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94, 027005 (2005). K. Kim, M. S. Heo, K. H. , Phys. Rev. A 72, 053402 (2005). K. Kim, M. S. Heo, K. H. , Phys. Rev. Lett. 96, 150601 (2006). L. D. Landau and E. M. 1, (1969). I. Siddiqi, R. Vijay, F. , cond-mat/0507248 (2005). M. I. Dykman, I. B. Schwartz, and M. Shapiro, Phys. Rev. E 72, 021102 (2005). D. Ryvkine and M. I. Dykman, Phys. Rev. E 74, 061118 (2006). Quantum Nanomechanics Pritiraj Mohanty Abstract Quantum Nanomechanics is the emerging field which pertains to the mechanical behavior of nanoscale systems in the quantum domain.

2 Classical and Quantum Regimes As listed in Table 2, a nanomechanical structure is described by a number of characteristic length scales, important for describing its mechanical motion in either quantum or classical regime. In addition to the scales corresponding to geometry and acoustic phonon wavelength, thermal length defines how far a phonon, the mechanical mode of vibration, extends within the thermal time τβ = h¯ /kB T , where τβ represents the timescale for the system to reach equilibrium with the thermal bath at temperature T .

I. Dykman and D. Ryvkine for useful discussions. This work was supported by NSF DMR-0645448. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. D. Rugar and P. Grutter, Phys. Rev. Lett. 67, 699 (1991). D. W. Carr, S. Evoy, L. , Appl. Phys. Lett. 77, 1545 (2000). L. Sekaric, M. Zalalutdinov, R. B. , Appl. Phys. Lett. 81, 2641 (2002). W. H. Zhang, R. Baskaran, and K. L. Turner, Sensors and Actuators a-Physical 102, 139 (2002). M. I. Dykman and M. A. Krivoglaz, Zh. Eksper.

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Numerische Mathematik Bd. 1 - 24

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