Zero bias anomaly in the density of states of low-dimensional metals

We consider the effect of Coulomb interactions on the average density of states (DOS) of disordered low-dimensional metals for temperatures T and frequencies ω smaller than the inverse elastic life-time 1/τ. Using the fact that long-range Coulomb interactions in two dimensions (2d) generate ln²-singularities in the DOS ν(ω) but only ln-singularities in the conductivity σ(ω), we can re-sum the most singular contributions to the average DOS via a simple gauge-transformation. If σ(ω) > 0, then a metallic Coulomb gapν(ω) ∝ |ω|/e ⁴ appears in the DOS at T = 0 for frequencies below a certain crossover frequency Ω ₂ which depends on the value of the DC conductivity σ(0). Here, - e is the charge of the electron. Naively adopting the same procedure to calculate the DOS in quasi 1d metals, we find ν(ω) ∝ (|ω|/Ω ₁)^1/2exp(- Ω ₁/|ω|) at T = 0, where Ω ₁ is some interaction-dependent frequency scale. However, we argue that in quasi 1d the above gauge-transformation method is on less firm grounds than in 2d. We also discuss the behavior of the DOS at finite temperatures and give numerical results for the expected tunneling conductance that can be compared with experiments. Received 28 August 2001 / Received in final form 28 January 2002 Published online 9 July 2002     

Functional bosonization of interacting fermions in arbitrary dimensions

We bosonize the long-wavelength excitations of interacting fermions in arbitrary dimension by directly applying a suitable Hubbard-Stratonowich transformation to the Grassmannian generating functional of the fermionic correlation functions. With this technique we derive a surprisingly simple expression for the singleparticle Greens-function, which is valid for arbitrary interaction strength and can describe Fermi- as well as Luttinger liquids. Our approach sheds further light on the relation between bosonization and the random-phase approximation, and enables us to study screening in a nonperturbative way.     

Fermi’s golden rule in a mesoscopic metal ring

We examine the time-dependent nonequilibrium current in a mesoscopic metal ring threaded by a static magnetic flux φ that is generated by a time-dependent electric field oscillating with frequency ω. We show that in quadratic order in the field there are three fundamentally different contributions to the current. (a) A time-independent contribution which can be obtained from a thermodynamic derivative. (b) A term increasing linearly in time that can be understood in terms of Fermi’s golden rule. The derivation of this term requires a careful treatment of the infinitesimal imaginary parts that are added to the real frequency ω when the electric field is adiabatically switched on. (c) Finally, there is also a time-dependent current oscillating with frequency 2 ω. We suggest an experiment to test our results.     

Zum mechanismus bei der photoinduzierten nachpolymerisation von polymethylmethacrylat

The photoinitiated polymerization of PMMA-blocks containing residual monomer leads at first to a decrease of the refractive index, the molar mass and the degree of conversion with time. Afterwards pronounced increase of these quantities is found. These phenomena are explained by photoinitiated chain breaks followed by depolymerisation of the polymer chains. This process is accompanied by growth of the radicals created from illumination of the PMMA-blocks. A mathematical model is proposed for calculation of the refractive index changes of PMMA-blocks.