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 resonance bound state of two fermions in a spin-singlet state, with corresponding scattering length a _F . Applying this approach to the calculation of the dimmer-dimer scattering length a _B , we recover exactly the already known result a _B = 0.6 a _F . We use the developed approach to obtain new results in 2D for fermions and bosons. Namely, we calculate bound state energies for three bbb and four bbbb resonantly interacting bosons in 2D. For the case of resonance interaction between fermions and bosons, we exactly calculate bound state energies of the following complexes: two bosons plus one fermion bbf, two bosons plus two fermions bf↑bf↓, and three bosons plus one fermion bbbf.     

Ground State Energy of the Low Density Hubbard Model

We derive a lower bound on the ground state energy of the Hubbard model for given value of the total spin. In combination with the upper bound derived previously by Giuliani (J. Math. Phys. 48:023302, [2007]), our result proves that in the low density limit the leading order correction compared to the ground state energy of a non-interacting lattice Fermi gas is given by 8π a ? _u ? _d , where ? _u(d) denotes the density of the spin-up (down) particles, and a is the scattering length of the contact interaction potential. This result extends previous work on the corresponding continuum model to the lattice case.     

Correlation between the properties of the deuteron and the low-energy triplet parameters of neutron-proton scattering

The correlation between the asymptotic normalization constant for the deuteron, A_S, and the neutron-proton scattering length for the triplet case, a_t, is investigated. It is found that 99.7% of the asymptotic constant A_S is determined by the scattering length a_t. It is shown that the linear correlation between the quantities A _S ^?2 and 1/a_t provides a good test of correctness of various models of nucleon-nucleon interaction. It is revealed that, for the normalization constant A_S and for the root-mean-square deuteron radius r_d, the results obtained with the experimental value recommended at present for the triplet scattering length a_t are exaggerated with respect to their experimental counterparts. By using the latest experimental data obtained for phase shifts by the group headed by Arndt, it proved to be possible to derive, for the low-energy parameters of scattering (a_t, r_t, P_t) and for the properties of the deuteron (A_S, r_d) results that comply well with experimental data.     

Hall coefficient in heavy fermion metals

Experimental studies of the antiferromagnetic (AF) heavy fermion metal YbRh₂Si₂ in a magnetic field B indicate the presence of a jump in the Hall coefficient at a magnetic-field tuned quantum state in the zero temperature limit. This quantum state occurs at B ≥ B_c0 and induces the jump even though the change of the magnetic field at B = B_c0 is infinitesimal. We investigated this by using the model of heavy electron liquid with the fermion condensate. Within this model, the jump takes place when the magnetic field reaches the critical value B_c0 at which the ordering temperature T_N(B = B_c0) of the AF transition vanishes. We show that at B → B_c0, this second order AF phase transition becomes the first order one, making the corresponding quantum and thermal critical fluctuations vanish at the jump. At T → 0 and B = B_c0 the Grüneisen ratio as a function of the temperature T diverges. We demonstrate that both the divergence and the jump are determined by the specific low temperature behavior of the entropy \(S(T) \propto S_0 + a\sqrt T + bT\) with S₀; a and b are temperature independent constants.     

Population Dynamics of Excited Atoms in Dissipative Cavities

Population dynamics of excited atoms in dissipative cavities is investigated in this work. We present a method of controlling populations of excited atoms in dissipative cavities. For the initial state |ee〉_AB|00〉_ab, the repopulation of excited atoms can be obtained by using atom-cavity couplings and non-Markovian effects after the atomic excited energy decays to zero. For the initial state |gg〉_AB|11〉_ab, the two atoms can also be populated to the excited states from the initial ground states by using atom-cavity couplings and non-Markovian effects. And the stronger the atom-cavity coupling or the non-Markovian effect is, the larger the number of repopulation of excited atoms is. Particularly, when the atom-cavity coupling or the non-Markovian effect is very strong, the number of repopulation of excited atoms can be close to one in a short time and will tend to a steady value in a long time.     

The electromagnetic effects in <Emphasis Type="Italic">K</Emphasis><Subscript><Emphasis Type="Italic">e</Emphasis>4</Subscript> decay

The final-state interaction of pions in K _e4 decay allows to obtain the value of the isospin and angular-momentum-zero ππ scattering length a ₀ ⁰ .We take into account the electromagnetic interaction of pions and isospin-symmetry-breaking effects caused by different masses of neutral and charged pions and estimate the impact of these effects on the procedure of scattering-length extraction from K _e4 decays.     

