Permanents, Pfaffian orientations, and even directed circuits

Given a 0-1 square matrix A, when can some of the 1's be changed to -1's in such a way that the permanent of A equals the determinant of the modified matrix? When does a real square matrix have the property that every real matrix with the same sign pattern (that is, the corresponding entries either have the same sign or are both zero) is nonsingular? When is a hypergraph with n vertices and n hyperedges minimally nonbipartite? When does a bipartite graph have a "Pfaffian orientation"? Given a digraph, does it have no directed circuit of even length? Given a digraph, does it have a subdivision with no even directed circuit? It is known that all of the above problems are equivalent. We prove a structural characterization of the feasible instances, which implies a polynomial-time algorithm to solve all of the above problems. The structural characterization says, roughly speaking, that a bipartite graph has a Pfaffian orientation if and only if it can be obtained by piecing together (in a specified way) planar bipartite graphs and one sporadic nonplanar bipartite graph.Comment: 47 pages, published versio

Atmospheric Circulation of Terrestrial Exoplanets

The investigation of planets around other stars began with the study of gas giants, but is now extending to the discovery and characterization of super-Earths and terrestrial planets. Motivated by this observational tide, we survey the basic dynamical principles governing the atmospheric circulation of terrestrial exoplanets, and discuss the interaction of their circulation with the hydrological cycle and global-scale climate feedbacks. Terrestrial exoplanets occupy a wide range of physical and dynamical conditions, only a small fraction of which have yet been explored in detail. Our approach is to lay out the fundamental dynamical principles governing the atmospheric circulation on terrestrial planets--broadly defined--and show how they can provide a foundation for understanding the atmospheric behavior of these worlds. We first survey basic atmospheric dynamics, including the role of geostrophy, baroclinic instabilities, and jets in the strongly rotating regime (the "extratropics") and the role of the Hadley circulation, wave adjustment of the thermal structure, and the tendency toward equatorial superrotation in the slowly rotating regime (the "tropics"). We then survey key elements of the hydrological cycle, including the factors that control precipitation, humidity, and cloudiness. Next, we summarize key mechanisms by which the circulation affects the global-mean climate, and hence planetary habitability. In particular, we discuss the runaway greenhouse, transitions to snowball states, atmospheric collapse, and the links between atmospheric circulation and CO2 weathering rates. We finish by summarizing the key questions and challenges for this emerging field in the future.Comment: Invited review, in press for the Arizona Space Science Series book "Comparative Climatology of Terrestrial Planets" (S. Mackwell, M. Bullock, and J. Harder, editors). 56 pages, 26 figure

Coherent spin-current oscillations in transverse magnetic fields

We address the coherence of the dynamics of spin-currents with components transverse to an external magnetic field for the spin-1/2 Heisenberg chain. We study current autocorrelations at finite temperatures and the real-time dynamics of currents at zero temperature. Besides a coherent Larmor oscillation, we find an additional collective oscillation at higher frequencies, emerging as a coherent many-magnon effect at low temperatures. Using numerical and analytical methods, we analyze the oscillation frequency and decay time of this coherent current-mode versus temperature and magnetic field.Comment: 4 pages, 5 figures (and supplemental material: 4 pages, 6 figures

Breathing mode for systems of interacting particles

We study the breathing mode in systems of trapped interacting particles. Our approach, based on a dynamical ansatz in the first equation of the Bogolyubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy allows us to tackle at once a wide range of power law interactions and interaction strengths, at linear and non linear levels. This both puts in a common framework various results scattered in the literature, and by widely generalizing these, emphasizes universal characters of this breathing mode. Our findings are supported by direct numerical simulations.Comment: 4 pages, 4 figure

Transition from diffusive to ballistic dynamics for a class of finite quantum models

The transport of excitation probabilities amongst weakly coupled subunits is investigated for a class of finite quantum systems. It is demonstrated that the dynamical behavior of the transported quantity depends on the considered length scale, e. g., the introduced distinction between diffusive and ballistic transport appears to be a scale-dependent concept, especially since a transition from diffusive to ballistic behavior is found in the limit of small as well as in the limit of large length scales. All these results are derived by an application of the time-convolutionless projection operator technique and are verified by the numerical solution of the full time-dependent Schroedinger equation which is obtained by exact diagonalization for a range of model parameters.Comment: 4 pages, 5 figures, approved for publication in Physical Review Letter

Excitation Spectrum of the Holstein Model

In this paper the polaron problem for the Holstein model is studied in the weak coupling limit. We use second order perturbation theory to construct renormalized electron and phonons. Eigenstates of the Hamiltonian are labelled and the excitation spectrum is constructed.Comment: 4 pages, revtex, 1 figures, more stuff at http://www.mpipks-dresden.mpg.de/~robin/robin.htm