Universal description of the rotational-vibrational spectrum of three particles with zero-range interactions

A comprehensive universal description of the rotational-vibrational spectrum for two identical particles of mass $m$ and the third particle of the mass $m_1$ in the zero-range limit of the interaction between different particles is given for arbitrary values of the mass ratio $m/m_1$ and the total angular momentum $L$. If the two-body scattering length is positive, a number of vibrational states is finite for $L_c(m/m_1) \le L \le L_b(m/m_1)$, zero for $L>L_b(m/m_1)$, and infinite for $L<L_c(m/m_1)$. If the two-body scattering length is negative, a number of states is either zero for $L \ge L_c(m/m_1)$ or infinite for $L<L_c(m/m_1)$. For a finite number of vibrational states, all the binding energies are described by the universal function $\epsilon_{LN}(m/m_1) = {\cal E}(\xi, \eta)$, where $\xi=\displaystyle\frac{N-1/2}{\sqrt{L(L + 1)}}$, $\eta=\displaystyle\sqrt{\frac{m}{m_1 L (L + 1)}}$,and $N$ is the vibrational quantum number. This scaling dependence is in agreement with the numerical calculations for $L > 2$ and only slightly deviates from those for $L = 1, 2$. The universal description implies that the critical values $L_c(m/m_1)$ and $L_b(m/m_1)$ increase as $0.401 \sqrt{m/m_1}$ and $0.563 \sqrt{m/m_1}$, respectively, while a number of vibrational states for $L \ge L_c(m/m_1)$ is within the range $N \le N_{max} \approx 1.1 \sqrt{L(L+1)}+1/2$

Macroscopic quantum tunneling in "small" Josephson junctions in magnetic field

We study the phenomenon of macroscopic quantum tunneling (MQT) in small Josephson junctions (JJ) with an externally applied magnetic field. The latter results in the appearance of the Fraunhofer type modulation of the current density along the barrier. The problem of MQT for a point-like JJ is reduced to the motion of the quantum particle in the washboard potential. In the case of a finite size JJ under consideration, this problem corresponds to a MQT in potential which itself, besides the phase, depends on space variables. Finally, the general expression for the crossover temperature T_0 between thermally activated and macroscopic quantum tunneling regimes and the escaping time tau_esc have been calculated

Collapse of an Instanton

We construct a two parameter family of collapsing solutions to the 4+1 Yang-Mills equations and derive the dynamical law of the collapse. Our arguments indicate that this family of solutions is stable. The latter fact is also supported by numerical simulations.Comment: 17 pages, 1 figur

Itinerant in-plane magnetic fluctuations and many-body correlations in Nax_xCoO2_2

Based on the {\it ab-initio} band structure for Na$_x$CoO$_2$ we derive the single-electron energies and the effective tight-binding description for the $t_{2g}$ bands using projection procedure. Due to the presence of the next-nearest-neighbor hoppings a local minimum in the electronic dispersion close to the $\Gamma$ point of the first Brillouin zone forms. Correspondingly, in addition to a large Fermi surface an electron pocket close to the $\Gamma$ point emerges at high doping concentrations. The latter yields the new scattering channel resulting in a peak structure of the itinerant magnetic susceptibility at small momenta. This indicates dominant itinerant in-plane ferromagnetic fluctuations above certain critical concentration $x_m$, in agreement with neutron scattering data. Below $x_m$ the magnetic susceptibility shows a tendency towards the antiferromagnetic fluctuations. We further analyze the many-body effects on the electronic and magnetic excitations using various approximations applicable for different $U/t$ ratio.Comment: 10 page