Excitonic representation: Collective excitation spectra in the quantized Hall regime and spin biexciton

The excitonic representation method for describing collective excitations in the quantized Hall regime makes it possible to simplify analysis of the spectra and to obtain new results in the strong magnetic field limit, when E _C ??ω_c (ω_c is the cyclotron frequency and E_C is the characteristic Coulomb energy). For an integer odd filling factor ν greater than unity (i.e., for ν = 3, 5, 7,...), the spectra of one-cyclotron magneto-plasma excitations are calculated. For unit filling factor, the existence of a spin biexciton (bound state of two spin waves) corresponding to excitation with a spin change (δ_S = δ_Sz = ?2) is proved. The exact equation determining the ground state of the biexciton is derived in the thermodynamic limit N_Φ → ∞ (_N? is the system degeneracy). The exchange energy of this state is lower than for a single spin wave (with δ_S = δ_Sz = ?1) for the same value of the 2D wavevector q. In the limit q → ∞ corresponding to the decay of a biexciton into a pair of quasiparticles one of which is a trion with a spin of ?3/2, the energy is found to be lower than the energy (e²/εl _B )√π/2 required for exciting an electron-hole pair in the strictly 2D case (l_B is the magnetic length and ε is the dielectric constant), although this energy is higher than another “classical” result (e²/εl _B )√π/2, corresponding to the excitation of a skyrmion-antiskyrmion pair (|δS|=|δS _z |?1). The solution of the exact equation gives the trion binding energy and the activation gap for quasiparticles whose excitation corresponds to a change in the total spin by δS = δ S_z =?3. The energy of a spin biexciton is calculated for values of the wavevector such that ql _B ?1.     

A hydrogen atom in a superstrong magnetic field and the Zeldovich effect

We consider the problem of a hydrogen atom in a superstrong magnetic field, B? B _a =2.35×10⁹ G. The analytical formulas that describe the energy spectrum of this atom are derived for states with various quantum numbers n_ρ and m. A comparison with available calculations shows their high accuracy for B?B _a . We note that the derived formulas point to a manifestation of the Zeldovich effect, i.e., a rearrangement of the atomic spectrum under the influence of strong short-range Coulomb potential distortion. We discuss the relativistic corrections to level energies, which increase in importance with magnetic field and become significant for B?10¹⁴ G. We suggest the parameters in terms of which the Zeldovich effect has the simplest form. Analysis of our precision numerical calculations of the energy spectrum for a hydrogen atom in a constant magnetic field indicates that the Zeldovich effect is observed in the spectrum of atomic levels for superstrong fields, B?5×10¹¹ G. Magnetic fields of such strength exist in neutron stars and, possibly, in magnetic white dwarfs. We set lower limits for the fields B_min required for the manifestation of this effect. We discuss some of the properties of atomic states in a superstrong magnetic field, including their mean radii and quadrupole moments. We calculated the probabilities of electric dipole transitions between odd atomic levels and a deep ground level.     

<Emphasis Type="Italic">η</Emphasis><Superscript>7</Superscript>Li Scattering in the <Emphasis Type="Italic">αt</Emphasis>-Cluster Model

The cross sections for elastic and inelastic η-meson scattering on ⁷Li nuclei are obtained on the basis of the αt-cluster representation of the target nucleus. The experimentally known values of the parameters of elastic ηα and αt scattering are used in exactly solving three-body Faddeev equations with separable two-body potentials. The η⁷Li elastic-scattering scattering length found from respective calculations is a_η7Li = ?0.310 ? i0.198 fm.     

Neutron scattering in argon and <Emphasis Type="Italic">ne</Emphasis> interaction

As a preparation for the new experiment to measure the ne scattering length a_ne the total neutron cross section of gaseous argon has been obtained by the time-of-flight method at the Dubna booster IBR-30 in the energy range from ～5 eV to ～30 keV. A combined one-level analysis of the newly obtained and other known data on cross sections of Ar and ³⁶Ar has made it possible to improve some neutron parameters and calculate the scattering cross section σ_s and the scattering length a separately for ³⁶Ar and ⁴⁰Ar at any energy.     

Quantifying Correlations via the Wigner-Yanase-Dyson Skew Information

In this paper, based on a discussion about the Wigner-Yanase-Dyson (WYD) skew information, the measure F_a,α(ρ_ab) for correlations in terms of the WYD skew information is introduced and discussed. The following conclusions are obtained. For a classical-quantum state ρ_ab, F_a,α(ρ_ab)=0 if and only if ρ_ab is a product state; F_a,α(ρ_ab) is locally unitary invariant and convex on the set of states with the fixed marginal ρ_a; F_a,α(ρ_ab) decreases under local random unitary operation on H_b; For a quantum-classical state ρ_ab, F_a,α(ρ_ab) decreases under local operation on H_b; Lastly, F_a,α(ρ_ab) is computed for the pure states and the Bell-diagonal states, respectively.     

