The neutrino mass matrix and (selected) variants of <Emphasis Type="Italic">A</Emphasis><Subscript>4</Subscript>

Recent neutrino oscillation experiments have measured leptonic mixing angles with considerable precision. Many theoretical attempts to understand the peculiar mixing structure, observed in these measurements, are based on non-Abelian flavour symmetries. This talk concentrates exclusively on models based on the non-Abelian symmetry A ₄. A ₄ is particularly well suited to describe three family mixing, and allows to explain the near tri-bimaximal mixing observed. Special emphasis is put here on the discussion of the neutrinoless double beta decay observable 〈:m _ν 〉. Different models based on A ₄ with very similar predictions for neutrino angles can yield vastly different expectations for 〈m _ν 〉. Neutrinoless double beta decay can thus serve, in principle, as a discriminator between different neutrino mass models.      

Swelling of two-dimensional polymer rings by trapped particles

The mean area of a two-dimensional Gaussian ring of N monomers is known to diverge when the ring is subject to a critical pressure differential, p _c ∼ N ^-1. In a recent publication (Eur. Phys. J. E 19, 461 (2006)) we have shown that for an inextensible freely jointed ring this divergence turns into a second-order transition from a crumpled state, where the mean area scales as 〈A〉 ∼ N, to a smooth state with 〈A〉 ∼ N ². In the current work we extend these two models to the case where the swelling of the ring is caused by trapped ideal-gas particles. The Gaussian model is solved exactly, and the freely jointed one is treated using a Flory argument, mean-field theory, and Monte Carlo simulations. For a fixed number Q of trapped particles the criticality disappears in both models through an unusual mechanism, arising from the absence of an area constraint. In the Gaussian case the ring swells to such a mean area, 〈A〉 ∼ NQ, that the pressure exerted by the particles is at p _c for any Q. In the freely jointed model the mean area is such that the particle pressure is always higher than p _c, and 〈A〉 consequently follows a single scaling law, 〈A〉 ∼ N ² f (Q/N), for any Q. By contrast, when the particles are in contact with a reservoir of fixed chemical potential, the criticality is retained. Thus, the two ensembles are manifestly inequivalent in these systems. An erratum to this article is available at .     

Smoothening transition of a two-dimensional pressurized polymer ring

We revisit the problem of a two-dimensional polymer ring subject to an inflating pressure differential. The ring is modeled as a freely jointed closed chain of N monomers. Using a Flory argument, mean-field calculation and Monte Carlo simulations, we show that at a critical pressure, p_c ∼ N^-1, the ring undergoes a second-order phase transition from a crumpled, random-walk state, where its mean area scales as 〈A〉 ∼ N, to a smooth state with 〈A〉 ∼ N². The transition belongs to the mean-field universality class. At the critical point a new state of polymer statistics is found, in which 〈A〉 ∼ N^3/2. For p ≫ p_c we use a transfer-matrix calculation to derive exact expressions for the properties of the smooth state.     

The Landauer resistance of a one-dimensional metal with periodically spaced random impurities

We find the dependence of the ensemble-averaged resistance, 〈ρ _L〉, of a one-dimensional chain consisting of periodically spaced random delta-function potentials of the chain length L, the incident-electron energy, and the chain disorder parameter w. We show that generally the 〈ρ _L〉 vs L dependence can be written as a sum of three exponential functions, two of which tend to zero as L℩∞. Hence the asymptotic expression for 〈ρ _L〉 is always an exponential function of L. Such an expression for 〈ρ _L〉 means that the electronic states are indeed localized and makes it possible (which is important) to find the dependence of the localization radius on the incident-electron energy and the force with which an electron interacts with the sites of the chain. We also derive a recurrence representation for 〈ρ _L〉, which proves convenient in numerical calculations. Zh. éksp. Teor. Fiz. 111, 575–584 (February 1997)     

