Form Factors of the Heisenberg Spin Chain in the Thermodynamic Limit: Dealing with Complex Bethe Roots

In this article we study the thermodynamic limit of the form factors of the XXX Heisenberg spin chain using the algebraic Bethe ansatz approach. Our main goal is to express the form factors for the low-lying excited states as determinants of matrices that remain finite dimensional in the thermodynamic limit. We show how to treat all types of the complex roots of the Bethe equations within this framework. In particular we demonstrate that the Gaudin determinant for the higher level Bethe equations arises naturally from the algebraic Bethe ansatz.

Root patterns and energy spectra of quantum integrable systems without U(1) symmetry: the antiperiodic XXZ spin chain

Finding out root patterns of quantum integrable models is an important step to study their physical properties in the thermodynamic limit. Especially for models without U(1) symmetry, their spectra are usually given by inhomogeneous T − Q relations and the Bethe root patterns are still unclear. In this paper with the antiperiodic XXZ spin chain as an example, an analytic method to derive both the Bethe root patterns and the transfer-matrix root patterns in the thermodynamic limit is proposed. Based on them the ground state energy and elementary excitations in the gapped regime are derived. The present method provides an universal procedure to compute physical properties of quantum integrable models in the thermodynamic limit.

Genome-Scale Analysis of Acetobacterium woodii Identifies Translational Regulation of Acetogenesis

Acetogens are capable of reducing CO 2 to multicarbon compounds (e.g., ethanol or 2,3-butanediol) via the Wood-Ljungdahl pathway. Given that protein synthesis in bacteria is highly energy consuming, acetogens living at the thermodynamic limit of life are inevitably under translation control.

Understanding land surface-atmosphere interactions at the diurnal scale from energetic and thermodynamic constraints

<p>Land-atmosphere interactions are typically evaluated using numerical simulation models of increasingly greater complexity.  But what are the key, major constraints that determine the first-order controls of the land-atmosphere system?  Here, we present an alternative approach that is solely based on energetic and thermodynamic constraints of the coupled land-atmosphere system and show that this approach can reproduce observations at the diurnal scale very well.  The key concept we use is that turbulent heat fluxes are predominantly the result of an atmospheric heat engine that is driven by the heat input from the surface and that operates at the thermodynamic limit of maximum power.  This provides a closure for the magnitude of turbulent fluxes in the surface energy balance.  Interactions enter this approach mainly in two ways: First, the cooling effect of turbulent heat fluxes on surface temperature lowers the engine's efficiency, thereby setting the maximum power limit, and second, by heat storage changes in the lower atmosphere, which represent an entropy term inside the heat engine and alter the thermodynamic limit for power output.  Both effects are, however, well constrained by energy balances, yielding analytical solutions for energy balance partitioning during the day without the need for empirical parameters. The further partitioning into sensible and latent heat fluxes is obtained from the assumption of thermodynamic equilibrium at the surface where heat and moisture is added to the atmosphere (if sufficient soil water is accessible).  We then show that this approach works remarkably well in reproducing FluxNet observations over the diurnal cycle.  What this implies is that these physical constraints determine the first-order dynamics of the land-atmosphere system, enabling us to derive simple, physics-based estimates of climate, the dominant effects of vegetation, and the response of the coupled system to global climate change.</p>

Symmetric matrix ensemble and integrable hydrodynamic chains

The partition function of the Symmetric Matrix Ensemble is identified with the $$\tau $$ τ -function of a particular solution of the Pfaff Lattice. We show that, in the case of even power interactions, in the thermodynamic limit, the $$\tau $$ τ -function corresponds to the solution of an integrable chain of hydrodynamic type. We prove that the hydrodynamic chain so obtained is diagonalisable and admits hydrodynamic reductions in Riemann invariants in an arbitrary number of components.

Thermodynamic limit of Nekrasov partition function for 5-brane web with O5-plane

In this paper, we study 5d $$ \mathcal{N} $$ N = 1 Sp(N) gauge theory with Nf (≤ 2N + 3) flavors based on 5-brane web diagram with O5-plane. On the one hand, we discuss Seiberg-Witten curve based on the dual graph of the 5-brane web with O5-plane. On the other hand, we compute the Nekrasov partition function based on the topological vertex formalism with O5-plane. Rewriting it in terms of profile functions, we obtain the saddle point equation for the profile function after taking thermodynamic limit. By introducing the resolvent, we derive the Seiberg-Witten curve and its boundary conditions as well as its relation to the prepotential in terms of the cycle integrals. They coincide with those directly obtained from the dual graph of the 5-brane web with O5-plane. This agreement gives further evidence for mirror symmetry which relates Nekrasov partition function with Seiberg-Witten curve in the case with orientifold plane and shed light on the non-toric Calabi-Yau 3-folds including D-type singularities.