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Equations of State for Simple Liquids from the Gaussian Equivalent Representation Method

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Abstract

Within the framework of Gaussian equivalent representation method a new procedure of obtaining equations of state for simple liquids is discussed in some technical details. The developed approach permits one to compute partition and distribution functions for simple liquids with arbitrary form of the central two-body potential of inter-molecular interaction. The proposed approach might become of great use for computing thermodynamic and structural quantities of simple particle and polymer systems. We believe that this technique can also provide an interesting possibility to reduce the sign problem of other methods of computer simulation based on a functional integral approach.

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References

  1. Hill, T.L.: Statistical Mechanics. Rinehart, New York (1954)

    Google Scholar 

  2. Tsonchev, S., Coalson, R.D., Duncan, A.: Statistical mechanics of charged polymers in electrolyte solutions: A lattice field theory approach. Phys. Rev. E 60, 4257 (1999)

    Article  ADS  Google Scholar 

  3. Matsen, M.W.: The standard Gaussian model for block copolymer melts. J. Phys., Condens. Matter 14, R21 (2002)

    Article  ADS  Google Scholar 

  4. Schmid, F.: Self-consistent-field theories for complex fluids. J. Phys., Condens. Matter 10, 8105 (1998)

    Article  ADS  Google Scholar 

  5. Efimov, G., Ganbold, G.: Functional integrals in the strong coupling regime and the polaron self-energy. Phys. Status Solidi B 168, 165 (1991)

    Article  Google Scholar 

  6. Efimov, G.V., Dineykhan, M., Ganbold, G., Nedelko, S.N.: Oscillator Representation in Quantum Physics. Lectures Notes in Physics, vol. 26. Springer, Berlin (1995)

    MATH  Google Scholar 

  7. Efimov, G.V.: Bound states in quantum field theory, scalar fields. Eprint arXiv:hep-ph/9907483 (1999)

  8. Efimov, G.V., Nogovitsin, E.A.: The partition function of classical systems in the Gaussian equivalent representation. Physica A 234, 506 (1996)

    Article  ADS  Google Scholar 

  9. Baeurle, S.A., Efimov, G.V., Nogovitsin, E.A.: Calculating field theories beyond the mean-field level. Europhys. Lett. 75, 378–384 (2006)

    Article  ADS  Google Scholar 

  10. Baeurle, S.A., Charlot, M., Nogovitsin, E.A.: Grand canonical investigations of prototypical polyelectrolyte models beyond the mean field level of approximation. Phys. Rev. E 75, 011804 (2007)

    Article  ADS  Google Scholar 

  11. Baeurle, S.A., Nogovitsin, E.A.: Challenging scaling laws of flexible polyelectrolyte solutions with effective renormalization concepts. Polymer 48, 4883–4899 (2007)

    Article  Google Scholar 

  12. Baeurle, S.A., Kiselev, M.G., Makarova, E.S., Nogovitsin, E.A.: Effect of the counterion behavior on the shear-compressive properties of chondroitin sulfate solutions. Polymer 50, 1805–1813 (2009)

    Article  Google Scholar 

  13. Baeurle, S.A.: Method of Gaussian equivalent representation: a new technique for reducing the sign problem of functional integral methods. Phys. Rev. Lett. 89, 080602 (2002)

    Article  ADS  Google Scholar 

  14. Baeurle, S.A.: Grand canonical auxiliary field Monte Carlo: a new technique for simulating open systems at high density. Comput. Phys. Commun. 157, 201–206 (2004)

    Article  ADS  Google Scholar 

  15. Hanson, J., McDonald, I.: Theory of Simple Liquids. Academic Press, New York (1986)

    Google Scholar 

  16. Pablo, J.. Yan, Q., Escobedo, F.: Simulation of phase transitions in fluids. Annu. Rev. Phys. Chem. 50, 377 (1999)

    Article  Google Scholar 

  17. Feynman, R.: Statistical Mechanics. Addison-Wesley, Reading (1981)

    Google Scholar 

  18. Balescu, R.: Equilibrium and Nonequilibrium Statistical Mechanics. Wiley, New York (1975)

    MATH  Google Scholar 

  19. Baeurle, S.A.: The stationary phase auxiliary field Monte Carlo method: a new strategy for reducing the sign problem of auxiliary field methodologies. Comput. Phys. Commun. 154, 111–120 (2003)

    Article  ADS  Google Scholar 

  20. Fredrickson, G.H., Ganesan, V., Drolet, F.: Field-theoretic computer simulation methods for polymers and complex fluids. Macromolecules 35, 16 (2002)

    Article  ADS  Google Scholar 

  21. Cardenas-Lizana, P., PinYi, H.: Stick-release patterns in stretching single condensed polyelectrolyte toroids. Macromolecules 42(8), 3211–3214 (2009)

    Article  Google Scholar 

  22. Baeurle, S.A., Martonak, R., Parrinello, M.: A field-theoretical approach to simulation in the classical canonical and grand-canonical ensemble. J. Chem. Phys. 117, 3027–3039 (2002)

    Article  ADS  Google Scholar 

  23. Baeurle, S.A., Efimov, G.V., Nogovitsin, E.A.: On a new self-consistent-field theory for the canonical ensemble. J. Chem. Phys 124, 224110 (2006)

    Article  ADS  Google Scholar 

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  1. Department of Physics, National Tsing Hua University, Hsinchu, 30013, Taiwan

    Dima Bolmatov

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  1. Dima Bolmatov
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Correspondence to Dima Bolmatov.

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Bolmatov, D. Equations of State for Simple Liquids from the Gaussian Equivalent Representation Method. J Stat Phys 137, 765–773 (2009). https://doi.org/10.1007/s10955-009-9874-2

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  • DOI: https://doi.org/10.1007/s10955-009-9874-2

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