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Instability of condensation in the zero-range process with random interaction

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Grosskinsky, Stefan, Chleboun, P. I. (Paul I.) and Schütz, G. M. (Gunter M.). (2008) Instability of condensation in the zero-range process with random interaction. Physical Review E, Vol.78 (No.3). Article no. 030101(R). ISSN 1539-3755

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Official URL: http://dx.doi.org/10.1103/PhysRevE.78.030101

Abstract

The zero-range process is a stochastic interacting particle system that is known to exhibit a condensation transition. We present a detailed analysis of this transition in the presence of quenched disorder in the particle interactions. Using rigorous probabilistic arguments, we show that disorder changes the critical exponent in the interaction strength below which a condensation transition may occur. The local critical densities may exhibit large fluctuations, and their distribution shows an interesting crossover from exponential to algebraic behavior.

Item Type:

Journal Article

Subjects:

Q Science > QC Physics

Divisions:

Faculty of Science > Centre for Complexity Science
Faculty of Science > Mathematics

Library of Congress Subject Headings (LCSH):

Stochastic systems, Condensation

Journal or Publication Title:

Physical Review E

Publisher:

American Physical Society

ISSN:

1539-3755

Official Date:

4 September 2008

Dates:

Date	Event
4 September 2008	Published

Volume:

Vol.78

Number:

No.3

Number of Pages:

Page Range:

Article no. 030101(R)

Identification Number:

10.1103/PhysRevE.78.030101

Status:

Peer Reviewed

Publication Status:

Published

Access rights to Published version:

Open Access

References:

[1] F. Spitzer, Adv. Math. 5, 246–290 (1970).
[2] M.R. Evans, T. Hanney, J. Phys. A: Math. Gen. 38,
R195–R239 (2005).
[3] J. Eggers, Phys. Rev. Lett. 83(25), 5322-5325 (1999).
D. van der Meer, J.P. van der Weele, D. Lohse, Phys.
Rev. Lett. 88, 174302 (2002). F. Coppex, M. Droz,
A. Lipowski, Phys. Rev. E 66, 011305 (2002).
[4] J. T¨or¨ok, Physica A 355, 374–382 (2005). D. van der
Meer, K. van der Weele, P. Reimann, D. Lohse, J. Stat.
Mech.: Theor. Exp. P07021 (2007).
[5] M.R. Evans, Europhys. Lett. 36, 13-18 (1996). J. Krug,
P.A. Ferrari, J. Phys. A: Math. Gen. 29, L465–
L471 (1996). I. Benjamini, P.A. Ferrari, C. Landim,
Stoch. Proc. Appl. 61, 181–204 (1996).
[6] M.R. Evans, T. Hanney, S.N. Majumdar, Phys. Rev.
Lett. 97, 010602 (2006).
[7] Y. Kafri, E. Levine, D. Mukamel, G.M. Sch¨utz, and J.
T¨or¨ok. Phys. Rev. Lett. 89(3), 035702 (2002).
[8] A.G. Angel, M.R. Evans, E. Levine, D. Mukamel, Phys.
Rev. E 72, 046132 (2005). A.G. Angel, T. Hanney, M.R.
Evans, Phys. Rev. E 73, 016105 (2006).
[9] J. Kaupuzs, R. Mahnke, R.J. Harris, Phys. Rev. E 72(5),
056125 (2005).
[10] M.R. Evans, Braz. J. Phys. 30(1), 42–57 (2000).
[11] S. Grosskinsky, G.M. Sch¨utz, H. Spohn, J. Stat. Phys.
113(3/4), 389–410 (2003).
[12] M.R. Evans, S.N. Majumdar, R.K.P. Zia, J. Stat. Phys.
123, 357–390 (2006).
[13] J.M. Luck, C. Godreche, J. Stat. Mech.: Theor. Exp.
P08005 (2007).
[14] A.G. Angel, M.R. Evans, E. Levine, D. Mukamel,
J. Stat. Mech.: Theor. Exp. P08017 (2007).
[15] S. Grosskinsky, G.M. Sch¨utz, J. Stat. Phys. 132(1), 77–
108 (2008).
[16] Y. Schwarzkopf, M.R. Evans, D. Mukamel, J. Phys. A:
Math. Theor. 41, 205001 (2008).
[17] Inhomogeneous p(x, y) leads to multiplication of the fugacity
= eμ in the steady state by site-dependent terms
which are the unique solutions of y = Px xp(x, y).
[18] E. Andjel, Ann. Probability 10(3), 525–547 (1982).
[19] O. Kallenberg, Foundations of Modern Probability, 2nd
edition (Springer, New York, 2002).
[20] P.A. Ferrari, C. Landim, V.V. Sisko, J. Stat. Phys. 128,
1153-1158 (2007).
[21] C. Kipnis, C. Landim, Scaling Limits of Interacting Particle
Systems (Springer, Berlin, 1999).
[22] A.G. Angel, M.R. Evans, D. Mukamel, J. Stat. Mech.:
Theor. Exp. P04001 (2004).
[23] The authors are only aware of results on integrals of
exponential Brownian motions with constant drift, e.g.
M. Yor, J. Appl. Prob. 29, 202-208 (1992).
[24] S. Grosskinsky, P. Chleboun, G.M. Sch¨utz (in prep.)