Quantum Tunneling of Spinor Bose–Einstein Condensates in an Optical Lattice

We have studied tunneling of spinor Bose–Einstein condensate in an optical lattice. It is found that, when the system being prepared in a squeezed coherent state, there exist the quantum tunneling between lattices l and l+1, l and l−1, respectively. In particular, when the optical lattice is infinitely long and the spin excitations are in the long-wavelength limit, quantum tunneling disappear between lattices l and l+1, and that l and l−1, in this case the magnetic soliton appears.     

Tunneling of a Dipolar Bose–Einstein Condensate in an Optical Lattice

We have studied the tunneling and fluctuations of a dipolar Bose–Einstein condensate in an optical lattice, it is found that there exist the tunneling and fluctuations between lattices l and l+1, l and l−1, respectively. In particular, when the optical lattice is infinitely long and the spin excitations are in the long-wavelength limit, tunneling effects disappear between lattices l and l+1, and that l and l−1, in this case the fluctuations are a constant, and the magnetic soliton appears.     

Existence of exotic proton-kaon four particle system

Existence of the exotic proton-kaon four particle system p ⁺ k ⁻ p ⁻ k ⁺ is investigated. The Rayleigh-Riyz variational technique is used in calculations. The system tested is found to exist as bound state and its binding energy is calculated.     

Resonance microwave photoresistance of a two-subband electron system at large filling factors

The microwave photoresistance of a double GaAs quantum well with two occupied size-quantization sub-bands E ₁ and E ₂ has been studied at the temperatures T = 1.6–4.2 K in the magnetic fields B < 0.5 T. The microwave photoresistance of such a system has been found to have a maximum amplitude when the maximum of the magneto-intersubband oscillations with the number k = (E ₂ − E ₁)ℏω_c coincides with the maximum or minimum of the ω/ω_c oscillations, where ω is the microwave frequency and ω_c is the cyclotron frequency. It has been shown that the resonance photoresistance that appears in the kth maximum of the magneto-intersubband oscillations is determined by the condition ℏω/(E ₂ − E ₁) = (j ± 0.2)/k, where k and j are positive integers.     

Rare t-quark decays t → clj+lk? and t → c?jvk induced by doublets of scalar leptoquarks within the minimal four-color-symmetry model

The rare t-quark decays t → cl _j ⁺ l _k ⁻ and t → cṽ _j k _k induced by scalar-leptoquark doublets are considered within the minimal model involving four-color quark-lepton symmetry and the Higgs mechanism of quark and lepton mass splitting. The partial widths with respect to the decays being considered and the total widths Γ(t → cl ⁺′l ⁻) = Σ_j,k Γ(t → cl _j ⁺ l _k ⁻ ) and Γ(t → cl ⁺′l ⁻) = Σ_j,kΓ(t → cṽ _j v _k ) with respect to, respectively, the charged leptonic and neutrino modes are calculated. It is shown that, at scalar-leptoquark masses higher than the t-quark mass (m _S > m _t), the branching ratios for these modes are Br(t → cl ⁺′l ⁻) ≈ (3.5−0.4) × 10⁻⁵ and Br(t → cṽ′v) ≈ (7.1−0.8) × 10⁻⁵ at m _s = 180–250 GeV and an appropriate value of the leptoquark-mixing angle (sin β ≈ 0.2) and can increase for m _S < m _t to Br(t → cl ⁺′l ⁻) ≈ 0.03−0.002 and Br(t → cl ⁺′l ⁻) ≈ 0.46−0.05 for the charged mode at m _S = 150–170 GeV for sin β ≈ 1 and sin β ≈ 0.2, respectively. In the cases being considered, t-quark decays to pairs of charged leptons can be accessible to detection at LHC. In the last case, these decays could manifest themselves (for example, in dilepton events) at the Tevatron as well. Original Russian Text ? P.Yu. Popov, A.D. Smirnov, 2006, published in Yadernaya Fizika, 2006, Vol. 69, No. 6, pp. 1006–1016.     

