Specific heats of quantum double-well systems

Abstract

Specific heats of quantum systems with symmetric and asymmetric double-well potentials have been calculated. In numerical calculations of their specific heats, we have adopted the combined method which takes into account not only eigenvalues of ${\epsilon }_n$ for $0\le n\le N_m$ obtained by the energy-matrix diagonalization but also their extrapolated ones for $N_m+1\le n<\infty$ ($N_m=20$ or 30). Calculated specific heats are shown to be rather different from counterparts of a harmonic oscillator. In particular, specific heats of symmetric double-well systems at very low temperatures have the Schottky-type anomaly, which is rooted to a small energy gap in low-lying two-level eigenstates induced by a tunneling through the potential barrier. The Schottky-type anomaly is removed when an asymmetry is introduced into the double-well potential. It has been pointed out that the specific-heat calculation of a double-well system reported by Feranchuk, Ulyanenkov and Kuz'min [Chem. Phys. 157, 61 (1991)] is misleading because the zeroth-order operator method they adopted neglects crucially important off-diagonal contributions.

27 pages, 12 figures; Correted figure numbers (accepted in Phys. Rev. E)

References in corpus (1)

• Specific heat anomalies of small quantum systems subjected to finite baths

Cited by in corpus (7)

• Calorimetry for active systems
• Bound states of the one-dimensional Dirac equation for scalar and vector double square-well potentials
• Gaussian wavepacket dynamics and quantum tunneling in asymmetric double-well systems
• Rattling Phonon Modes in Quadruple Perovskites
• Ehrenfest approach to open double-well dynamics
• Validity of the time-dependent variational approximation to the Gaussian wavepacket method applied to double-well systems
• Anomalous lattice specific heat and rattling phonon modes in quadruple perovskites