One-dimensional Bose chemistry: effects of nonintegrability

Three-body collisions of ultracold identical Bose atoms under tight cylindrical confinement are analyzed. A Feshbach resonance in two-body collisions is described by a two-channel zero-range interaction. Elimination of the closed channel in the three-body problem reduces the interaction to a one-channel zero-range one with an energy-dependent strength. The related integrable Lieb-Liniger-McGuire (LLMG) model, with an energy-independent strength, forbids all chemical processes, such as three-atom association and diatom dissociation, as well as reflection in atom-diatom collisions. The resonant case is analyzed by a numerical solution of the Faddeev equations. The results demonstrate that as the internal symmetry of the LLMG model is lifted, reflection and chemical reactions become allowed and may be observed in experiments.     

Characterizing the Typical Information Curves of Diverse Languages

Optimal coding theories of language predict that speakers will keep the amount of information in their utterances relatively uniform under the constraints imposed by their language, but how much do these constraints influence information structure, and how does this influence vary across languages? We present a novel method for characterizing the information structure of sentences across a diverse set of languages. While the structure of English is broadly consistent with the shape predicted by optimal coding, many languages are not consistent with this prediction. We proceed to show that the characteristic information curves of languages are partly related to a variety of typological features from phonology to word order. These results present an important step in the direction of exploring upper bounds for the extent to which linguistic codes can be optimal for communication.     

Stretching,Amplification, and Compression of Microwave Pulses Using Helically Corrugated Waveguides

Radiophysics and Quantum Electronics - We demonstrate the possible implementation of the chirped pulse amplification (CPA) method, which is widely used in optics, for the microwave frequency band....     

Relaxation in a completely integrable many-body quantum system: an ab initio study of the dynamics of the highly excited states of 1D lattice hard-core bosons

In this Letter we pose the question of whether a many-body quantum system with a full set of conserved quantities can relax to an equilibrium state, and, if it can, what the properties of such a state are. We confirm the relaxation hypothesis through an ab initio numerical investigation of the dynamics of hard-core bosons on a one-dimensional lattice. Further, a natural extension of the Gibbs ensemble to integrable systems results in a theory that is able to predict the mean values of physical observables after relaxation. Finally, we show that our generalized equilibrium carries more memory of the initial conditions than the usual thermodynamic one. This effect may have many experimental consequences, some of which have already been observed in the recent experiment on the nonequilibrium dynamics of one-dimensional hard-core bosons in a harmonic potential [T. Kinoshita et al., Nature (London) 440, 900 (2006)10.1038/nature04693].     

On spin wavefunctions and young orthogonal matrices

Electron spin wavefunctions are expressed in the Young orthogonal representation. The normalization factor is calculated. An explicit expression for the first column elements of the Young orthogonal matrices is obtained by a comparison to the branching diagram wavefunctions. These matrix elements are used in a multideterminant representation of the total wavefunction. © 2012 Wiley Periodicals, Inc.