1205.2058 (Hideo Hasegawa)

Thermodynamical properties of quantum double-well systems    [PDF]

Hideo Hasegawa

We have studied thermodynamical properties of two kinds of quantum double-well systems with a quadratic-quartic potential (model A) and a quadratic potential perturbed by a Gaussian barrier (model B). In numerical calculations of their specific heat and entropy, we have taken into account eigenvalues of $\epsilon_n$ for $0 \leq n \leq N_m$ obtained by diagonalization of the energy matrix as well as their extrapolated ones for $N_m+1 \leq n < \infty$ where $N_m=20$ or 30. Calculated quantum specific heat and entropy in both models A and B with symmetric potentials have the Schottky-type anomaly at very low temperatures, which arises from low-lying eigenstates with a small gap due to tunneling through the potential barrier. This anomaly is removed when an asymmetry is introduced into the double-well potential. In the high-temperature limit, the specific heat of model A approaches $C = (3/4) k_B$, while that of model B becomes $C = k_B$ which agrees with that of the harmonic oscillator. Results of the present study are in contrast to a previous study using the operator method [Feranchuk, Ulyanenkov and Kuz'min, Chem. Phys. {\bf 157}, 61 (1991)].

View original: http://arxiv.org/abs/1205.2058