Lattice mechanical properties of noble and transition metals

A model pseudopotential depending on an effective core radius but otherwise parameter free is used to study the interatomic interactions, phonon dispersion curves (inq and r-space analysis), phonon density of states, mode Grüneisen parameters, dynamical elastic constants (C ₁₁,C ₁₂ andC ₄₄), bulk modulus (B), shear modulus (C′), deviation from Cauchy relation (C ₁₂–C ₄₄), Poisson’s ratio (σ), Young’s modulus (Y), behavior of phonon frequencies in the elastic limit independent of the direction (Y ₁), limiting value in the [110] direction (Y ₂), degree of elastic anisotropy (A), maximum frequencyω _max, mean frequency 〈ω〉, 〈ω ²〉^1/2=(〈ω〉/〈ω ⁻¹〉)^1/2, fundamental frequency 〈ω ²〉, and propagation velocities of the elastic constants in Cu, Ag, Au, Ni, Pd, and Pt. The contribution of s-like electrons is calculated in the second-order perturbation theory for the model potential while that of d-like electrons is taken into account by introducing repulsive short-range Born-Mayer like term. Very recently proposed screening function due to Sarkar et al. has been used to obtain the screened form factor. The theoretical results are compared with experimental findings wherever possible. A good agreement between theoretical investigations and experimental findings has proved the ability of our model potential for predicting a large number of physical properties of transition metals.     

Quantum and Classical Disparity and Accord

Discrepancies and accords between quantum (QM) and classical mechanics (CM) related to expectation values and periods are generally found for both the harmonic oscillator (SHO) and a free particle in a box (FPB), which may apply generally. These indicate non-locality is expected throughout QM. The FPB energy states violate the Correspondence Principle. Previously unexpected accords are found and proven that 〈x ²〉 _CM =〈x ²〉 _QM and τ _CM =τ _QMb (beat period i.e. beats between the phases for adjoining energy states) for the SHO for all quantum numbers, n. However, for the FPB the beat periods differ at small n. It is shown that a particle’s velocity in an infinite square well varies, no matter how wide the box, nor how far the particle is from the walls. The quantum free particle variances share an indirect commonality with the Aharonov-Bohm and Aharonov-Casher effects in that there is a quantum action in the absence of a force. The concept of an “Expectation Value over a Partial Well Width” is introduced. This paper raises the question as to whether these inconsistencies are undetectable, or can be empirically ascertained. These inherent variances may need to be fixed, or nature is manifestly more non-classical than expected.     

Orientation dependence of electrical properties of 0.96Na<Subscript>0.5</Subscript>Bi<Subscript>0.5</Subscript>TiO<Subscript>3</Subscript>-0.04BaTiO<Subscript>3</Subscript> lead-free piezoelectric single crystal

In this paper, a single crystal of 0.96Na_0.5Bi_0.5TiO₃-0.04BaTiO₃ with dimensions of Φ 30×10 mm was grown by the top-seeded-solution growth method. X-ray powder diffraction results show that the as-grown crystal possesses the rhombohedral perovskite-type structure. The dielectric, piezoelectric and electrical conductivity properties were systematically investigated with 〈001〉, 〈110〉 and 〈111〉 oriented crystal samples. The room-temperature dielectric constants for the 〈001〉, 〈110〉 and 〈111〉 oriented crystal samples are found to be 650, 740 and 400 at 1 kHz. The (T _m, ε _m) values of the dielectric temperature spectra are almost independent of the crystal orientations; they are (306°C, 3718), (305°C, 3613) and (307°C, 3600) at 1 kHz for the 〈001〉, 〈110〉 and 〈111〉 oriented crystal. The optimum poling conditions were obtained by investigating the piezoelectric constants d ₃₃ as a function of poling temperature and poling electric field. For the 〈001〉 and 〈110〉 crystal samples, the maximum d ₃₃ values of 146 and 117 pC/N are obtained when a poling electric field of 3.5 kV/mm and a poling temperature of 80°C were applied during the poling process. The as-grown 0.96Na_0.5Bi_0.5TiO₃-0.04BaTiO₃ crystal possesses a relatively large dc electrical conductivity, especially at higher temperature, having a value of 1.98×10⁻¹¹ Ω⁻¹⋅m⁻¹ and 3.95×10⁻⁹ Ω⁻¹⋅m⁻¹ at 25°C and 150°C for the 〈001〉 oriented crystal sample.     

