The ground state problem in the infinite-U Hubbard model

The problem of the ground state of the electronic system in the Hubbard model for U=∞ is discussed. The author investigates the normal (singlet or nonmagnetic) N state of the electronic system over the entire range of electron densities n⩽1. It is shown that the energy of the N state ɛ ₀ ⁽¹⁾ (n) in a one-particle approximation, such as (e.g.) the extended Hartree-Fock approximation, is lower than the energy of the saturated ferromagnetic FM state ɛ _FM(n) for all n. The dynamic magnetic susceptibility is calculated in the random phase approximation, and it is shown that the N state is stable over the entire range of electron densities: The static susceptibility (ω=0) does not have a band singularity in the zero-wave vector limit q→0. A formally exact representation is obtained for the mass operator of the one-particle Green’s function, and an approximation of this operator is proposed: M _k(E)⋍λF(E), where λ=n(1−n)/(1−n/2)z is the kinematic interaction parameter, z is the number of nearest neighbors, and F(E) is the total single-site Green’s function. For an elliptical density of states the integral equation for F(E) is solved exactly, ad it is shown that the spectral intensity rigorously satisfies the sum rule. The calculated energy of the strongly correlated N state ɛ ₀(n)<ɛ _FM(n) for all n, and in light of this relationship the author discusses the hypothesis that the ground state of the system is the normal (singlet) state in the thermodynamic limit. The electron distribution function at T=0 differs significantly from the Fermi step; it is “smeared” along the entire energy spectrum, and discontinuities do not occur in the region of the chemical potential m. Fiz. Tverd. Tela (St. Petersburg) 39, 193–203 (February 1997)     

Level statistics inside the core of a superconductive vortex

A microscopic theory of the Efetov supermatrix sigma-model type is constructed for the low-lying electron states in a mixed superconductive-normal system with disorder. This technique is used for the study of the localized states in the core of a vortex in a moderately clean superconductor with τ ⁻¹≫ω ₀∼Δ²/E _F . At low energies ε≪ω _Th∼ (ω ₀/τ)^1/2, the energy level statistics is described by the “zero-dimensional” limit of this supermatrix theory, and the result for the density of states is equivalent to that obtained within Altland-Zirnbauer random matrix model. Nonzero modes of the sigma model increase the mean interlevel distance by the relative amount [2 ln (1/ω ₀ τ)]⁻¹. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 1, 78–83 (10 July 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Level density and shape changes in excited sd shell nuclei

In the present calculation we have used the Monte Carlo method of generating collective spin and total energy of the nucleus for various configurations of the system with N ₀ single particle states available for n number of particles. The different configurations (arrangements of occupied single particle states) leading to a particular energy E and spin J are then collected to get the density of states for the given energy E and spin J. We find that if we use the cranked Nilsson model single particle states for the rotational frequency Ω = 0.0ħω, 0.05ħω and 0.1ħω there is a shift in the maximum density of states W _max with a tendency for the system to become more oblate or prolate depending on the shift in the maximum density of states as the angular momentum decreases or increases. The change in nuclear level density with collectivity, i.e. with the use of cranked Nilsson model single particle levels has been noticed.      

Comment on vortex mass and quantum tunneling of vortices

Vortex mass in Fermi superfluids and superconductors and its influence on quantum tunneling of vortices are discussed. The vortex mass is essentially enhanced due to the fermion zero modes in the core of the vortex: the bound states of the Bogoliubov quasiparticles localized in the core. These bound states form the normal component, which is nonzero even in the low-temperature limit. In the collisionless regime ω ₀ τ≫1 the normal component trapped by the vortex is unbound from the normal component in a bulk superfluid/superconductor and adds to the inertial mass of the moving vortex. In a d-wave superconductor the vortex mass has an additional factor of (B _c2/B)^1/2 due to the gap nodes. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 2, 201–206 (25 January 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Nature of conduction via impurities in uncompensated silicon

