Google Scholar 

  29. Das, A. & Chakrabati, B. K. Quantum annealing and analog quantum computation. Rev. Mod. Phys. 80, 1061–1081 (2008).

    Article  ADS  MathSciNet  Google Scholar 

  30. Foini, L., Semerjian, G. & Zamponi, F. Solvable model of quantum random optimization problems. Phys. Rev. Lett 105, 167204 (2010).

    Article  ADS  Google Scholar 

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Acknowledgements

B.J.B. acknowledges support from NSF grant No. CHE-0910943. D.R.R. would like to thank the NSF through grant No. CHE-0719089. K.M. acknowledges support from Kakenhi grant No. 21015001 and 2154016. The authors acknowledge G. Biroli and L. Cugliandolo for useful discussions.

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Authors and Affiliations

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Contributions

D.R.R. and E.R. developed the QMCT approach. K.M. and E.R. carried out the QMCT calculations. T.E.M. carried out the RPMD calculations and analysed the results with B.J.B. and J.A.M. All authors contributed to the preparation of the manuscript.

Corresponding authors

Correspondence to Eran Rabani or David R. Reichman.

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The authors declare no competing financial interests.

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Markland, T., Morrone, J., Berne, B. et al. Quantum fluctuations can promote or inhibit glass formation. Nature Phys 7, 134–137 (2011). https://doi.org/10.1038/nphys1865

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