Table of contents

We find that the exponential operator V≡exp[iλ(Q₁P₂+Q₂P₃+⋅⋅⋅+Q_n−1P_n+Q_nP₁)], Q_i, P_i are, respectively, the coordinate and momentum operators, is an n-mode squeezing operator which engenders standard squeezing. By virtue of the technique of integration within an ordered product of operators we derive V's normally ordered expansion and obtain the n-mode squeezed vacuum states, its Wigner function is calculated by using the Weyl ordering invariance under similar transformations.

We investigate the dynamics of a disk bouncing on a vibrating platform – a variation of the classic bouncing ball problem – that captures the physics of pizza tossing and the operation of certain standing-wave ultrasonic motors (SWUMs). The system's dynamics explains why certain tossing motions are used by dough-toss performers for different tricks: a helical trajectory is used in single tosses because it maximizes energy efficiency and the dough's airborne rotational speed, a semi-elliptical motion is used in multiple tosses because it is easier for maintaining dough rotation at the maximum rotational speed. The system's bifurcation diagram and basins of attraction also informs SWUM designers about the optimal design for high speed and minimal sensitivity to perturbation.

A mixture of two fermionic species with different masses is studied in an optical lattice. The heavy fermions are subject only to thermal fluctuations, the light fermions also to quantum fluctuations. We derive the Ising-like distribution for the heavy atoms and study the localization properties of the light fermions numerically by a transfer-matrix method. In a two-dimensional system one-parameter scaling of the localization length is found with a transition from delocalized states at low temperatures to localized states at high temperature. The critical exponent of the localization length is ν≈0.88.

The two-component interacting Bose gas confined in a one-dimensional optical lattice with infinite intra-component repulsive interactions and tunable inter-component repulsions is studied. By a generalized Jordan-Wigner transformation, it is shown that this model can be solved exactly. The energy spectrum and explicit wave function are obtained. The physical quantities such as the off-diagonal density matrix, momentum distribution and single-particle von Neumann entropy of the present model display different properties from those of the Fermi-Hubbard model due to the different intrinsic symmetry of particles.

Zero-lag synchronization (ZLS) is achieved in a very restricted mutually coupled chaotic systems, where the delays of the self-coupling and the mutual coupling are identical or fulfil some restricted ratios. Using a set of multiple self-feedbacks and mutual couplings we demonstrate both analytically and numerically that ZLS is achieved for a wide range of mutual delays. It indicates that ZLS can be achieved without the knowledge of the mutual distance between the communicating partners and has an important implication in the possible use of ZLS in communications networks as well as in the understanding of the emergence of such synchronization in the neuronal activities.

We study the state of a nanometric helium bubble in bcc-iron as a function of temperature and He content using atomistic calculations. It appears that up to moderate temperatures the Fe lattice can confine He to solid state, in good agreement with known solid-liquid transition diagram of pure He. However, He in the bubble forms an amorphous phase, while an fcc structure is expected at the same temperature and He density. In addition, the He bubble forms a polyhedron whose morphology depends on either the surface energy or the elastic-plastic properties of Fe at either low or high pressure, respectively. Indeed, at high He contents the bubble surface breaks down at the mechanical stability limit of the Fe crystal, leading to a pressure decrease in the bubble.

The entropy of the extremal Reissner-Nordström black hole due to the gravitational, electromagnetic, neutrino and scalar fields is investigated by using the brick-wall model. Whether extremalization or quantization are carried out first, the entropy satisfies the Nernst theorem when the inner Cauchy horizon is taken into account. Therefore the quantum entropy of the extremal black hole, calculated via the brick-wall model, does not require any regularization.

We identify the operational conditions for maximum power of a nanothermoelectric engine consisting of a single quantum level embedded between two leads at different temperatures and chemical potentials. The corresponding thermodynamic efficiency agrees with the Curzon-Ahlborn expression up to quadratic terms in the gradients, supporting the thesis of universality beyond linear response.

We derive a master stability function (MSF) for synchronization in networks of coupled dynamical systems with small but arbitrary parametric variations. Analogous to the MSF for identical systems, our generalized MSF simultaneously solves the linear-stability problem for near-synchronous states (NSS) for all possible connectivity structures. We also derive a general sufficient condition for stable near-synchronization and show that the synchronization error scales linearly with the magnitude of parameter variations. Our analysis underlines the significant role played by the Laplacian eigenvectors in the study of network synchronization of near-identical systems.

We study the direct mediation of metastable supersymmetry breaking by a Φ²-deformation to the ISS model and extend it by splitting both TrΦ and TrΦ² terms in the superpotential and gauging the flavor symmetry. We find that with such an extension enough-long-lived metastable vacua can be obtained and the proper gaugino masses can be generated. Also, this allows for constructing a kind of models which can avoid the Landau pole problem. Especially, in our metastable vacua there exist a large region for the parameter m₃ which can satisfy the phenomenology requirements and allow for a low SUSY-breaking scale (hμ₂∼100 TeV).

