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 -