Dynamics of the biased two-level system in metals

Ulrich Weiss; Matthias Wollensak

doi:10.1103/PhysRevLett.62.1663

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Dynamics of the biased two-level system in metals

Ulrich Weiss and Matthias Wollensak

Institut für Theoretische Physik, Universität Stuttgart, D-7000 Stuttgart 80, Germany

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Phys. Rev. Lett. 62, 1663 – Published 3 April, 1989

DOI: https://doi.org/10.1103/PhysRevLett.62.1663

Abstract

We study the influence of conduction electrons on spectral and dynamical properties of the biased two-level system using path-integral methods. The structure factor for inelastic neutron scattering is calculated in the case of weak coupling (K≪1) and for a special value of the coupling strength (K=1/2). The effect of interbounce interactions is systematically taken into account at low temperatures, thus removing shortcomings of the dilute-bounce-gas approximation. The method and results are relevant also for the ‘‘macroscopic-quantum-coherence’’ problem.

References (14)

J. Kondo, Physica (Amsterdam) 84B, 40 (1976); ibid. 125B, 279 (1984).
D. Richter, in Quantum Aspects of Molecular Motion in Solids, edited by A. Heidemann et al., Springer Proceedings in Physics Vol. 17 (Springer-Verlag, Heidelberg, 1987), and references therein.
H. Wipf, D. Steinbinder, K. Neumaier, P. Gutsmiedl, A. Magerl and A. J. Dianoux, Europhys. Lett. 4, 1379 (1987).
A. J. Leggett, S. Chakravarty, A. T. Dorsey, M. P. A. Fisher, A. Garg and W. Zwerger, Rev. Mod. Phys. 59, 1 (1987).
J. Kondo, in Fermi Surface Effects, Springer Series in Solid State Sciences Vol. 77 (Springer-Verlag, Heidelberg, 1988).
U. Weiss, H. Grabert and S. Linkwitz, J. Low Temp. Phys. 68, 213 (1987).
H. Grabert, S. Linkwitz, S. Dattagupta and U. Weiss, Europhys. Lett. 2, 631 (1986).
D. Steinbinder, H. Wipf, A. Magerl, D. Richter, A. J. Dianoux and K. Neumaier, Europhys. Lett. 6, 535 (1988).
We intend to give further details and extensions of this work elsewhere.
J. L. Black, in Glassy Metals I, Springer Topics in Applied Physics Vol. 46 (Springer-Verlag, Heidelberg, 1987).
U. Weiss, H. Grabert, P. Hänggi and P. Riseborough, Phys. Rev. B 35, 9535 (1987).
S. Dattagupta, in Relaxation Phenomena in Condensed Matter Physics (Academic, New York, 1987).
The DBGA formula for j ( ν ) was also found by S. Dattagupta, H. Grabert, and R. Jung (to be published) using quantum relaxation theory and calculating the self-energy in second order in the tunnel splitting.
We note that $P_{\inf}$ is exactly related to the partition function Z through $P_{\inf}$ = 2 τ partial ln Z / partial sigma. By substituting Z = cosh ( $σ_{b}$ / 2 τ ), we find the formula (10).

[c1] J. Kondo, Physica (Amsterdam) 84B, 40 (1976); ibid. 125B, 279 (1984).

[c2] D. Richter, in Quantum Aspects of Molecular Motion in Solids, edited by A. Heidemann et al., Springer Proceedings in Physics Vol. 17 (Springer-Verlag, Heidelberg, 1987), and references therein.

[c3] H. Wipf, D. Steinbinder, K. Neumaier, P. Gutsmiedl, A. Magerl and A. J. Dianoux, Europhys. Lett. 4, 1379 (1987).

[c4] A. J. Leggett, S. Chakravarty, A. T. Dorsey, M. P. A. Fisher, A. Garg and W. Zwerger, Rev. Mod. Phys. 59, 1 (1987).

[c5] J. Kondo, in Fermi Surface Effects, Springer Series in Solid State Sciences Vol. 77 (Springer-Verlag, Heidelberg, 1988).

[c6] U. Weiss, H. Grabert and S. Linkwitz, J. Low Temp. Phys. 68, 213 (1987).

[c7] H. Grabert, S. Linkwitz, S. Dattagupta and U. Weiss, Europhys. Lett. 2, 631 (1986).

[c8] D. Steinbinder, H. Wipf, A. Magerl, D. Richter, A. J. Dianoux and K. Neumaier, Europhys. Lett. 6, 535 (1988).

[c9] We intend to give further details and extensions of this work elsewhere.

[c10] J. L. Black, in Glassy Metals I, Springer Topics in Applied Physics Vol. 46 (Springer-Verlag, Heidelberg, 1987).

[c11] U. Weiss, H. Grabert, P. Hänggi and P. Riseborough, Phys. Rev. B 35, 9535 (1987).

[c12] S. Dattagupta, in Relaxation Phenomena in Condensed Matter Physics (Academic, New York, 1987).

[c13] The DBGA formula for j ( ν ) was also found by S. Dattagupta, H. Grabert, and R. Jung (to be published) using quantum relaxation theory and calculating the self-energy in second order in the tunnel splitting.

[c14] We note that $P_{\inf}$ is exactly related to the partition function Z through $P_{\inf}$ = 2 τ partial ln Z / partial sigma. By substituting Z = cosh ( $σ_{b}$ / 2 τ ), we find the formula (10).

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Dynamics of the biased two-level system in metals

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