Exact relations for quantum-mechanical few-body and many-body problems with short-range interactions in two and three dimensions

We derive relations between various observables for N particles with zero-range or short-range interactions, in continuous space or on a lattice, in two or three dimensions, in an arbitrary external potential. Some of our results generalise known relations between large-momentum behavior of the momentum distribution, short-distance behavior of the pair correlation function and of the one-body density matrix, derivative of the energy with respect to the scattering length or to time, and the norm of the regular part of the wavefunction; in the case of finite-range interactions, the interaction energy is also related to dE/da. The expression relating the energy to a functional of the momentum distribution is also generalised, and is found to break down for Efimov states with zero-range interactions, due to a subleading oscillating tail in the momentum distribution. We also obtain new expressions for the derivative of the energy of a universal state with respect to the effective range, the derivative of the energy of an efimovian state with respect to the three-body parameter, and the second order derivative of the energy with respect to the inverse (or the logarithm in the two-dimensional case) of the scattering length. The latter is negative at fixed entropy. We use exact relations to compute corrections to exactly solvable three-body problems and find agreement with available numerics. For the unitary gas, we compare exact relations to existing fixed-node Monte-Carlo data, and we test, with existing Quantum Monte Carlo results on different finite range models, our prediction that the leading deviation of the critical temperature from its zero range value is linear in the interaction effective range r_e with a model independent numerical coefficient.Comment: 51 pages, 5 figures. Split into three articles: Phys. Rev. A 83, 063614 (2011) [arXiv:1103.5157]; Phys. Rev. A 86, 013626 (2012) [arXiv:1204.3204]; Phys. Rev. A 86, 053633 (2012) [ arXiv:1210.1784

Three-boson problem near a narrow Feshbach resonance

We consider a three-boson system with resonant binary interactions and show that three-body observables depend only on the resonance width and the scattering length. The effect of narrow resonances is qualitatively different from that of wide resonances revealing novel physics of three-body collisions. We calculate the rate of three-body recombination to a weakly bound level and the atom-dimer scattering length and discuss implications for experiments on Bose-Einstein condensates and atom-molecule mixtures near Feshbach resonances.Comment: published versio

Circular photon drag effect in bulk tellurium

The circular photon drag effect is observed in a bulk semiconductor. The photocurrent caused by a transfer of both translational and angular momenta of light to charge carriers is detected in tellurium in the mid-infrared frequency range. Dependencies of the photocurrent on the light polarization and on the incidence angle agree with the symmetry analysis of the circular photon drag effect. Microscopic models of the effect are developed for both intra- and inter-subband optical absorption in the valence band of tellurium. The shift contribution to the circular photon drag current is calculated. An observed decrease of the circular photon drag current with increase of the photon energy is explained by the theory for inter-subband optical transitions. Theoretical estimates of the circular photon drag current agree with the experimental data.Comment: 8 pages, 4 figure

Can an electric current orient spins in quantum wells?

A longstanding theoretical prediction is the orientation of spins by an electrical current flowing through low-dimensional carrier systems of sufficiently low crystallographic symmetry. Here we show by means of terahertz transmission experiments through two-dimensional hole systems a growing spin orientation with an increasing current at room temperature.Comment: 5 pages, 2 figure

Studying of the 9Be Structure

Experimental data on inelasti

The Structure and Mechanical Properties of Bridge Steel Weldings With Glass-Steel Liners

A new technology is developed for welding multi-span bridge constructions. The mechanical properties and structure of the low-carbon bridge steel welds have been studied. The welding parameters and application of steel-glass liners provide for long-term service of steel constructions in conformity with the welding industry specifications

Method for direct identification of optimum modal values of dynamical systems

The synthesis method of a dynamic system by successive solutions of two systems of algebraic equations, variables that are characteristic polynomial coefficients and mechanical parameters of the system

Global in Time Solutions to Kolmogorov-Feller Pseudodifferential Equations with Small Parameter

The goal in this paper is to demonstrate a new method for constructing global-in-time approximate (asymptotic) solutions of (pseudodifferential) parabolic equations with a small parameter. We show that, in the leading term, such a solution can be constructed by using characteristics, more precisely, by using solutions of the corresponding Hamiltonian system and without using any integral representation. For completeness, we also briefly describe the well-known scheme developed by V.P.Maslov for constructing global-in-time solutions.Comment: 27 page