Static structure factor of electrons around a heavy positively charged impurity in a one-component quantum rare plasma

An expression for the static structure factor,g ⁺⁻ (r), of electrons at a distancer from an infinitely heavy positively charged particle in a one component quantum rare plasma has been obtained in linear response theory using an appropriate quantum dielectric function of the rare plasma. The expression is a complicated function of the electron plasma frequency, Debye screening length andr, but reduces to that of classical plasma when quantum corrections are neglected. Forr<r _s (2r _s being the mean distance between two electrons), the temperature dependentg ⁺⁻ (r) has larger values in quantum case in comparison to that in classical situation and keeps increasing with decrease inr, more so at low temperatures when de-Broglie wavelength becomes larger and a considerable fraction ofr _s.     

D-dimensional massless particle with extended gauge invariance

We propose the model ofD-dimensional massless particle whose Lagrangian is given by theN-th extrinsic curvature of world-line. The system hasN+1 gauge degrees of freedom constitutingW-like algebra; the classical trajectories of the model are space-like curves which obey the conditionsk _N+a=k_N−a, k_2N =0,a=1, ...,N−1,N≤[(D−2)/2], while the firstN curvaturesk _i remain arbitrary. We show that the model admits consistent formulation on the anti-DeSitter space. The solutions of the system are the massless irreducible representations of Poincaré group withN nonzero helicities, which are equal to each other. Presented at the 9th Colloquium “Quantum Groups and Integrable Systems”, Prague, 22–24 June 2000.     

Overcoming of the gamow tunneling insufficiencies by maximizing the damp-matching resonant tunneling

The resonant quantum tunneling current through the barrier between two wells may be maximized when the damp (absorption) in one well matches the barrier parameters. The maximum resonant tunneling current is much greater than the conventional expectation by a factor ofθ (1/θ ² is the Gamow tunneling factor). It is shown that with all the established quantum mechanics, very much higher reaction probabilities between nuclei in contrary to the Gamow theory can be explained in agreement with experiments. Particularly, the resonance will select the sub-barrier fusion with a suitable fusion rate which matches the barrier parameters. This selective resonant tunneling model is able to explain both the hot fusion data (e.g. the width of resonance in¹¹B(p,α)2α reaction) and the cold fusion data (e.g. “excess heat” without any commensurate neutron andγ radiation). This work is supported by the State Commission of Science and Technology, the Natural Science Foundation of China (Contract #19645005), and the Fundamental Research Fund of Tsinghua University.     

On Meson Masses

It is shown that in the framework of an analytical confinement, when quark and gluon propagators are induced by a vacuum self-dual gluon field with constant strength, the masses of mesons with quantum numbers Q = (J ^P ,n), where n is the radial quantum number, and quark constituents m ₁, m ₂ are described with reasonable accuracy by the formula The positive parameter A _Q is unique for all mesons with a fixed quantum number Q. Sets of mesons J ^P = 1⁻, 0⁺, 1⁺, 2⁺, 3⁻ for n = 0 and 1⁻ , 2⁺ for n > 0 and different flavor constituent quarks (u = d, s, c, b) are considered.     

Tight-binding calculations of the subband structures of zincblende-semiconductor [001] quantum wells

The scattering-theoretic T-matrix method is used to calculate the subband structures of GaAs−ZnSe and ZnSe−ZnS_xSe_1−x [001] quantum wells within an empirical tight-binding model, that includes the bulk Г₆, Г₇ and Г₈ valence- and conduction bands. The resulting confinement energies for vanishing lateral crystal momentumk _‖ are compared with those, that are obtained from a simple effective mass model and effects are found and predicted which the effective mass model cannot account for. The effect of the band nonparabolicity and the influence of the microscopic sequence of atomic layers, which determines the symmetry properties of a quantum well, are studied for the GaAs−ZnSe wells.     

