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Temperature gradient and Fourier's law in gradient-mass harmonic systems
1Ioffe Physical-Technical Institute, 194021 St. Petersburg, Russia. Reich@mail.ioffe.ru
Summary
A temperature gradient can form in a one-dimensional harmonic lattice with varying masses, even under standard Langevin conditions. This study demonstrates that Fourier
Area of Science:
- Condensed matter physics
- Statistical mechanics
- Thermodynamics
Background:
- Understanding heat transport in low-dimensional systems is crucial.
- Lattice dynamics with non-uniform properties present unique challenges.
- The thermodynamic limit simplifies analysis of macroscopic properties.
Purpose of the Study:
- To investigate heat flow and thermal profiles in a 1D harmonic lattice.
- To explore the impact of coordinate-dependent masses on thermal behavior.
- To determine if Fourier's law is obeyed under specific conditions.
Main Methods:
- Calculations performed in the thermodynamic limit.
- Analysis of a one-dimensional harmonic lattice model.
- Application of standard Langevin conditions for thermal contact.
Main Results:
- Heat flow and thermal profiles were successfully calculated.
- A temperature gradient was shown to form in the lattice.
- Fourier's law was observed to be obeyed in the studied system.
Conclusions:
- Coordinate-dependent masses do not prevent temperature gradient formation.
- The 1D harmonic lattice with varying masses can exhibit classical heat conduction behavior.
- Standard Langevin conditions are compatible with non-uniform lattice thermal properties.
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