It is shown that the Λ_c⁺Λ_c^- signal recently reported by the Belle Collaboration (Phys. Rev. Lett., 101 (2008) 172001) contains clear signs of the ψ(5S) and the ψ(4D) c vector states, and also some indication for the masses and widths of the ψ(6S) and ψ(5D). Moreover, it is argued that the threshold behaviour of the Λ_c⁺Λ_c^- cross-section suggests the presence of the hitherto undetected ψ(3D) state not far below the Λ_c⁺Λ_c^- threshold.

A study of multifragmentation of gold nuclei is reported at incident energies of 400, 600 and 1000 MeV/nucleon using microscopic theory. The present calculations are done within the framework of quantum molecular dynamics (QMD) model. The clusterization is performed with an advanced sophisticated algorithm namely the simulated annealing clusterization algorithm (SACA) along with the conventional spatial correlation method. A quantitative comparison of the mean multiplicity of intermediate mass fragments with experimental findings of the ALADiN group gives excellent agreement showing the ability of the SACA method to reproduce the fragment yields. It also emphasizes the importance of the clustering criterion in describing the fragmentation process within the semi-classical model.

We study the structures of a ribbon or ladder polymer immersed in poor solvents. The anisotropic bending rigidity coupled with the surface tension leads ribbon polymers to spontaneous formation of highly anisotropic condensates in poor solvents. Unlike ordinary flexible polymers these condensates undergo a number of distinct layering transitions as a function of chain length or solvent quality, and the size of condensates becomes a non-monotonic function of chain length. We show that the fluctuations of the condensates are in general small and these condensates are stable.

Pure tin metals were centrifuged at 1 × 10⁶g and at 220°C for 100 hours, at 0.40 × 10⁶g at 220–230°C for 24 hours, and at 0.25 × 10⁶g at 220°C for 24 hours. Their isotopic compositions were measured by a secondary ion mass spectrometer (SIMS). ¹¹⁶Sn/¹²⁰Sn and ¹²⁴Sn/¹²⁰Sn ratios of the 1.02 × 10⁶g sample were considerably different than the initial compositions, and the magnitude of isotopic fractionation reached 2.6 ± 0.1%. A three-isotope diagram of ¹¹⁶Sn/¹²⁰Sn vs.¹²⁴Sn/¹²⁰Sn shows conclusively that isotopic fractionation caused by a gravitational field depended only on the isotopic mass.

The nature of the α-Sn/Ge(111) surface is still a matter of debate. In particular, two possible configurations have been proposed for the 3×3 ground state of this surface: one with two Sn adatoms in a lower position with respect to the third one (1U2D) and the other with opposite configuration (2U1D). We report ab initio GW calculations for the α-Sn/Ge(111) system, simulating STM images as a function of bias voltage and comparing them with STM experimental results at 78 K. The concurrent application of theory and experiments and the very good match between their results provide unambiguous indications that the stable configuration for the α-Sn/Ge(111) surface is the 1U2D. The possible inequivalence of the two down Sn adatoms is also discussed.

The phonon echo excited by radio-frequency pulses in superconducting MgB₂ in external magnetic field was studied. Using the echo technique two contributions to ultrasound attenuation are observed: low-temperature relaxation, which depends on the magnetic field, and a decay connected to the superconducting energy gap at temperatures close to T_c. The value of about 7k_BT_c for the energy gap was extracted from the experimental data.

We have performed high-resolution angle-resolved photoemission spectroscopy on the optimally doped Ba_0.6K_0.4Fe₂As₂ compound and determined the accurate momentum dependence of the superconducting (SC) gap in four Fermi-surface sheets including a newly discovered outer electron pocket at the M-point. The SC gap on this pocket is nearly isotropic and its magnitude is comparable (Δ∼11 meV) to that of the inner electron and hole pockets (∼12 meV), although it is substantially larger than that of the outer hole pocket (∼6 meV). The Fermi-surface dependence of the SC gap value is basically consistent with the Δ(k)=Δ₀ cos k_x cos k_y formula expected for the extended s-wave symmetry. The observed finite deviation from the simple formula suggests the importance of multi-orbital effects.

We have successfully synthesized the fluoride-arsenide compounds Ca_1−xRE_xFeAsF (RE=Nd, Pr; x=0,0.6). The X-ray powder diffraction confirmed that the main phases of our samples are Ca_1−xRE_xFeAsF with the ZrCuSiAs structure. By measuring resistivity, superconductivity was observed at 56 K in Nd-doped and 52 K in Pr-doped samples with x=0.6. Bulk superconductivity was also proved by the DC magnetization measurements in both samples. Hall effect measurements revealed hole-like charge carriers in the parent compound CaFeAsF with a clear resistivity anomaly below 118 K, while the Hall coefficient R_H in the normal state is negative for the superconducting samples Ca_0.4Nd_0.6FeAsF and Ca_0.4Pr_0.6FeAsF. This indicates that the rare-earth element doping introduces electrons into CaFeAsF, which induces high-temperature superconductivity.

