Stimulating Mechanisms in Ecologically Motivated Regulation: Will Ecological Policies in Transition and Developing Countries Become Efficient?

In this paper, the theory of stimulating mechanisms is used to study the relationship between characteristics of polluting firms and results of ecological policy. It is shown that the optimal ecologically motivated policy can qualitatively change in accordance with a relative effectiveness of types of firms. Two models are proposed. In the first of them the regulator has no information on a type of firm but possesses information about cost functions of the types of firms. In the second (game) model, moreover, the regulator has no information about levels of investment chosen by the types of firms.ecological policy, regulation, stimulating mechanism, contract, relative economic effectiveness, Nash equilibrium, developing and transition economies

One-dimensional two-component fermions with contact even-wave repulsion and SU(2) breaking near-resonant odd-wave attraction

We consider a one-dimensional (1D) two-component atomic Fermi gas with contact interaction in the even-wave channel (Yang-Gaudin model) and study the effect of an SU(2) symmetry breaking near-resonant odd-wave interaction within one of the components. Starting from the microscopic Hamiltonian, we derive an effective field theory for the spin degrees of freedom using the bosonization technique. It is shown that at a critical value of the odd-wave interaction there is a first-order phase transition from a phase with zero total spin and zero magnetization to the spin-segregated phase where the magnetization locally differs from zero.Comment: 18 pages, 3 fugures; references adde

Finite size effects for the gap in the excitation spectrum of the one-dimensional Hubbard model

We study finite size effects for the gap of the quasiparticle excitation spectrum in the weakly interacting regime one-dimensional Hubbard model with on-site attraction. Two type of corrections to the result of the thermodynamic limit are obtained. Aside from a power law (conformal) correction due to gapless excitations which behaves as $1/N_a$, where $N_a$ is the number of lattice sites, we obtain corrections related to the existence of gapped excitations. First of all, there is an exponential correction which in the weakly interacting regime ($|U|\ll t$) behaves as $\sim \exp (-N_a \Delta_{\infty}/4 t)$ in the extreme limit of $N_a \Delta_{\infty} /t \gg 1$, where $t$ is the hopping amplitude, $U$ is the on-site energy, and $\Delta_{\infty}$ is the gap in the thermodynamic limit. Second, in a finite size system a spin-flip producing unpaired fermions leads to the appearance of solitons with non-zero momenta, which provides an extra (non-exponential) contribution $\delta$. For moderate but still large values of $N_a\Delta_{\infty} /t$, these corrections significantly increase and may become comparable with the $1/N_a$ conformal correction. Moreover, in the case of weak interactions where $\Delta_{\infty}\ll t$, the exponential correction exceeds higher order power law corrections in a wide range of parameters, namely for $N_a\lesssim (8t/\Delta_{\infty})\ln(4t/|U|)$, and so does $\delta$ even in a wider range of $N_a$. For sufficiently small number of particles, which can be of the order of thousands in the weakly interacting regime, the gap is fully dominated by finite size effects.Comment: 17 pages, 5 figure

Zero sound in a two-dimensional dipolar Fermi gas

We study zero sound in a weakly interacting 2D gas of single-component fermionic dipoles (polar molecules or atoms with a large magnetic moment) tilted with respect to the plane of their translational motion. It is shown that the propagation of zero sound is provided by both mean field and many-body (beyond mean field) effects, and the anisotropy of the sound velocity is the same as the one of the Fermi velocity. The damping of zero sound modes can be much slower than that of quasiparticle excitations of the same energy. One thus has wide possibilities for the observation of zero sound modes in experiments with 2D fermionic dipoles, although the zero sound peak in the structure function is very close to the particle-hole continuum.Comment: 15 pages, 2 figure

Vortex structures in rotating Bose-Einstein condensates

We present an analytical solution for the vortex lattice in a rapidly rotating trapped Bose-Einstein condensate (BEC) in the lowest Landau level and discuss deviations from the Thomas-Fermi density profile. This solution is exact in the limit of a large number of vortices and is obtained for the cases of circularly symmetric and narrow channel geometries. The latter is realized when the trapping frequencies in the plane perpendicular to the rotation axis are different from each other and the rotation frequency is equal to the smallest of them. This leads to the cancelation of the trapping potential in the direction of the weaker confinement and makes the system infinitely elongated in this direction. For this case we calculate the phase diagram as a function of the interaction strength and rotation frequency and identify the order of quantum phase transitions between the states with a different number of vortex rows.Comment: 17 pages, 12 figures, with addition

Stripe phase: analytical results for weakly coupled repulsive Hubbard model

Motivated by the stripe developments in cuprates, we review some analytical results of our studies of the charge- and spin density modulations (CDW and SDW) in a weakly coupled one dimensional repulsive electron system on a lattice. It is shown that close to half filling, in the high temperature regime above the mean field transition temperature, short range repulsions favor charge density fluctuations with wave vectors bearing special relations with those of the spin density fluctuations. In the low temperature regime, not only the wave vectors, but also the mutual phases of the CDW and SDW become coupled due to a quantum interference phenomenon, leading to the stripe phase instability in a quasi one-dimensional repulsive electron system. It is shown that away from half filling periodic lattice potential causes cooperative condensation of the spin and charge superlattices. "Switching off" this potential causes vanishing of the stripe order. The leading spin-charge coupling term in the effective Landau functional is derived microscopically. Results of the 1D renormalization group (parquet) analysis away from half filling are also presented, which indicate transient-scale correlations resembling the mean-field pattern. Farther, the self-consistent solution for the spin-charge solitonic superstructure in a quasi-one-dimensional electron system is obtained in the framework of the Hubbard model as a function of hole doping and temperature. Possible relationship with the stripe phase correlations observed in high T_c cuprates is discussed.Comment: 29 pages,10 figures, Late

Conditions of contaminant distribution in the wetland water of Western Siberia (the Russian Federation)

The models of pollutants' distribution in the wetland waters of Western Siberia (Tomsk Oblast, Russia) have been considered. The models' application allows describing the observed changes in the chemical composition of active layer of wetland waters with satisfactory accuracy. With these models, the most significant impact of sewage discharge on the local wetland water composition is observed in wetland edge area of up to 150–300 m in width. Even in this area it is possible to minimize the impact of sewage discharge on the wetlands provided the concentration in sewage water is 1.14-1.3 time more than the background concentration

Superfluid transition in quasi-two-dimensional disordered dipolar Fermi gases

We investigate the effect of weak disorder on the superfluid properties of two-component quasi-two-dimensional dipolar Fermi gases. The dipole-dipole interaction amplitude is momentum dependent, which violates the Anderson theorem claiming that the weak disorder has practically no influence on the superfluid transition temperature in the weakly interacting regime. We find that for dipolar fermions the transition temperature in this regime can be strongly increased by the disorder like in the purely two-dimensional case. However, the effect becomes smaller with increasing the intercomponent fermion-fermion interaction, and in the strongly interacting regime the superfluid transition temperature in the weak disorder becomes very close to that in the absence of disorder