Statistical mechanics of braided Markov chains: I. Analytic methods and numerical simulations

We investigate numerically and analytically the statistics of Markov chains on so-called braid (B _n ) and locally free (ℒℱ _n ) groups. Namely, we compute the mean length 〈μ〉 and the variance 〈μ²〉−〈μ〉² of the shortest word which remains after applying of all group relations to the randomly generatedN-letter word (Markov chain). We express the conjecture (numerically justified) that the mean value 〈μ〉 for the random walk on the groupB _n (n≫1) coincides with high accuracy with the same value for the random walk on the “locally free group weth errors” if the number of errors is of order of 20%.     

Theory of melting,vacancy model

A theory of melting based on vacancy model is formulated. The polymer solution theory is used for derivation of the melting equation for a two-species model of melting solid. Under simplifying assumptions the analysis leads to a simple correlation betweenT _m and 〈v〉, the average energy of interaction between the vibrating atoms. Pseudopotential method is used for calculating 〈v〉 for the alkali metals lithium, sodium, potassium and rubidium at temperatureT _m. The calculated values ofT _m〈v〉 are in accord with those expected from our model. Application to the high pressure melting curves of solids is also discussed.     

Observation of spin-reduction anisotropy in the quasi-one-dimensional antiferromagnet CsMnI3

The NMR of ⁵⁵Mn in the quasi-one-dimensional noncollinear antiferromagnet CsMnI₃ at T=1.3 K is investigated in magnetic fields up to ∼40 kOe. Six NMR branches corresponding to six manganese spins per magnetic unit cell are observed. The NMR spectra correspond satisfactorily to the well-known magnetic structure of CsMnI₃, taking into account the dynamic frequency shift due to the interaction with the low-lying AFMR modes. The average spins 〈S _A〉=1.86 and 〈S _B〉=1.74 of the magnetically nonequivalent Mn²⁺ ions are determined from the measured values of the hyperfine fields. The results obtained agree qualitatively with the calculations of spin reduction in quasi-one-dimensional antiferromagnets [Y. Watabe, T. Suzuki, and Y. Natsume, Phys. Rev. B 52, 3400 (1995)]. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 9, 661–665 (10 May 1998)     

Anisotropy of the upper critical field and specific heat in V3Si — a superconductor with cubic symmetry

The specific heat of a V₃Si single crystal (T _c=17 K, H _c2=20 T) in magnetic fields up to 8 T isinvestigated experimentally for three orientations of the field relative to the crystallographic directions — H∥〈001〉, H∥〈110〉, and H∥〈111〉. Both the upper critical magnetic field and the specific heat of the mixed state are observed to depend on the orientation of the magnetic field relative to the crystallographic directions (anisotropy): The critical field reaches its maximum value and the specific heat its minimum value in a field along the 〈001〉 direction. The anisotropy scale in both phenomena increases as the magnetic field and reaches 3% in a 6 T field. The interrelationship of the upper critical field anisotropy and the specific-heat anisotropy in type-II superconductors is studied. It is shown that the anisotropy of the specific heat in the mixed state in weak fields can serve as a criterion for nontrivial pairing. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 1, 26–29 (10 January 1999)     

Mean square number fluctuation for a fermion source and its dependence on neutrino mass for the universal cosmic neutrino background

Using the general formulation for obtaining chemical potentialμ of an ideal Fermi gas of particles at temperature T, with particle rest mass m₀ and average density 〈N〉/V, the dependence of the mean square number fluctuation 〈ΔN ²〉/V on the particle mass m₀ has been calculated explicitly. The numerical calculations are exact in all cases whether rest mass energym ₀c² is very large (non-relativistic case), very small (ultra-relativistic case) or of the same order as the thermal energy k_BT. Application of our results to the detection of the universal very low energy cosmic neutrino background (CNB), from any of the three species of neutrinos, shows that it is possible to estimate the neutrino mass of these species if from approximate experimental measurements of their momentum distribution one can extract, someday, not only the density 〈N _v〉/V but also the mean square fluctuation 〈Δ _v ² 〉/V. If at the present epoch, the universe is expanding much faster than thermalization rate for CNB, it is shown that our analysis leads to a scaled neutrino massm _v instead of the actual massm _0v .     

