Maximin-optimal sustainable growth with nonrenewable resource and externalities

I offer an approach linking a welfare criterion to the “sustainable development opportunities” of the economy. This implies a dependence of a criterion on the information about the current state. I consider the problem for the Dasgupta-Heal-Solow-Stiglitz model with externalities. The economy-linked criterion is constructed on an example of the maximin principle applied to a hybrid level-growth measure. This measure includes as special cases the conventional measures of consumption level and percent change as a measure of growth. The hybrid measure or geometrically weighted percent can be used for measuring sustainable growth as an alternative to percent. The closed form solutions are obtained for the optimal paths including the paths, dynamically consistent with the updates in reserve estimates.Essential nonrenewable resource, modified Hotelling Rule, economy-linked criterion, geometrically weighted percent, normative resource peak.

A constant-utility criterion linked to an imperfect economy affected by irreversible global warming

The question of formulation of a social planner criterion for an imperfect economy is examined using an example of a polluting economy negatively affected by growing temperature. Imperfection of the economy is expressed here in deviations from the optimal initial state. It is shown that a criterion not linked to a specific initial state almost always implies either unsustainable or inefficient paths in the economy. In this paper, I link the constant-utility criterion to the initial amount of the resource reserve. This criterion implies efficient resource use and the paths of utility asymptotically approaching some constants, which depend on the parameters of the temperature function. The criterion can be formulated for the cases when the reserve estimate changes over time and when the high level of temperature can cause extinction.Essential nonrenewable resource, imperfect polluting economy, economy-linked criterion, semisustainable development, semiefficient extraction.

Analytical results for the Coqblin-Schrieffer model with generalized magnetic fields

Using the approach alternative to the traditional Thermodynamic Bethe Ansatz, we derive analytical expressions for the free energy of Coqblin-Schrieffer model with arbitrary magnetic and crystal fields. In Appendix we discuss two concrete examples including the field generated crossover from the SU(4) to the SU(2) symmetry in the SU(4)-symmetric model.Comment: 5 page

Integrable Circular Brane Model and Coulomb Charging at Large Conduction

We study a model of 2D QFT with boundary interaction, in which two-component massless Bose field is constrained to a circle at the boundary. We argue that this model is integrable at two values of the topological angle, $\theta =0$ and $\theta=\pi$. For $\theta=0$ we propose exact partition function in terms of solutions of ordinary linear differential equation. The circular brane model is equivalent to the model of quantum Brownian dynamics commonly used in describing the Coulomb charging in quantum dots, in the limit of small dimensionless resistance $g_0$ of the tunneling contact. Our proposal translates to partition function of this model at integer charge.Comment: 20 pages, minor change

Hyperelliptic curves for multi-channel quantum wires and the multi-channel Kondo problem

We study the current in a multi-channel quantum wire and the magnetization in the multi-channel Kondo problem. We show that at zero temperature they can be written simply in terms of contour integrals over a (two-dimensional) hyperelliptic curve. This allows one to easily demonstrate the existence of weak-coupling to strong-coupling dualities. In the Kondo problem, the curve is the same for under- and over-screened cases; the only change is in the contour.Comment: 7 pages, 1 figure, revte

Interplay of the Scaling Limit and the Renormalization Group: Implications for Symmetry Restoration

Symmetry restoration is usually understood as a renormalization group induced phenomenon. In this context, the issue of whether one-loop RG equations can be trusted in predicting symmetry restoration has recently been the subject of much debate. Here we advocate a more pragmatic point of view and expand the definition of symmetry restoration to encompass all situations where the physical properties have only a weak dependence upon an anisotropy in the bare couplings. Moreover we concentrate on universal properties, and so take a scaling limit where the physics is well described by a field theory. In this context, we find a large variety of models that exhibit, for all practical purposes, symmetry restoration: even if symmetry is not restored in a strict sense, physical properties are surprisingly insensitive to the remaining anisotropy. Although we have adopted an expanded notion of symmetry restoration, we nonetheless emphasize that the scaling limit also has implications for symmetry restoration as a renormalization group induced phenomenon. In all the models we considered, the scaling limit turns out to only permit bare couplings which are nearly isotropic and small. Then the one-loop beta-function should contain all the physics and higher loop orders can be neglected. We suggest that this feature generalizes to more complex models. We exhibit a large class of theories with current-current perturbations (of which the SO(8) model of interest in two-leg Hubbard ladders/armchair carbon nanotubes is one) where the one-loop beta-functions indicates symmetry restoration and so argue that these results can be trusted within the scaling limit.Comment: 20 pages, 11 figures, RevTe

Tunneling in quantum wires I: Exact solution of the spin isotropic case

We show that the problem of impurity tunneling in a Luttinger liquid of electrons with spin is solvable in the spin isotropic case ($g_\sigma=2$, $g_\rho$ arbitrary). The resulting integrable model is similar to a two channel anisotropic Kondo model, but with the impurity spin in a "cyclic representation" of the quantum algebra $su(2)_q$ associated with the anisotropy. Using exact, non-perturbative techniques we study the RG flow, and compute the DC conductance. As expected from the analysis of Kane and Fisher we find that the IR fixed point corresponds to two separate leads. We also prove an exact duality between the UV and IR expansions of the current at vanishing temperature.Comment: Revtex, epsf, 14pgs, 4 figs. One reference adde

A unified framework for the Kondo problem and for an impurity in a Luttinger liquid

We develop a unified theoretical framework for the anisotropic Kondo model and the boundary sine-Gordon model. They are both boundary integrable quantum field theories with a quantum-group spin at the boundary which takes values, respectively, in standard or cyclic representations of the quantum group $SU(2)_q$. This unification is powerful, and allows us to find new results for both models. For the anisotropic Kondo problem, we find exact expressions (in the presence of a magnetic field) for all the coefficients in the ``Anderson-Yuval'' perturbative expansion. Our expressions hold initially in the very anisotropic regime, but we show how to continue them beyond the Toulouse point all the way to the isotropic point using an analog of dimensional regularization. For the boundary sine-Gordon model, which describes an impurity in a Luttinger liquid, we find the non-equilibrium conductance for all values of the Luttinger coupling.Comment: 36 pages (22 in double-page format), 7 figures in uuencoded file, uses harvmac and epsf macro

Spinons in more than one dimension: Resonance Valence Bond state stabilized by frustration

For two spatially anisotropic, SU(2)-invariant models of frustrated magnets in arbitrary space dimension we present a non-perturbative proof of the existence of neutral spin-1/2 excitations (spinons). In one model the frustration is static and based on fine tuning of the coupling constants, whereas in the other it is dynamic and does not require adjusting of the model parameters. For both models we derive a low-energy effective action which does not contain any constraints. Though our models admit the standard gauge theory treatment, we follow an alternative approach based on Abelian and non-Abelian bosonization. We prove the existence of propagating spin-1/2 excitations (spinons) and consider in detail certain exactly solvable limits. A qualitative discussion of the most general case is also presented.Comment: 42 pages, 7 figures, replaced with revised versio

Thermodynamics and conformal properties of XXZ chains with alternating spins

The quantum periodic XXZ chain with alternating spins is studied. The properties of the related R-matrix and Hamiltonians are discussed. A compact expression for the ground state energy is obtained. The corresponding conformal anomaly is found via the finite-size computations and also by means of the Bethe ansatz method. In the presence of an external magnetic field, the magnetic susceptibility is derived. The results are also generalized to the case of a chain containing several different spins.Comment: 28 pages, LaTeX2