The static conductivity σ(E) and photoconductivity (PC) at radiation frequencies ħω=10 and 15 meV in Si doped with shallow impurities (density N=10¹⁶−6×10¹⁶ cm⁻³, ionization energy ε₁≃45 meV) with compensation K=10⁻⁴−10⁻⁵ in electric fields E=10–250 V/cm are measured at liquid-helium temperatures T. Special measures are taken to prevent the high-frequency part of the background radiation (ħω>16 meV) from striking the sample. It is found that the conductivity σ(E) is due to carrier motion along the D ⁻ band, which is filled with carriers under the influence of the field E. In fields E<E _q (E _q ≃100–200 V/cm) the carrier motion consists of hops along localized D ⁻ states in a 10–15 meV energy band below the bottom of the free band (energy ε=ε₁); for E>E _q carriers drift along localized D ⁻ states with energy ε∞ε₁−10 meV. An explanation is proposed for the threshold behavior of the field dependence of the photo-and static conductivities. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 4, 232–236 (25 August 1997)     

Oscillator rule of the trap activation energies in NaCl crystals

The energy spectra of traps in NaCl crystals have been studied in detail by the method of thermoluminescence. Crystals of NaCl were undoped but treated thermally in different ways. The activation energies of traps form a single oscillator series, E _n =ℏω _TL (n+1/2), ℏω _TL =903 cm^-1. Contrary to other previously studied crystals with complex lattices, the corresponding line ℏω _Ram =ℏω _TL was not found in Raman spectra of NaCl. It is assumed that the oscillator rule is governed by the polaron nature of traps. The trap activation energy is determined by the vibration level from which the transition of the charge carrier to the excited luminescence centre is made possible and depends on the distance between these centres.     

Combined polaron states in magnetooptical effects in a quantum well

Combined polaron states in a rectangular quantum well in a strong magnetic field perpendicular to the well plane are discussed. These states are due to interaction between two discrete electron levels with different Landau quantum numbers (n and n ₁) and different size-quantization quantum numbers (m and m ₁) on the one hand and a confined LO phonon on the other under conditions of low temperature when the energy difference between the electronic levelsis equal or close to the energy of the confined LO phonon. The expression for the resonant magnetic field H _res at which a combined polaron is formed contains the energy difference between size-quantized levels, so it is a function of quantum well parameters. The separation ΔE _res between branches in the energy spectrum of a combined polaron and H _res has been calculated as a function of the quantum well width d. The resonant field H _res can be reduced dramatically in comparison with the case m=m ₁. The case of size-quantization with n=n ₁ has been analyzed. The energy difference ΔE _res is in the range (1–5)· 10⁻³ eV. The damping of combined polaron states due to the effect of anharmonicity on the LO phonon has been studied. Interband absorption and features in the reflection spectrum due to interband transitions have been calculated for an arbitrary ratio between the radiative and “phonon” lifetime of a combined polaron have been investigated. Zh. éksp. Teor. Fiz. 116, 1419–1439 (October 1999)     

Is the Abrikosov model applicable for describing electronic vortices in plasmas?

A new model of electronic vortices in plasma is studied. The model assumes that the profile of the Lagrangian invariant I, equal to the ratio I=Ω/n of the electronic vorticity to the electron density, is given. The proposed approach takes into account the magnetic Debye scale r _B ≃B/4πen, which leads to breakdown of plasma quasineutrality. It is shown that the Abrikosov singular model cannot be used to describe electron vortices in plasmas because of the fundamental limitation on the electron vorticity on the axis of a vortex in a plasma. Analysis of the equations shows that in the model considered for the electronic vorticity, the total magnetic flux decreases when the size r ₀ of the region in which I≠0 becomes less than c/ω_pe (ω_pe is the electron plasma frequency). For ω _pe r ₀/c≪1, an electronic vortex is formed in which the magnetic flux decreases as r ₀ ² and the inertial component predominates in the electronic vorticity. The structure arising as ω _pe r ₀/c⇒0 is a narrow “hole” in the electron density, which can be identified from the spectrum of electromagnetic waves in this region. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 7, 461–466 (10 April 1998)     

Two-photon fluorescence spectrum in an atom + dielectric microsphere system

A strong resonant interaction of a two-level atom with a dielectric microsphere is studied on the basis of quantum electrodynamics. The initial condition considered is one in which the atom is initially excited and the resonant mode of the microsphere has been excited by a single photon. The spectrum of two emitted photons depends strongly on the method used to excite the microsphere, i.e., on the spatial distribution of the photon energy. The most characteristic feature of the two-photon fluorescence spectrum is a strong energy correlation of the emitted photons. This correlation is expressed in the fact that the energies of the emitted photons are related by the equation of an ellipse (ω+ω ₂−2ω _vA )²+3(ω ₁−ω ₂)²= 4Ω _Rabi ² . The relation between the results obtained and the predictions of the theory of dressed states is discussed. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 3, 192–197 (10 August 1999)     