Quantum beats in excitons in Cu2O

A theoretical study is carried out of quantum beats (QB) in the time-dependent intensities of absorption of a test pulse and of spontaneous luminescence in a Cu₂O crystal under conditions of double optical resonance. It is assumed that pumping is effected by a CO₂-laser pulse which dynamically couples the exciton levels 1s(Γ ₅ ⁺ ) and 2p(Γ ₄ ⁻ ,Γ ₅ ⁻ ,Γ ₃ ⁻ Γ ₂ ⁻ ) and splits them into two or three pairs of quasi-energy levels. The frequency of the test pulse is in resonance with the frequency Γ ₅ ⁺ of the exciton. The corresponding intensities for various directions of the electric vector of the pump field E _L, the polarization vector ξ, and the wave vector q of the test pulse are obtained. The frequency of the quantum beats is twice the Rabi frequency, which for different values of E _L, ξ and q contains different sets of matrix elements of the dipole transitions between the levels 1s(Γ ₅ ⁺ ) and 2p(Γ ₄ ⁻ ,Γ ₅ ⁻ ,Γ ₃ ⁻ Γ ₂ ⁻ ). Thus, by measuring the period of the quantum beats it is possible to determine the unknown matrix elements of the indicated transitions. Fiz. Tverd. Tela (St. Petersburg) 39, 844–847 (May 1997)     

Spectrum of Kelvin-wave turbulence in superfluids

We derive a type of kinetic equation for Kelvin waves on quantized vortex filaments with random large-scale curvature, that describes step-by-step (local) energy cascade over scales caused by 4-wave interactions. Resulting new energy spectrum E _LN(k) ∝ k ^−5/3 must replace in future theory (e.g., in finding the quantum turbulence decay rate) the previously used spectrum E _KS(k) ∝ k ^−7/5, which was recently shown to be inconsistent due to nonlocality of the 6-wave energy cascade.     

Ergodic Jacobi Matrices and Conformal Maps

We study structural properties of the Lyapunov exponent γ and the density of states k for ergodic (or just invariant) Jacobi matrices in a general framework. In this analysis, a central role is played by the function w = − γ + iπ k as a conformal map between certain domains. This idea goes back to Marchenko and Ostrovskii, who used this device in their analysis of the periodic problem.     

Interwell exciton relaxation in semimagnetic asymmetric double quantum wells

The possibility of magnetic field control of the spectral and polarization characteristics of exciton recombination is examined in Cd(Mg, Mn) Te-based asymmetric double quantum wells. At low fields, the exciton transition in a semimagnetic well is higher in energy than that in a nonmagnetic well and the interwell exciton relaxation is fast. In contrast, when the energy order of the exciton transitions reverses at high fields, unexpectedly slow relaxation of σ⁻ polarized excitons from the nonmagnetic well to the σ⁺-polarized ground state in the semimagnetic well is observed. Strong dependence of the total circular polarization degree on the heavy-light hole splitting Δ _hh-lh in the nonmagnetic well is found and attributed to the spin dependent interwell tunneling controlled by exciton spin relaxation. Such a slowing down of the relaxation allows separation of oppositely spin-polarized excitons in adjacent wells. The text was submitted by the authors in English.     

Generalized Ginzburg-Landau equation and the properties of superconductors with Ginzburg-Landau parameter κ close to 1

An expression is derived for the free energy of a superconductor near the critical temperature, taking account of the terms of next highest order in the parameter 1−T/T _c. These terms become important for Ginzburg-Landau parameter values |κ−1|≪1, and in this case, in an external magnetic field H ₀ close to H _c2, the structure of the order parameter is determined by the relative values of the three small parameters |κ−1|, 1−T/T _c, and (H _c2−H ₀)/H _c2. Three types of lattices are investigated: triangular with one and two flux quanta per cell and square with one flux quantum per cell. Zh. éksp. Teor. Fiz. 115, 726–739 (February 1999)     

On the spin correlations of muons generated in the annihilation process e + e ? → μ+μ?

