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Specific heats of quantum double-well systems
1Department of Physics, Tokyo Gakugei University, Koganei, Tokyo 184-8501, Japan.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 2, 2013
Summary
Specific heats in quantum systems with double-well potentials differ significantly from harmonic oscillators. Symmetric double wells exhibit a Schottky-type anomaly at low temperatures due to tunneling, which is absent in asymmetric wells.
Area of Science:
- Quantum mechanics
- Thermodynamics
- Computational physics
Background:
- Specific heat calculations are crucial for understanding quantum systems.
- Double-well potentials are fundamental models in quantum mechanics, exhibiting unique behaviors like tunneling.
- Previous calculations using simplified methods may have overlooked critical contributions.
Purpose of the Study:
- To calculate and analyze the specific heats of quantum systems with symmetric and asymmetric double-well potentials.
- To compare the thermal properties of double-well systems with those of a harmonic oscillator.
- To investigate the origin and characteristics of anomalies in specific heat behavior.
Main Methods:
- Employed a combined numerical method incorporating both calculated and extrapolated eigenvalues.
- Utilized energy-matrix diagonalization for eigenvalues within a specified range (N(m) = 20 or 30).
- Extrapolated eigenvalues for higher energy levels to ensure comprehensive heat capacity calculations.
Main Results:
- Specific heats of double-well systems markedly differ from harmonic oscillator counterparts.
- Symmetric double-well systems display a Schottky-type anomaly at very low temperatures, attributed to tunneling-induced energy gaps.
- The Schottky-type anomaly disappears upon introducing asymmetry into the double-well potential.
Conclusions:
- The study highlights the distinct thermal behavior of quantum systems with double-well potentials compared to simpler models.
- Tunneling in symmetric double wells is identified as the cause of low-temperature specific heat anomalies.
- Asymmetry effectively removes the observed anomaly, offering insights into potential-based thermal properties.
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