Polarization of leading Λ hyperons produced by neutrons on target nuclei

The polarization of the leading Λ hyperons produced on carbon and lead target nuclei by 4–10 GeV neutrons in the angle range Θ<8.5° with respect to the beam and with only neutral-particle accompaniment is measured: 〈Π〉=−0.096±0.018 for C and 〈Π〉=− 0.128±0.047 for Pb. The dependence of the polarization on the transverse momentum and the Feynman variable is measured. The normalized invariant cross section as a function of p _⊥ ² is found to be approximated by the function A exp(−Bp _⊥ ² ), where the parameter B is independent of the kind of nucleus (B=8.71±0.09 (GeV/c)⁻² for carbon and B=8.83±0.18 (GeV/c)⁻² for lead). Pis’ma Zh. éksp. Teor. Fiz. 64, No. 4, 237–240 (25 August 1996)     

Donors in a strong magnetic field and elastic magnetic-impurity resonance in diamondlike semiconductors

The possibility of resonance during elastic intravalley scattering in n-type semiconductors is investigated in connection with the crossing (due to anisotropy of the effective mass) of the energy levels of excited states of a shallow donor as functions of the magnetic field. The hybridization of states of different frequencies in the vicinity of a crossing is attributed to the emergence of a nonzero dipole moment of the excited impurity atom and, accordingly, a long-range potential, which creates carrier-transport anomalies. The lower part of the donor spectrum is calculated as a function of the magnetic field in Si with B∥〈001〉 and in Ge with B∥〈111〉 or B∥〈110〉. A crossing occurs in Ge in the field range 9.9 T<B<16.7 T and in Si in the field range 10.5 T<B<37.7 T. The characteristic longitudinal relaxation time and the transverse conductivity, which are determined by scattering at excited donors in the presence of the hybridization of states, are calculated. Zh. éksp. Teor. Fiz. 112, 975–1010 (September 1997)     

Sum-of-Squares Results for Polynomials Related to the Bessis–Moussa–Villani Conjecture

We show that the polynomial S _m,k (A,B), that is the sum of all words in noncommuting variables A and B having length m and exactly k letters equal to B, is not equal to a sum of commutators and Hermitian squares in the algebra R〈X,Y〉, where X ²=A and Y ²=B, for all even values of m and k with 6≤k≤m−10, and also for (m,k)=(12,6). This leaves only the case (m,k)=(16,8) open. This topic is of interest in connection with the Lieb–Seiringer formulation of the Bessis–Moussa–Villani conjecture, which asks whether Tr (S _m,k (A,B))≥0 holds for all positive semidefinite matrices A and B. These results eliminate the possibility of using “descent + sum-of-squares” to prove the BMV conjecture.     

Electron paramagnetic resonance of deep boron acceptors in 4H-SiC and 3C-SiC crystals

EPR spectra of deep boron in 4H-SiC and 3C-SiC crystals have been observed and studied. Two sites in 4H-SiC produced deep-boron EPR signals, quasi-cubic k and hexagonal h. In both cases the deep-boron center symmetry is close to axial along the c crystal axis, and the g factor anisotropy is about an order of magnitude larger than that for shallow boron centers. In the 3C-SiC crystal, the deep-boron symmetry is also close to axial along one of the four 〈111〉 directions. The model proposed for the deep boron center with acceptor properties is B_Si-v _C, where B_Si is the boron substituting for silicon, and v _C is the carbon vacancy, with the B_Si-v _C direction coinciding in 4HSiC with the hexagonal axis of the crystal for both k and h positions. In the cubic 3C-SiC crystal, there are four equivalent deep boron centers, which represent B_Si-v _C pairs with the bond directed along one of the four 〈111〉 crystal directions. Fiz. Tverd. Tela (St. Petersburg) 40, 36–40 (January 1998)     

