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 n for 0 ≤ n ≤ N m obtained by the energy-matrix diagonalization but also their extrapolated ones for N m + 1 ≤ n < ∞ (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.

Gaussian wavepacket dynamics and quantum tunneling in asymmetric double-well systems

“…The purpose of the present study is to numerically study dynamics of Gaussian wavepackets and to examine the effect of the asymmetry on quantum tunneling in asymmetric DW systems. Quite recently it has been pointed out that a potential asymmetry of a DW system has significant effects on its specific heat [10]. We expect that it is the case also for dynamical properties of DW systems.…”

Validity of the time-dependent variational approximation to the Gaussian wavepacket method applied to double-well systems

“…where We expect that SM with N m = 30 adopted in our numerical calculations is fairly accurate [23,24]. Some results of SM have been cross-checked, by solving the Schrödinger equation with the use the MATHEMATICA resolver for the partial differential equation.…”

A simulated annealing based study of the effect of Gaussian perturbation in quartic oscillator and quadratic double well potentials

“…Here, it can be concluded from the energy spectrum that as the nature of the spectrum is almost same for low and moderate strength with the unperturbed potential, then, these type of potentials also have Schottky-type anomaly in their specific heat at very low temperature. In case of first column of Table 5 the quasi degeneracy is removed so it can be expected that for this potential there will be no Schottky-type anomaly in very low temperature specific heat [17]. Thus, one can hope that proper choice of Gaussian field can remove the Schottky-type anomaly.…”

“…A single harmonic oscillator is unable to describe these types of motion, and a number of approaches have been proposed to construct double-or multiple-well potential surfaces. Prominent approaches include the quadratic potential perturbed by a Gaussian function barrier [17], the quartic-quadratic potential [18,19], the hyperbolic secant functions [20] and the linear combination of cosine functions etc. It is, however, curious that studies on the effect of Gaussian perturbation on quartic double well potential.…”