TY - JOUR
T1 - Quantum tunneling in the presence of an arbitrary linear dissipation mechanism
AU - Leggett, A. J.
PY - 1984
Y1 - 1984
N2 - This paper considers the tunneling out of a metastable state at T=0 of a system whose classical equation of motion is, in Fourier-transformed form, K()q()=-[V(q)q]() where V(q) is a conservative potential and K() represents the effects of arbitrary linear dissipative and/or reactive elements. It is shown that, provided a few commonly satisfied conditions obtain, there is a simple prescription for writing down the imaginary-time effective action functional which determines the tunneling rate in the Wentzel-Kramers-Brillouin limit; namely, it contains the usual term in V(q), plus a term of the form (12) -12 K(-i| |)| qi() |2d, where qi() is the Fourier transform of the imaginary-time trajectory. Previously obtained results are special cases of this prescription. Applications are made to the case of "anomalous" dissipation (rate of dissipation proportional to the squared velocity of the momentum conjugate to the tunneling variable), to the "mixed" case (relaxation by collisions subject to a conservation law), and to more realistic models of a rf superconducting quantum-interference device.
AB - This paper considers the tunneling out of a metastable state at T=0 of a system whose classical equation of motion is, in Fourier-transformed form, K()q()=-[V(q)q]() where V(q) is a conservative potential and K() represents the effects of arbitrary linear dissipative and/or reactive elements. It is shown that, provided a few commonly satisfied conditions obtain, there is a simple prescription for writing down the imaginary-time effective action functional which determines the tunneling rate in the Wentzel-Kramers-Brillouin limit; namely, it contains the usual term in V(q), plus a term of the form (12) -12 K(-i| |)| qi() |2d, where qi() is the Fourier transform of the imaginary-time trajectory. Previously obtained results are special cases of this prescription. Applications are made to the case of "anomalous" dissipation (rate of dissipation proportional to the squared velocity of the momentum conjugate to the tunneling variable), to the "mixed" case (relaxation by collisions subject to a conservation law), and to more realistic models of a rf superconducting quantum-interference device.
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U2 - 10.1103/PhysRevB.30.1208
DO - 10.1103/PhysRevB.30.1208
M3 - Article
AN - SCOPUS:4244116402
SN - 0163-1829
VL - 30
SP - 1208
EP - 1218
JO - Physical Review B
JF - Physical Review B
IS - 3
ER -