Using the technique of helicity amplitudes, the electromagnetic process e ⁺ e ⁻ → μ⁺μ⁻ is theoretically investigated in the one-photon approximation. The structure of the triplet states of the final (μ⁺μ⁻) system is analyzed. It is shown that in the case of unpolarized electron and positron the finalmuons are also unpolarized, but their spins are strongly correlated. Explicit expressions for the components of the correlation tensor of the final (μ⁺μ⁻) system are derived. The formula for the angular correlation at the decays of final muons μ⁺ and μ⁻, produced in the process e ⁺ e ⁻ → μ⁺μ⁻, is obtained. It is demonstrated that spin correlations of muons in the process of electron-positron pair annihilation have the purely quantum character, since one of the incoherence inequalities for the correlation-tensor components is always violated. The additional contribution of the weak interaction of lepton neutral currents through the virtual Z ⁰ boson is considered; it is established that, taking into account the weak interaction, the qualitative character of the muon spin correlations does not change. The text was submitted by the authors in English.     

Spin correlations of muons in the process of electron-positron pair annihilation e + e ? → μ+μ?

Using the technique of helicity amplitudes, the electromagnetic process e ⁺ e ⁻ → μ⁺μ⁻ is theoretically investigated in the one-photon approximation. The structure of the triplet states of the final (μ⁺μ⁻) system is analyzed. It is shown that in the case of unpolarized electron and positron the final muons are also unpolarized, but their spins are strongly correlated. Explicit expressions for the components of the correlation tensor of the final (μ⁺μ⁻) system are derived. The formula for the angular correlation at the decays of final muons μ⁺ and μ⁻, produced in the process e ⁺ e ⁻ → μ⁺μ⁻, is obtained. It is demonstrated that spin correlations of muons in the process of electron-positron pair annihilation have the purely quantum character, since one of the incoherence inequalities for the correlation tensor components is always violated. The additional contribution of the weak interaction of lepton neutral currents through the virtual Z ⁰ boson is considered; it is established that, taking into account the weak interaction, the qualitative character of the muon spin correlations does not change.     

Momentum conservation in the luminescence of modulation-doped Ga x In1−x As−Al y In1−y As quantum wells

Summary Thek-conserving selection rule in the electron-hole recombination is investigated by intensity-dependent photoluminescence measurements inn-type modulation-doped Ga _x In_1−x As−Al _y In_1−y As single quantum wells intentionally doped with Be acceptors in the well centre. Thek-non-conserving recombination process involves electrons with momentum up to the Fermi edge and holes localized on the Be acceptors. The transition from a one-component electron plasma to a two-component electron-hole plasma is studied by comparing the experimental results with theoretical line shape models. The density-dependent band gap renormalization is determined for the one-component and the two-component electron-hole plasma. The obtained results are found to agree well with recent theoretical calculations.     

Wavevector and frequency dependent dielectric function dynamic structure factor and the instability of plasma waves in two component hot rare quantum and classical plasmas

The full wavevector and frequency dependent complex dielectric function for two component classical and quantum rare hot plasmas have been derived. The real part of dielectric function is obtained in the form of a series. Difference between quantum and classical real and imaginary parts of dielectric function have been brought out by making explicit calculations. The quantum nature of the plasma brings about significant changes in both parts depending upon the magnitude of quantum parameter,R (= 8.93(λ_th)/λ). Expressions for the dynamic structure factors for both two component classical and quantum plasma have been evaluated for different values of the mass of the positive componentm ₊, temperature T₊ and wavevector k. It is found that the plasma exhibits well defined collective modes for certain values of |k| accompanied by varying disorder which depends upon the values of m₊ as well as on |k| and T₊. For the quantum case the collective modes are less well defined as compared to the corresponding classical case, thus proving that quantum nature introduces inherent disorder in the system. But for both the cases, increase in temperature destroys collective modes. Another feature is the appearance of a hump near Ω = 0 which becomes smaller and vanishes as the quantum parameter is decreased. Instability of plasma modes in the presence of constant electric field has also been worked out for the quantum case.