Physical Review Letters

Theory of a two-level system strongly interacting with a degenerate Fermi gas

Károly Vladár, Gergely T. Zimányi, A. Zawadowski

Published Jan 27, 1986• 52 citations

Abstract

A two-level system is treated which interacts with a degenerate fermionic heat bath. Arbitrarily strong screening by fermions is taken into account. The hopping of the two-level system may be spontaneous or assisted by the fermionic bath. By derivation of scaling equations it is shown for the spin-(1/2) case that because of the assisted hops the two-level system cannot be localized in one of the states.

DOI: 10.1103/physrevlett.56.286

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Physical Review Letters

Theory of a two-level system strongly interacting with a degenerate Fermi gas

Károly Vladár, Gergely T. Zimányi, A. Zawadowski

Published Jan 27, 1986• 52 citations

Publisher

Abstract

DOI: 10.1103/physrevlett.56.286

Related papers

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{N}_{s}

>2. That clearly demonstrates that a particle moving in a double potential well may have different dissipative behavior depending upon whether it is coupled to a fermionic or a bosonic heat bath. The screening of the TLS by electrons is described by an arbitrarily large phase shift \ensuremath{\delta} which renormalizes towards the value \ensuremath{\delta}=\ensuremath{\pi}/2

{N}_{s}

, but the scaling equations lose their validity as the fugacities corresponding to the TLS transitions become of the order of unity. The method developed is a very general one, and thus it can be applied to other similar one-dimensional gases as well.

We study how a system of one-dimensional spin-

\frac{1}{2}

fermions at temperatures well below the Fermi energy approaches thermal equilibrium. The interactions between fermions are assumed to be weak and are accounted for within the perturbation theory. In the absence of an external magnetic field, spin degeneracy strongly affects relaxation of the Fermi gas. For sufficiently short-range interactions, the rate of relaxation scales linearly with temperature. Focusing on the case of the system near equilibrium, we linearize the collision integral and find the exact solution of the resulting relaxation problem. We discuss the application of our results to the evaluation of the transport coefficients of the one-dimensional Fermi gas.

{\mathbf{p}}_{\mathbf{F}}

retains the Fermi-liquid form. However, the 2

{\mathit{p}}_{\mathit{F}}

susceptibility ${\mathrm{\ensuremath{\chi}}}_{2\mathit{p}\mathit{F}}$ either diverges as T\ensuremath{\rightarrow}0 or remains finite but with nonanalytic wave-vector, frequency, and temperature dependence. We express our results in the language of recently discussed scaling theories, give the fixed-point action, and show that at this fixed point the fermion-gauge-field interaction is marginal in d=2, but irrelevant at low energies in d\ensuremath{\ge}2.