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

Zero Range Process and Multi-Dimensional Random Walks

The special limit of the totally asymmetric zero range process of the low-dimensional non-equilibrium statistical mechanics described by the non-Hermitian Hamiltonian is considered. The calculation of the conditional probabilities of the model are based on the algebraic Bethe ansatz approach. We demonstrate that the conditional probabilities may be considered as the generating functions of the random multi-dimensional lattice walks bounded by a hyperplane. This type of walks we call the walks over the multi-dimensional simplicial lattices. The answers for the conditional probability and for the number of random walks in the multi-dimensional simplicial lattice are expressed through the symmetric functions

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

Probing quantum-mechanical level repulsion in disordered systems by means of time-resolved selectively-excited resonance fluorescence

We argue that the time-resolved spectrum of selectively-excited resonance fluorescence at low temperature provides a tool for probing the quantum-mechanical level repulsion in the Lifshits tail of the electronic density of states in a wide variety of disordered materials. The technique, based on detecting the fast growth of a fluorescence peak that is red-shifted relative to the excitation frequency, is demonstrated explicitly by simulations on linear Frenkel exciton chains.Comment: 4 pages, 4 figures, to appear in Phys. Rev. Let

Low-temperature dynamics of weakly localized Frenkel excitons in disordered linar chains

We calculate the temperature dependence of the fluorescence Stokes shift and the fluorescence decay time in linear Frenkel exciton systems resulting from the thermal redistribution of exciton population over the band states. The following factors, relevant to common experimental conditions, are accounted for in our kinetic model: (weak) localization of the exciton states by static disorder, coupling of the localized excitons to vibrations in the host medium, a possible non-equilibrium of the subsystem of localized Frenkel excitons on the time scale of the emission process, and different excitation conditions (resonant or non resonant). A Pauli master equation, with microscopically calculated transition rates, is used to describe the redistribution of the exciton population over the manifold of localized exciton states. We find a counterintuitive non-monotonic temperature dependence of the Stokes shift. In addition, we show that depending on experimental conditions, the observed fluorescence decay time may be determined by vibration-induced intra-band relaxation, rather than radiative relaxation to the ground state. The model considered has relevance to a wide variety of materials, such as linear molecular aggregates, conjugated polymers, and polysilanes.Comment: 15 pages, 8 figure