Specific heat from an unsymmetrical double well potential

Феранчук, И. Д.; Ulyanenkov, A.; Kuz'min, V. S.

doi:10.1016/0301-0104(91)87130-n

Cited by 9 publications

(28 citation statements)

References 10 publications

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“…In Sec. IV we critically examine a validity of the specific heat calculated by FUK [15] with the use of ZOM [16]. Specific heats of the triple-well system are studied also.…”

Section: IVmentioning

confidence: 99%

“…In Sec. III, the combined method is applied to DW systems with a quartic potential (model A), a quadratic potential with Gaussian barrier (model B) and the DW potential adopted by FUK (FUK model) [15]. In Sec.…”

Section: IVmentioning

confidence: 99%

“…These models have been commonly adopted for studies of tunneling and stochastic resonance in DW systems. It is, however, curious that studies on their thermodynamical properties are scanty [12][13][14][15]. Feymann and Kleinert applied the path-integral method to a calculation of an effective classical partition function of DW systems [12,13].…”

Section: Introductionmentioning

confidence: 99%

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Specific heats of quantum double-well systems

Hasegawa

2012

Phys. Rev. E

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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.

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“…In Sec. IV we critically examine a validity of the specific heat calculated by FUK [15] with the use of ZOM [16]. Specific heats of the triple-well system are studied also.…”

Section: IVmentioning

confidence: 99%

Section: IVmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Specific heats of quantum double-well systems

Hasegawa

2012

Phys. Rev. E

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“…[35], the equation, which describes the motion of an individual particle in a system of large number of gravitational bosons in fact coincides with equation (11). Therefore, the solutions obtained here for the polaron are simultaneously solutions for the above-mentioned problem.…”

Section: Discussionmentioning

confidence: 98%

“…In agreement with the results obtained in these and subsequent works (see, for example, refs. [4][5][6][7][8][9][10][11][12]), the solution in the zeroth approximation of the OM gives quite a simple and universal algorithm for obtaining an approximation, which is uniformly applicable in a wide range of variation of parameters of the Hamiltonian. Another advantage of the OM is connected with the possibility of regularly calculating the correction to the zeroth approximation.…”

Section: Introductionmentioning

confidence: 99%