Quasiparticle states of the Hubbard model near the Fermi level

The spectra of the t-U and t-t'-U Hubbard models are investigated in the one-loop approximation for different values of the electron filling. It is shown that the four-band structure which is inherent in the case of half-filling and low temperatures persists also for some excess or deficiency of electrons. Besides, with some departure from half-filling an additional narrow band of quasiparticle states arises near the Fermi level. The dispersion of the band, its bandwidth and the variation with filling are close to those of the spin-polaron band of the t-J model. For moderate doping spectral intensities in the new band and in one of the inner bands of the four-band structure decrease as the Fermi level is approached which leads to the appearance of a pseudogap in the spectrum.Comment: 8 pages, 7 figure

Electronic theory for itinerant in-plane magnetic fluctuations in Nax_xCoO2_2

Starting from {\it ab-initio} band structure for Na$_x$CoO$_2$, we derive the single-electron energies and the effective tight-binding description for the $t_{2g}$ bands using a projection procedure. We find that due to the presence of the next-nearest-neighbor hoppings a local minimum in the electronic dispersion close to the $\Gamma$ point of the first Brillouin zone forms. Therefore, in addition to a large Fermi surface an electron pocket close to the $\Gamma$ point emerges at high doping concentrations. The latter yields the new scattering channel resulting in a peak structure of the itinerant magnetic susceptibility at small momenta. This indicates itinerant in-plane ferromagnetic state above certain critical concentration $x_m$, in agreement with neutron scattering data. Below $x_m$ the magnetic susceptibility shows a tendency towards the antiferromagnetic fluctuations. We estimate the value of $0.58 < x_m < 0.7$ within the rigid band model and within the Hubbard model with infinite on-site Coulomb repulsion consistent with the experimental phase diagram.Comment: 4 pages, 4 figures; LDA calculations were done with Na in the symmetric 2d position contrary to the 6h position in a previous version of this pape

Electronic and magnetic properties of [Fe(3-MeO-Qsal)2]y•n solvent (n = 0,1) complexes

© Kazan Federal University (KFU).[Fe(3-MeO-Qsal)2]Y (Y = PF6, BF4, NCS, NO3, BPh4) compounds were synthesized using the diffusion method and studied by the electron spin resonance and the magnetic susceptibility methods in the temperature range (5-300) K. Coexistence of spatially separated high-spin and low-spin fractions in these compounds was observed. Low-spin fraction of all compounds reveals the antiferromagnetic correlations at low temperatures. High-spin fraction of complexes with Y = PF6 demonstrate the weak ferromagnetic properties due to exchange interaction between complexes in whole temperature range. Influence of outer-sphere anion on the spin state, the electronic properties of low-spin Fe(III) complexes is demonstrated

Specific features of spin-variable properties of [Fe(acen)pic2]BPh4 · nH2O

© 2016, Pleiades Publishing, Ltd. The [Fe(acen)pic2]BPh4 · nH2O compound has been synthesized and studied in the temperature interval of 5–300 K by the methods of EPR and magnetic susceptibility. The existence of ferromagnetic interactions between Fe(III) complexes in this compound has been revealed, in contrast to unhydrated [Fe(acen)pic2]BPh4. The reduction in the integrated intensity of the magnetic resonance signal as the temperature decreases below 80 K has been explained by the transition of high-spin ions to the low-spin state. It has been shown that the phase transition temperature in the presence of intermolecular (ferromagnetic) interactions is lower than that in the case of noninteracting centers

Specific features of spin-variable properties of [Fe(acen)pic2]BPh4 · nH2O

© 2016, Pleiades Publishing, Ltd. The [Fe(acen)pic2]BPh4 · nH2O compound has been synthesized and studied in the temperature interval of 5–300 K by the methods of EPR and magnetic susceptibility. The existence of ferromagnetic interactions between Fe(III) complexes in this compound has been revealed, in contrast to unhydrated [Fe(acen)pic2]BPh4. The reduction in the integrated intensity of the magnetic resonance signal as the temperature decreases below 80 K has been explained by the transition of high-spin ions to the low-spin state. It has been shown that the phase transition temperature in the presence of intermolecular (ferromagnetic) interactions is lower than that in the case of noninteracting centers