Classical limit of relativistic quantal system with attractive Coulomb interaction

Using the appropriate harmonic oscillator states and reasonable approximations, we construct coherent wavepackets corresponding to the solutions of the Klein-Gordon equation for the attractive potentialV(r)=−k/r, k>0, in two and three space dimensions. We deduce the corresponding classical limit in two dimension by requiring that the expectation value 〈r〉 of the radial variable is large. In the case of three dimensions, besides the condition of large 〈r〉, we make the uncertainty Δr=[〈r ²〉 − 〈r〉²]^1/2 a minimum with respect to certain parameter of the wavepacket. We then investigate the trajectory traversed by the wavepacket in the classical limit. We find that the classical limit of this relativistic quantal problem gives, in the leading order, the same expression for the rate of motion of the perihelion as that given by the solution of the corresponding special relativistic classical dynamical problem. We also briefly discuss some of the subtle aspects of the classical limit of the relativistic quantal system, in general.     

Wavelet Transform of Even- and Odd-Coherent States

By employing the technique of integral within an ordered product (IWOP) of operators we recast classical wavelet transform to a matrix element of the squeezing-displacing operator U(μ,s) between the mother wavelet vector 〈ψ| and the state vector |f〉 to be transformed, i.e., we propose that 〈ψ|U(μ,s)|f〉 can be considered as a new kind of spectrum for analyzing the quantum state |f〉. In this way we do numerical calculation of wavelet-transform spectrum for the even- and odd-coherent states and then plot their figures, respectively. Thus this kind of spectrum can be used to recognize a variety of quantum optical states.     

Exchangeability and Conditionally Identical Common Cause Systems

A pair (A, B) of events in a classical probability measure space (Ω, p) is called exchangeable iff p(A ) = p( B). Conditionally identical common cause system of size n for the correlation is an n-partition of Ω such that (i) any member of the partition screens the correlation off and (ii) for any member {C _i } _{i ∊ I} of the partition p(A|C _i ) = p(B|C _i ). The common cause system is called proper if p(A|C _i )≠(A|C _j ) for some i ≠ j. In the paper it is shown that exchangeable correlations be explained by proper conditionally identical common cause systems in the following sense. (i) Given a proper conditionally identical common cause system of size n for the two events A and B in Ω, then the pair (A, B) will be an exchangeable (positively) correlating pair. (ii) Given any exchangeable (positively) correlating pair of events in Ω and given any finite number n > 2, then the probability space can be embedded into a larger probability space in such a way that the larger space contains a proper conditionally identical common cause system of size n for the correlation.     

Realization of a heavily doped and fully compensated semiconductor state in a crystalline semiconductor with a deep impurity band

We use the data on the pressure (up to P=1.5 GPa) and field (up to H=17 kOe) dependence of the Hall coefficient and the resistivity at 77.6 and 300 K in p-CdSnAs₂〈Cu〉 to calculate the effective kinetic characteristics of the charge carriers, the density and mobility of the conduction electrons and the holes of the deep acceptor and valence bands, in an interval of excess-acceptor densities N _ext ranging from 10¹⁰–10¹⁷ cm⁻³. We establish that in a heavily doped semiconductor with a deep impurity band at the tail of the density of states of the intrinsic band, with unequal donor and acceptor densities, a a heavily doped and fully compensated semiconductor state is realized under hydrostatic compression. The threshold value of the pressure that initiates the transition into such a state, P _c, depends on the extent to which the impurity band is populated. In p-CdSnAs₂〈Cu〉 at N _ext=N _A, where N _A is the density of deep acceptors, and T⩽77.6 K the value of P _c amounts to 10⁻⁴ GPa. As the population of the deep acceptor band grows, P _c increases and in the limit becomes infinite. We discuss the special features of the electrophysical properties of p-CdSnAs₂〈Cu〉 arising from the absence of an energy gap between the states of the conduction band and those of the deep acceptor band. Zh. éksp. Teor. Fiz. 111, 562–574 (February 1997)