One dimensional electron systems (e.g. quantum wires or carbon nanotubes) exhibit different behaviour. They form a Tomonaga-Luttinger liquid with bosonic excitations. Electron transport in one dimensional systems takes place through tunneling events treated in second quantisation. Nonequilibrium transport is exhibited in quantum ratchet systems which generate a tunneling current in the presence of dissipation. An irradiated quantum wire attached to leads is a concrete experimental device of a quantum ratchet when electrons interact with external gates through Rashba spin orbit interaction. It then generates a spin current where the time averaged current density depends on the amplitude of the irradiation. The eigenstates of the ratchet Hamiltonian are delocalised Bloch states or Bloch spinors. For periodic boundary conditions the position operator in the Bloch basis yields with periodicity a discrete set of Bloch states. It is then possible to introduce a tight binding model with nearest neighbour couplings using the discretised Bloch basis or discrete variable representation (DVR). However for a quantum wire of finite length open boundary conditions are considered which do not yield eigenvalues like the ones for periodic boundary conditions. If they are completely different then the eigenstates do not form a basis valid for a tight binding description. On the other hand one can assume that the behaviour of the eigenvalues is similar for a large length near the middle and that it deviates only at the end of the length. I would like to verify this numerically and I am looking for people to help me with the problem.(adsbygoogle = window.adsbygoogle || []).push({});

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# Quantum ratchet on a quantum wire

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