Transmission spectra of thin CdS and CdSe crystals near higher-order isotropic points

Summary For photon energies below the absorption edge in CdS, CdSe and other II–VI crystals the polariton dispersion curves forE⊥c andE‖c (c-axis in a wurtzite crystal) corss at some points called isotropic points (IP). The occurrence of isotropic points provides the possibility of mode coupling between ordinary and extraordinary waves. Since the consequences of mode coupling on the optical properties for photon energies near the lowest IP lying much below the first excitonic state were widely discussed in recent years, more attention is now paid to isotropic points lying near the band gap and related to then=2,3, … excitonic states (?higher isotropic points?). Making use of Stahl's real density matrix approach we derive the polariton dispersion relationsk _⊥ (ω), andk _‖ (ω), for CdS and CdSe bulk crystals and determine the positions of IP's due to the crossing of theB-polariton with higherA-excitonic resonances. By the method of multiple internal reflection we calculate the transmission spectra for various crystal thicknesses (between 3 μm and 0.5 mm) and coupling mechanisms. The calculated transmission shows sharply peaked structures centred at the isotropic points.     

On a possibility for observing the neutron electric polarizability

A new method is proposed for setting a lower or upper limit a α _n * on the neutron electric polarizability α _an . It is based on the fact that the real part of the s-wave scattering amplitude changes sign near the s-wave neutron resonance at E=E*. The methods consist of the observation of the energy behavior of the forward-backward scattering asymmetry ω ₁ which experiences a jump at E=E*. If the jump is such that dω ₁/dE>0, then α _n >α _n *, while if dω ₁/dE<0, then α _n <α _n *, and if dω ₁/dE∼0, then α _n ∼α _n *. Seven even-even nuclei are found with α _n * from 0.5 to 3.1 in 10⁻³ fm³. Some details of a possible experiment with ¹⁸²W are described. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 3, 171–174 (10 August 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Raman spectroscopy of resonance exciton tunneling in GaAs/AlAs superlattices in electric fields

Optical-resonance-Raman scattering by acoustic phonons is used to study the effect of an electric field on the state of excitons in GaAs/AlAs superlattices. When the energy of the exciting photon coincides with the energy of an exciton bound to Wannier-Stark states of a heavy hole and electron with Δn=0,±1, the acoustic Raman scattering is enhanced. Oscillations in the intensity of the Raman spectrum in the electric field are explained by resonance delocalization of the exciton ground state as it interacts with Wannier-Stark states of neighboring quantum wells or with Wannier-Stark states of a higher electron miniband. Fiz. Tverd. Tela (St. Petersburg) 40, 827–829 (May 1998)     

Nonadiabatic effects in the phonon spectra of superconductors

The nonadiabatic corrections to the self-energy part Σ_s(q, ω) of the phonon Green’s function are studied for various values of the phonon vectors q resulting from electron-phonon interactions. It is shown that the long-range electron-electron Coulomb interaction has no direct influence on these effects, aside from a possible renormalization of the corresponding constants. The electronic response functions and Σ_s(q, ω) are calculated for arbitrary vectors qand energy ω in the BCS approximation. The results obtained for q=0 agree with previously obtained results. It is shown that for large wave numbers q, vertex corrections are negligible and Σ_s(q, ω) possesses a logarithmic singularity at ω=2Δ, where Δ is the superconducting gap. It is also shown that in systems with nesting, Σ_s(Q, ω) (where Q is the nesting vector) possesses a square-root singularity at ω=2Δ, i.e., exactly of the same type as at q=0. The results are used to explain the recently published experimental data on phonon anomalies, observed in nickel borocarbides in the superconducting state, at large q. It is shown, specifically, that in these systems nesting must be taken into account in order to account for the emergence of a narrow additional line in the phonon spectral function S(q, ω)≈−π ⁻¹ Im D _s (q, ω), where D _s (q, ω) is the phonon Green’s function, at temperatures T<T _c . Zh. éksp. Teor. Fiz. 115, 1799–1817 (May 1999)     

Selective photoconductivity induced in PbTe(Ga) by a local phonon mode

Selective photoconductivity at frequency ω=155 cm⁻ was discovered in PbTe(Ga) narrow-gap semiconductors at liquid-nitrogen temperatures. The corresponding energy is much lower than all characteristic energies of the electronic spectrum of the semiconductor. The effect is attributed to optical excitation of a local vibrational mode of an impurity center leading to delocalization of the electrons. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 5, 342–346 (10 March 1996)     

