Possibility of Geometric Description of Quasiparticles in Solids

New phenomenological approach for the description of elementary collective excitations is proposed. The crystal is considered to be an anisotropic space-time vacuum with a prescribed metric tensor in which the information on electromagnetic crystalline fields is included. The quasiparticles in this space are supposed to be described by the equations structurally similar to the relativistic wave equations for particles in empty space. The generalized Klein-Gordon-Fock equation and the generalized Dirac equation in external electromagnetic field are considered. The applicability of the proposed approach to the case of conduction electron in a crystal is discussed.Comment: 17 pages, latex; to appear in Int. Jnl. Mod. Phy

Differential Form of the Skornyakov--Ter-Martirosyan Equations

The Skornyakov--Ter-Martirosyan three-boson integral equations in momentum space are transformed into differential equations. This allows us to take into account quite directly the Danilov condition providing self-adjointness of the underlying three-body Hamiltonian with zero-range pair interactions. For the helium trimer the numerical solutions of the resulting differential equations are compared with those of the Faddeev-type AGS equations.Comment: 4 pages, 2 figure

Radio-frequency Bloch-transistor electrometer

A quantum-limited electrometer based on charge modulation of the Josephson supercurrent in the Bloch transistor inserted into a superconducting ring is proposed. As this ring is inductive coupled to a high-Q resonance tank circuit, the variations of the charge on the transistor island (input signal) are converted into variations of amplitude and phase of radio-frequency oscillations in the tank. These variations are amplified and then detected. The output noise, the back-action fluctuations and their cross-correlation are computed. It is shown that our device enables measurements of the charge with a sensitivity which is determined by the energy resolution of its amplifier, that can be reduced down to the standard quantum limit of \hbar/2. On the basis of this setup a "back-action-evading" scheme of the charge measurements is proposed.Comment: 5 pages incl. 2 figure

Thin structure of steel St52, 3N and possible reasons of defect of large-capacity billets AT "YURMASH"

Electron-microscopic and x-ray investigations of structurally-phase and intense-deformed condition of material made of defective and conditional forged billet at «Yurmash» have been carried out. It is ascertained that in steel made from the defective forged piece the fraction of perlite is 1,5...2 times higher and lamellar perlite prevails. Local long-range tensions in both conditions of material are commensurable with fluidity limit. The content of sulfides is considerably higher in the steel made from the defective billet. They are located in the body of ferrite grains and along the interfaces. In the material made from the conditional forging they are located only inside of grains. The scalar density of dislocations in ferrite grains and in ferrite layers of perlite of the defected billet is one and a half time higher than in conditional metal. All the totality of the listed above circumstances allows stating that the main cause of cracking of large-capacity billets made of steel St52, 3N is not a full conformity of the chemical compound to branded requirements

Bound states of three and four resonantly interacting particles

We present an exact diagrammatic approach for the problem of dimer-dimer scattering in 3D for dimers being a resonant bound state of two fermions in a spin-singlet state, with corresponding scattering length $a_F$. Applying this approach to the calculation of the dimer-dimer scattering length $a_B$, we recover exactly the already known result $a_B=0.60 a_F$. We use the developed approach to obtain new results in 2D for fermions as well as for bosons. Namely, we calculate bound state energies for three $bbb$ and four $bbbb$ resonantly interacting bosons in 2D. For the case of resonant interaction between fermions and bosons we calculate exactly bound state energies of the following complexes: two bosons plus one fermion $bbf$, two bosons plus two fermions $bf_{\uparrow}bf_{\downarrow}$, and three bosons plus one fermion $bbbf$.Comment: 10 pages, 9 figure