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Nonequilibrium dynamics of a fast oscillator coupled to Glauber spins

Bonilla, L.L. and Prados , A. and Carpio Rodríguez, Ana María (2010) Nonequilibrium dynamics of a fast oscillator coupled to Glauber spins. Journal of Statistical Mechanics: Theory and Experiment (9). ISSN 1742-5468

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Abstract

A fast harmonic oscillator is linearly coupled with a system of Ising spins that are in contact with a thermal bath, and evolve under a slow Glauber dynamics at dimensionless temperature theta. The spins have a coupling constant proportional to the oscillator position. The oscillator spin interaction produces a second order phase transition at theta = 1 with the oscillator position as its order parameter: the equilibrium position is zero for theta > 1 and nonzero for theta < 1. For theta < 1, the dynamics of this system is quite different from relaxation to equilibrium. For most initial conditions, the oscillator position performs modulated oscillations about one of the stable equilibrium positions with a long relaxation time. For random initial conditions and a sufficiently large spin system, the unstable zero position of the oscillator is stabilized after a relaxation time proportional to theta. If the spin system is smaller, the situation is the same until the oscillator position is close to zero, then it crosses over to a neighborhood of a stable equilibrium position about which it keeps oscillating for an exponentially long relaxation time. These results of stochastic simulations are predicted by modulation equations obtained from a multiple scale analysis of macroscopic equations.


Item Type:Article
Uncontrolled Keywords:Dimensional ising-model; Molecular dynamics; Phase-transition; Stochastic-model; System; Resonator; Noise
Subjects:Sciences > Physics > Mathematical physics
ID Code:14876
References:

[1] Feder J and Pytte E, 1973 Phys. Rev. B 8 3978

[2] Rikvold P A, 1977 Z. Phys. B 26 195

[3] Rikvold P A, 1978 Z. Phys. B 30 339

[4] Leggett A J, Chakravarty S, Dorsey A T, Fisher M P A, Garg A and Zwerger W, 1987 Rev. Mod. Phys.

59 1

[5] Bonilla L L and Guinea F, 1992 Phys. Rev. A 45 7718

[6] Hicke C and Dykman M I, 2008 Phys. Rev. B 78 024401

[7] Boisen A, 2009 Nat. Nanotechnol. 4 404

[8] Hofheinz M, Wang H, Ansmann M, Bialczak R C, Lucero E, Neeley M, O’Connell A D, Sank D, Wenner J,

Martinis J M and Cleland A N, 2009 Nature 459 546

[9] O’Connell A D, Hofheinz M, Ansmann M, Bialczak R C, Lenander M, Lucero E, Neeley M, Sank D,

Wang H, Weides M, Wenner J, Martinis J M and Cleland A N, 2010 Nature 464 697

[10] Riste T, Samuelsen E J, Otnes K and Feder J, 1971 Solid State Commun. 9 1455

[11] Ishibashi Y and Takagi Y, 1972 J. Phys. Soc. Japan 33 1

[12] Schneider T and Stoll E P, 1973 Phys. Rev. Lett. 31 1254

[13] Schneider T and Stoll E P, 1977 Phys. Rev. B 17 1302

[14] Koehler T R and Gillis N S, 1976 Phys. Rev. B 13 4183

[15] Rikvold P A, 1980 Bussei Kenkyu 33 E43

[16] Glauber R J, 1963 J. Math. Phys. 4 294

[17] Prados A, Bonilla L L and Carpio A, 2010 J. Stat. Mech. P06016

[18] Reiss H, 1980 Chem. Phys. 47 15

[19] Brey J J and Prados A, 1994 Phys. Rev. B 49 984

[20] Brey J J and Prados A, 1993 Physica A 197 569

[21] Brey J J and Prados A, 1996 Phys. Rev. E 53 458

[22] Bouchaud J P, 1992 J. Physique I 2 1705

[23] Bouchaud J P, Cugliandolo L F, Kurchan J and Mezard M, 1998 Spin Glasses and Random Fields

ed A P Young (Singapore: World Scientific) pp 161–224

[24] Bender C M and Orszag S A, 1999 Advanced Mathematical Methods for Scientists and Engineers

(New York: Springer)

[25] Freidlin M I, 2001 J. Stat. Phys. 103 283

[26] Muratov C B, Vanden-Eijnden E and Weinan E, 2007 Proc. Nat. Acad. Sci. 104 702

[27] Van Kampen N G, 1997 Stochastic Processes in Physics and Chemistry (Amsterdam: North-Holland)

[28] Crisanti A and Sompolinsky H, 1988 Phys. Rev. A 37 4865

[29] Shraiman B I, 1986 Phys. Rev. Lett. 57 325

Deposited On:19 Apr 2012 08:35
Last Modified:06 Feb 2014 10:11

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