Determination of the spectral parameters of nuclear quadrupole resonance from nutation spectra of powdered samples

An analytical expression I(ω) is obtained for a normalized function of the shape of an idealized nuclear quandrupole resonance nutation line of a powdered sample for spins I=3/2 (η≠0). Calculations are made of the initial moments <ωⁿ> of the nutation spectrum of the powder in the form of functions of ω₀=γB₁ and the asymmetry parameter η of the electric field gradient tensor. A method is proposed for determining the spectral parameters η and eQq_zz from the experimentally measured values of <ω>, <ω²>, <ω⁴>, and ω_1/2 of the nuclear quadrupole resonance nutation spectrum of the powder. State University, Kaliningrad. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 3–8, July, 1997.     

The Probability of Entanglement

We show that states on tensor products of matrix algebras whose ranks are relatively small are almost surely entangled, but that states of maximum rank are not. More precisely, let and be full matrix algebras with m ≥  n, fix an arbitrary state ω of N, and let E(ω) be the set of all states of that extend ω. The space E(ω) contains states of rank r for every r = 1, 2, . . . , m · rank ω, and it has a filtration into compact subspaces

Integral energy spectrum of primary cosmic rays at high energies

The integral energy spectrum of primary cosmic rays has been obtained. In the energy range (2.4×10³−1.1×10⁵ GeV), the spectrum of all nuclei is consistent with a power law of indexγ=1.55±0.06 and the flux of all nuclei is:N(⩾E ₀)⋍(5.1±1.8)×10⁻¹×E ₀ ^−1.55 particles/cm² sterad. sec., whereE ₀ is in GeV. The spectrum of primaryα-particles in the energy range (4.4×10³−4.8×10⁴) GeV is also consistent with a power law of indexγ=1.71±0.12 and the flux is:N(⩾E ₀)=(4.2±1.4)×10⁻¹×E ₀ ^−1.71 , particles per cm² sterad. sec, whereE ₀ is in GeV.     

Spectrum of charged particle oscillations in an RF quadrupole field

Variations in the spectral composition of ion oscillations within several stability regions of a quadrupole mass filter were studied. The frequency spectrum was shown to consist of two line systems. Side lines ω_n=nω₀±βω₀/2 were observed in the oscillation spectrum near harmonics nω₀ (n=0, 1, 2,...), where ω₀ is the circular frequency of an RF field and β is the stability parameter. Near the boundaries of the stability regions, the oscillations took the form of beatings. For even values of the stability parameter, β=2k (k=1, 2,...), the beat frequency coincides with the fundamental frequency ω₀ and, for β=2k−1, the main beat frequencies are ω₀/2 and 3ω₀/2.     

Specific heat of the harmonic oscillator within generalized equilibrium statistics

Summary Within the generalized equilibrium statistics recently introduced by Tsallis (p _n ∝[1−β(q−-1) _εn ]^1/(q−)), we calculate the thermal dependence of the specific heat corresponding to a harmonic-oscillator-like spectrum, namely ε _n ω(n−α) (∀ω>0,n=0,1,2,...). The influences ofq and α are exhibited. Physically inaccessible and/or thermally frozen gaps are obtained in the low-temperature region, and, forq>1, oscillations are observed in the high-temperature region. The specific heat of the two-level system is also shown.     

An improved model for band tail states inn-type degenerate semiconductors

Summary Using two screened donor potential energy models and a wave vectork-positionr uncertainty relation, the results of the exponential band tail states, inn-type degenerate semiconductors, obtained in our previous paper, are improved. The second-order cumulant or the correlation functionW (ϱ,E) is expressed as a function of the total donor concentration ϱ and total carrier energyE. Near band edges, the conduction and valence band tails are, respectively, proportional to exp [E/E ₀(ϱ)] and exp [−E/E ₀(ϱ)], whereE ₀(ϱ) is the energy characteristic of the appropriate band tail, in good accordance with those experimentally obtained by Pankove. Far below the conduction band edge, our result of the conduction band tail is proportional to exp [−BE ² exp [A ]], whereA andB are the functions of ϱ, which is reduced to zero more rapidly in comparison with the corresponding result obtained by Halperin and Lax (i.e. exp [−|E| ⁿ , wheren varies between 1/2 and 2). To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.