In the framework of the Dimmock model of the energy spectrum in IV-VI narrow-gap semiconductors (like PbTe, SnTe, and their alloys), we calculate the intrinsic contribution to spin Hall conductivity. The calculations show that a strong spin-orbit interaction in these compounds leads to a nonvanishing spin Hall effect. Moreover, this effect is associated with kinetic terms which describe the deviation of the Dimmock model from a simpler model of Dirac. The nonzero spin Hall conductivity, however, occurs only when the effective mass of electrons in the conduction band is different from the effective mass of holes in the valence band.

The modulation with magnetic field of the sheet inductance measured on proximity effect Josephson-junction arrays (JJAs) is progressively vanishing on lowering the temperature, leading to a low-temperature field-independent response. This behaviour is consistent with the decrease of the two-dimensional penetration length below the lattice parameter. Low-temperature data are quantitatively compared with theoretical predictions based on the XY model in the absence of thermal fluctuations. The results show that the description of a JJA within the XY model is incomplete and the system is put well beyond the weak screening limit which is usually assumed in order to invoke the well-known frustrated XY model describing classical Josephson-junction arrays.

We have carried out a systematic theoretical investigation of Fe-doped AlH₃ to study its magnetic properties and to assess the stability of the ferromagnetic phase in this material. All calculations were performed using the projector augmented-wave method and generalized-gradient approximation (GGA) as well as GGA+U. The magnetic moment is found to be constant at 1.1 μ_B per Fe-atom in the ferromagnetic configuration for distances between adjacent Fe atoms varying from 3.25 Å to 7.41 Å. We conclude that the ferromagnetic phase in Fe-doped AlH₃ is stable both for near and far configurations of Fe. The stability of the ferromagnetic phase is due to the holes created by Fe-doping and the larger level splitting of the interacting gap states within the ferromagnetic phase.

We investigate structural, magnetic, and electronic properties of SrFeAsF as a new parent for superconductors using a state-of-the-art density-functional theory method. Calculated results show that the striped antiferromagnetic order is the magnetic ground state in the Fe layer and the interlayer magnetic interaction is tiny. Calculated As and Sr positions are in good agreement with experiment. There are only two quasi–two-dimensional bands near the Fermi level. The valence charge is mainly in the Fe and F layers, and the magnetic moment is confined to the Fe atoms. All the spin couplings within the Fe layer are antiferromagnetic due to the superexchange through the nearest As atoms. These results, with the record-equaling phase-transition temperature in the latest Sm-doped SrFeAsF, show that the SrFeAsF, sharing the same structure with LaFeAsO, is promising for achieving better superconductors.

We investigate the dynamics of excitons created in a quantum well embedded in a double-barrier resonant-tunneling diode under applied bias. We find that the exciton dynamics is highly correlated with carrier tunneling processes. The tunneling favors exciton relaxation via exciton-carrier scattering processes.

We utilize a superconducting stripline resonator containing a dc-SQUID as a strong intermodulation amplifier exhibiting a signal gain of 24 dB and a phase modulation of 30 dB. Studying the system response in the time domain near the intermodulation amplification threshold reveals a unique noise-induced spikes behavior. We account for this response qualitatively via solving numerically the equations of motion for the integrated system. Furthermore, employing this device as a parametric amplifier yields an abrupt rise of 38 dB in the generated side-band signal.

When moving from native to light-activated bacteriorhodospin, modification of charge transport consisting of an increase of conductance is correlated to the protein conformational change. A theoretical model based on a map of the protein tertiary structure into a resistor network is implemented to account for a sequential tunneling mechanism of charge transfer through neighbouring amino acids. The model is validated by comparison with current-voltage experiments. The predictability of the model is further tested on bovine rhodopsin, a G-protein coupled receptor (GPCR) also sensitive to light. In this case, results show an opposite behaviour with a decrease of conductance in the presence of light.

A new class of 32n² boron cages which are made closed by six squares is proposed and a procedure to build such cages using an α-boron sheet is described. Each member from this infinite set of boron cages has a structure that is compatible with the most stable α-boron sheet that maintains an optimal balance of the two-center and three-center bonds. Accurate density functional calculations with a large polarized Gaussian basis set show that B₃₂, B₉₆, B₁₂₈, and B₂₈₈ are energetically stable structures. The smallest B₃₂ cage from this class has the HOMO-LUMO gap of 1.32 eV, the largest amongst the boron cages and boron fullerenes studied so far.

The functional consequences of local and global dynamics can be very different in natural systems. Many such systems have a network description that exhibits strong local clustering as well as high communication efficiency, often termed as small-world networks (SWN). We show that modular organization in otherwise random networks generically give rise to SWN, with a characteristic time-scale separation between fast intra-modular and slow inter-modular processes. The universality of this dynamical signature, that distinguishes modular networks from earlier models of SWN, is demonstrated by processes as different as spin-ordering, synchronization and diffusion.