The Correlation Functions of the XXZ Heisenberg Chain for Zero or Infinite Anisotropy and Random Walks of Vicious Walkers

The XXZ Heisenberg chain is considered for two specific limits of the anisotropy parameter: \Dl\to 0 and \Dl\to -\infty. The corresponding wave functions are expressed by means of the symmetric Schur functions. Certain expectation values and thermal correlation functions of the ferromagnetic string operators are calculated over the base of N-particle Bethe states. The thermal correlator of the ferromagnetic string is expressed through the generating function of the lattice paths of random walks of vicious walkers. A relationship between the expectation values obtained and the generating functions of strict plane partitions in a box is discussed. Asymptotic estimate of the thermal correlator of the ferromagnetic string is obtained in the limit of zero temperature. It is shown that its amplitude is related to the number of plane partitions.Comment: 22 pages, 1 figure, LaTe

Correlation Functions of XX0 Heisenberg Chain, q-Binomial Determinants, and Random Walks

The XX0 Heisenberg model on a cyclic chain is considered. The representation of the Bethe wave functions via the Schur functions allows to apply the well-developed theory of the symmetric functions to the calculation of the thermal correlation functions. The determinantal expressions of the form-factors and of the thermal correlation functions are obtained. The q-binomial determinants enable the connection of the form-factors with the generating functions both of boxed plane partitions and of self-avoiding lattice paths. The asymptotical behavior of the thermal correlation functions is studied in the limit of low temperature provided that the characteristic parameters of the system are large enough.Comment: 27 pages, 2 figures, LaTe

Excitation energy transfer between closely spaced multichromophoric systems: Effects of band mixing and intraband relaxation

We theoretically analyze the excitation energy transfer between two closely spaced linear molecular J-aggregates, whose excited states are Frenkel excitons. The aggregate with the higher (lower) exciton band edge energy is considered as the donor (acceptor). The celebrated theory of F\"orster resonance energy transfer (FRET), which relates the transfer rate to the overlap integral of optical spectra, fails in this situation. We point out that in addition to the well-known fact that the point-dipole approximation breaks down (enabling energy transfer between optically forbidden states), also the perturbative treatment of the electronic interactions between donor and acceptor system, which underlies the F\"orster approach, in general loses its validity due to overlap of the exciton bands. We therefore propose a nonperturbative method, in which donor and acceptor bands are mixed and the energy transfer is described in terms of a phonon-assisted energy relaxation process between the two new (renormalized) bands. The validity of the conventional perturbative approach is investigated by comparing to the nonperturbative one; in general this validity improves for lower temperature and larger distances (weaker interactions) between the aggregates. We also demonstrate that the interference between intraband relaxation and energy transfer renders the proper definition of the transfer rate and its evaluation from experiment a complicated issue, which involves the initial excitation condition.Comment: 13 pages, 6 PostScript figure

DNA double helices for single molecule electronics

The combination of self-assembly and electronic properties as well as its true nanoscale dimensions make DNA a promising candidate for a building block of single molecule electronics. We argue that the intrinsic double helix conformation of the DNA strands provides a possibility to drive the electric current through the DNA by the perpendicular electric (gating) field. The transistor effect in the poly(G)-poly(C) synthetic DNA is demonstrated within a simple model approach. We put forward experimental setups to observe the predicted effect and discuss possible device applications of DNA. In particular, we propose a design of the single molecule analog of the Esaki diode.Comment: 4 pages, 4 figur