This paper deals with the transfer of soliton-like heat waves in nonlinear
lattices with cubic on- site potential and quartic interparticle interaction
potential. A model Hamiltonian was proposed using the second quantized operators
and the same was averaged using a suitable wavefunction. The equations were
derived numerically in the discrete form for the field amplitude. Moreover the
resulting equations were analyzed analytically using the continuous
approximation technique and the properties of heat transfer were examined
theoretically.
Cite this paper
Perseus, R. and Latha, M. M. (2014). Solitons and Heat Transfer in Nonlinear Lattices with Cubic On-Site and Quartic Interaction Potentials. Open Access Library Journal, 1, e822. doi: http://dx.doi.org/10.4236/oalib.1100822.
Zurcher, U. and Talkner, P. (1900) Quantum-Mechanical Harmonic Chain Attached to Heat Baths. II. Nonequilibrium Properties. Physical Review A, 42, 3278.
http://dx.doi.org/10.1103/PhysRevA.42.3278
Roy, D. and Dhar, A. (2008) Role of Pinning Potentials in Heat Transport through Disordered Harmonic Chains. Physical Review E, 78, Article ID: 051112.
http://dx.doi.org/10.1103/PhysRevE.78.051112
Eckmann, J.P., Pillet, C.A. and Rey-Bellet L. (1999) Non-Equilibrium Statistical Mechanics of Anharmonic Chain Coupled to Two Heat Baths at Different Temperatures. Communications in Mathematical Physics, 201, 657.
Verheggen, T. (1979) Transmission Coefficient and Heat Conduction of a Harmonic Chain with Random Masses: Asymptotic Estimates on Products of Random Matrices. Communications in Mathematical Physics, 68, 69.
Mejia-Monasterio, C., Larralde, H. and Leyvraz, F. (2001) Coupled Normal Heat and Matter Transport in a Simple Model System. Physical Review Letters, 86, 5417.s
Li, B., Wang, J. and Casati, G. (2003) Heat Conductivity in Linear Mixing Systems. Physical Review E, 67, 021204.
http://dx.doi.org/10.1103/PhysRevE.67.021204
Dhar, A. and Roy, D. (2006) Heat Transport in Harmonic Lattices. Journal of Statistical Physics, 125, 801-820.
http://dx.doi.org/10.1007/s10955-006-9235-3
Li, B.W., Wang, L. and Hu, B. (2002) Finite Thermal Conductivity in 1D Models Having Zero Lyapunov Exponents. Physical Review Letters, 88, Article ID: 223901.
http://dx.doi.org/10.1103/PhysRevLett.88.223901
Li, B.W., Zhao, H. and Hu, B. (2001) Can Disorder Induce a Finite Thermal Conductivity in 1D Lattices? Physical Review Letters, 86, 63.
http://dx.doi.org/10.1103/PhysRevLett.86.63
Mountain, R.D. and MacDonald, R.A. (1983) Thermal Conductivity of Crystals: A Molecular-Dynamics Study of Heat Flow in a Two-Dimensional Crystal. Physical Review B, 28, 3022.
http://dx.doi.org/10.1103/PhysRevB.28.3022
Jackson, E.A. and Mistriotis, A.D. (1989) Thermal Conductivity of One- and Two-Dimensional Lattices. Journal of Physics: Condensed Matter, 1, 1223.
http://dx.doi.org/10.1088/0953-8984/1/7/006
Lepri, S., Livi, R. and Politi, A. (1997) Heat Conduction in Chains of Nonlinear Oscillators. Physical Review Letters, 78, 1896.
http://dx.doi.org/10.1103/PhysRevLett.78.1896
Shiba, H. and Ito, N. (2008) Anomalous Heat Conduction in Three-Dimensional Nonlinear Lattices. Journal of the Physical Society of Japan, 77, Article ID: 054006.
http://dx.doi.org/10.1143/JPSJ.77.054006
Bourbonnais, R. and Maynard, R. (1990) Energy Transport in One- and Two-Dimensional Anharmonic Lattices with Isotopic Disorder. Physical Review Letters, 64, 1397.
http://dx.doi.org/10.1103/PhysRevLett.64.1397
Terraneo, M., Peyrard, M. and Casati, G. (2002) Controlling the Energy Flow in Nonlinear Lattices: A Model for a Thermal Rectifier. Physical Review Letters, 88, Article ID: 094302.
http://dx.doi.org/10.1103/PhysRevLett.88.094302
Gaul, C. and Büttner, H. (2007) Quantum Mechanical Heat Transport in Disordered Harmonic Chains. Physical Review E, 76, Article ID: 011111.
http://dx.doi.org/10.1103/PhysRevE.76.011111
Stock, G. (2009) Classical Simulation of Quantum Energy Flow in Biomolecules. Physical Review Letters, 102, Article ID: 118301.
http://dx.doi.org/10.1103/PhysRevLett.102.118301
Wu, L.A. and Segal, D. (2011) Quantum Heat Transfer: A Born-Oppenheimer Method. Physical Review E, 83, Article ID: 051114.
http://dx.doi.org/10.1103/PhysRevE.83.051114
Imai, H., Wada, H. and Shiga, M. (1995) Effects of Spin Fluctuations on the Specific-Heat in YMN2 and Y0.97SC- 0.03MN2. Journal of the Physical Society of Japan, 64, 2198.
Theodorakopoulos, N. and Bacalis, N.C. (1992) Thermal Solitons in the Toda Chain. Physical Review B, 46, 10706.
http://dx.doi.org/10.1103/PhysRevB.46.10706
Takayama, H. and Ishikawa, M. (1986) Classical Thermodynamics of the Toda Lattice as a Classical Limit of the Two- Component Bethe Ansatz Scheme. Progress of Theoretical Physics, 76, 820.
Theodorakopoulos, N. (1984) Ideal-Gas Approach to the Statistical Mechanics of Integrable Systems: The Sine-Gordon Case. Physical Review B, 30, 4071.
http://dx.doi.org/10.1103/PhysRevB.30.4071
Li, N.B., Zhan, F., Hanggi, P. and Li, B.W. (2009) Shuttling Heat across One-Dimensional Homogenous Nonlinear Lattices with a Brownian Heat Motor. Physical Review E, 80, Article ID: 011125.
http://dx.doi.org/10.1103/PhysRevE.80.011125
Baldwin, D., Goklas, U. and Hereman, W. (2004) Symbolic Computation of Hyperbolic Tangent Solutions for Nonlinear Differential-Difference Equations. Computer Physics Communications, 162, 203-217.
http://dx.doi.org/10.1016/j.cpc.2004.07.002