Vergleich der Davydov-Theorie mit dem Modell des achsialsymmetrischen Kreisels mit Rotation-Vibrations-Wechselwirkung für deformiertegg-Kerne

For deformed even-mass nuclei the model of the axial-symmetric vibrating top with rotation-vibration-interaction is compared to the Davydov-model without and with aβ-band. TheE2-transition-probabilities are calculated. The coefficientsB _ze andC fromE=A I(I+1) ?B _ze I ²(I+1)²+C I ³(I+1)³ are obtained. For the transition-probabilities from the states of the γ-band to the states of the ground state band as well as forB andC the Davydov-model yields values only about half of those obtained from the RV-theory. A comparision to the present availuable experimental data is made. In the RV-model the agreement is better than in the Davydov-theory.     

Microwave photoresistance of a two-dimensional electron gas in a ballistic microbar

The effect of millimeter microwave radiation on the electron transport of two-dimensional (2D) ballistic microbars formed on the basis of individual GaAs quantum wells at a temperature of T = 4.2 K in magnetic fields B < 0.6 T has been investigated. Differences have been revealed in the magnetic field dependences of the microwave photoresistance of a 2D electron gas in Hall bars with a length L and a width W for the cases L, W > l _p and L, W < l _p , where l _p is the electron mean free path for momentum. The microwave photoresistance in macroscopic bars (L, W > l _p ) is a periodic alternating function of the inverse magnetic field; in microbars (L, W < l _p ), it is a periodic positive function of 1/B. The experimental results indicate that the mechanisms of the microwave photoresistance of a 2D electron gas are different for macroscopic and microscopic bars.     

A new look at the KLOE data on the decay <Emphasis Type="Italic">φ</Emphasis>→<Emphasis Type="Italic">ηπ</Emphasis><Superscript>0</Superscript><Emphasis Type="Italic">γ</Emphasis>

We present an analysis of recent high-statistical KLOE data on φ → ηπ⁰γ decay. This decay mainly goes through the a₀γ intermediate state, which makes it possible to investigate properties of the a₀. It is shown that KLOE data prefer a higher a0 mass and a considerably larger a0 coupling to the K\(\bar K\) than those obtained in the analysis of the KLOE group.     

Searching for Exotic States with b and c Quarks in D0 Experiment

The latest results of searching for exotic multiquark states with heavy quarks obtained in the D0 experiment (Fermi National Accelerator Laboratory, USA) are presented. In particular, the evidence of existence of a possible four-quark state X(5568) → B _s ⁰ π^±in the cases with hadronic and semileptonic decay channels of B _s ⁰ meson is considered, as well as the results of searching for the five-quark states in the J/ψΛ system.     

A Note on Quantum Coherence

In this paper, we discuss the coherence of the reduced state in system H _A ?H _B under taking different quantum operations acting on subsystem H _B . Firstly, we show that for a pure bipartite state, the coherence of the final subsystem H _A under the sum of two orthonormal rank 1 projections acting on H _B is less than or equal to the sum of the coherence of the state after two orthonormal projections acting on H _B , respectively. Secondly, we obtain that the coherence of reduced state in subsystem H _A under random unitary channel \({\Phi }(\rho )={\sum }_{s}\lambda _{s}U_{s}\rho U_{s}^{\ast }\) acting on H _B , is equal to the coherence of the state after each operation \({\Phi }_{s}(\rho )=\lambda _{s}U_{s}\rho U_{s}^{\ast }\) acting on H _B for every s. In addition, for general quantum operation \({\Phi }(\rho )={\sum }_{s}F_{s}\rho F_{s}^{\ast }\) on H _B , we get the relation

$$ C\left (\left ((I\otimes {\Phi })\rho ^{AB}\right )^{A}\right )\leq \sum \limits _{s}C\left (\left ((I\otimes {\Phi }_{s})\rho ^{AB}\right )^{A}\right ). $$

     

Berechnung des Magnetisierungs-„Ripple“ in ferromagnetischen dünnen Schichten

By means of straight forward analysis a complete calculation is given of magnetization ripple in polycrystalline ferromagnetic films. Wavelenghts and practical relations for ripple amplitude, length of coherence, and angle fluctuation are derived (which were so far only rather incompletely available from a very rough model of the ripple, given previously by the author). The dependence of ripple wavelength (λ ₀) on average crystallite sizea reaches a plateau at a definite critical valuea=a _g ∶λ ₀≈4a fora<a _g ,λ ₀ independent ofa fora>a _g , as has been found most recently byBaltz andDoyle.     

Ionization potential of a metal cluster containing vacancies

A consistent procedure for determining the ionization potential of a large metal cluster of radius R _{N, v} , consisting of N atoms and N _v vacancies, is proposed. The perturbation theory in small parameters R _v /R _{N, v} and L _v /R _v (Rv and L _v are average distance between vacancies and the length of electron scattering on vacancies, respectively) is constructed in the effective-medium approximation for the electron ground state energy. The effective vacancy potential profile, the electron scattering phase and length are calculated by the Kohn–Sham method for a macroscopic metal in the stable jelly model. The obtained analytical dependences can be useful to analyze the results of photoionization experiments and to determine the size dependence of the vacancy concentration, including that near the melting temperature.