Table of contents

The Boussinesq equation can be considered as the first model for nonlinear dispersive wave propagation. In the light of the principle of homogeneous balance and with the aid of some suitable transformations, the multiple soliton solutions of the Boussinesq equation are given.

We assume that an N-level moving atom interacts with an (N − 1) mode electromagnetic cavity field. The model includes the detuning and the intensity-dependent coupling. The constants of motion and the wave function for the atomic system is obtained. Some statistical aspects of the considered atomic system such as momentum increment and momentum diffusion have been calculated. The influence of the initial mean photon number, the detuning parameter and the intensity dependent coupling on the momentum increment are investigated when the atom is initially in excited state and the field is in a squeezed state. It is found that the momentum of the atom is unchanged for large initial mean photon number.

We consider time-dependent Gaussian wave packet solutions of the Schrödinger equation, with arbitrary initial central position, x₀, and momentum, p₀, for an otherwise free particle, but with an infinite wall at x = 0, so-called bouncing wave packets. We show how difference or mirror solutions of the form ψ(x,t) − ψ(−x,t) can, in this case, be normalized exactly, allowing for the evaluation of a number of time-dependent expectation values and other quantities in closed form. For example, we calculate ⟨p²⟩_t explicitly which illustrates how the free-particle kinetic (and hence total energy) is affected by the presence of the distant boundary. We also discuss the time dependence of the expectation values of position, ⟨x⟩_t, and momentum, ⟨p⟩_t, and their relation to the impulsive force during the `collision' with the wall. Finally, the x₀, p₀ → 0 limit is shown to reduce a special case of a non-standard free-particle Gaussian solution. The addition of this example to the literature then expands of the relatively small number of Gaussian solutions to quantum mechanical problems with familiar classical analogs (free particle, uniform acceleration, harmonic oscillator, unstable oscillator, and uniform magnetic field) available in closed form.

We present a simple electrical circuit that consists of a Van der Pol oscillator coupled to a Duffing type oscillator. The equations of the model are derived. The stability of the system is investigated. Approximate analytical solutions are obtained and a quenching phenomenon is observed. Finally, synchronization of two identical such systems is investigated.

We analyse numerically a model for the Josephson Junction and show that it combines the features of a bistable system as well as a threshold system. A study of stochastic resonance in these two contexts reveals some novel features of the phenomenon regarding the amplification of multisignal inputs. Some interesting practical applications are also indicated.

Radiative transition probabilities and oscillator strengths for 164 lines arising from 5s²ns, 5s²np, 5s²nd, 5s²nf, 5s²ng and 5s5p² configurations of Sn II have been calculated. These values were obtained in intermediate coupling (IC) and using ab initio relativistic HartreeFock (HFR) calculations. We use for the IC calculations the standard method of least square fitting of experimental energy levels by means of computer codes from Cowan. The results of calculations for radiative transition probabilities are presented and compared with the experimental result presents in the literature and with other theoretical values. These values, although in general agreement with the rare experimental data, do present some noticeable discrepancies.

High resolution laser spectroscopy has been applied to study the hyperfine structure of excited levels of Tm I. In the wavelength range from 570 nm to 595 nm 31 transitions were measured using a hollow cathode discharge and a tunable single-mode cw ring dye laser. Precise values for the magnetic dipole hyperfine structure constants A of 24 even and 19 odd levels were determined.

Transition probabilities have been calculated with the pseudorelativistic Hartree–Fock (HFR) approach in which core-polarization effects have been included for Δn = 0 and Δn = 1 transitions connecting the 5s²5p², 5s²5p6p, 5s²5p4f and the 5s5p³, 5s²5p5d and 5s²5p6s configurations of Xe V. The accuracy of the present set of results is partly assessed through comparisons with the few experimental radiative lifetimes available. The reasons for the discrepancies between theory and experiment are outlined.

The radiative lifetimes of eleven levels belonging to the 5p⁵nd (n = 6,7,8,9) configuration of XeI have been measured using high frequency deflection technique with a delayed coincidence single photon counting arrangement. Lifetimes of some of the levels have been measured for the first time. A comparison with other results is presented.

Energy levels, oscillator strengths and transition probabilities for a portion of the S II spectrum up to and including 3p²(¹D)3d ²D_3/2 were computed using the multiconfiguration Hartree–Fock (MCHF) method with relativistic effects included in the Breit–Pauli (BP) approximation. While term mixing in this spectrum is small, the ¹D, ¹S and ³P parents of the 3p²3d configuration states were found to be highly mixed for many terms. A_ki values for E1 and some E2 and M1 transitions were computed from which lifetimes for excited states were determined. The energy levels are analyzed by comparison with observation and transition probabilities compared with available theory. The lifetimes for 3s3p⁴⁴P levels are in excellent agreement with experiment.

Electron impact double ionization cross sections of Ti⁺ and Ti²⁺ have been calculated in the modified double binary encounter model incorporating the focussing action of the target ion on the incident electron along the line suggested by Thomas and Garcia. Accurate expression for σ_ΔE (cross section for energy transfer ΔE) and Hartree–Fock velocity distributions for the target electrons have been used throughout the calculations. The present results show satisfactory agreement with experimental observations. It is concluded that the discrepancy in the high energy region is due to non-inclusion of the ionization processes arising from the L-shell in the present calculations.

Using the semiclassical approach by Sahal-Bréchot [Astron. Astrophys.1, 91 (1969), ibid. 2, 322 (1969)], we have calculated Stark shifts for CII, NII and OII spectral lines. The needed oscillator strengths have been obtained from the sophisticated atomic structure data base "TOPbase". Then we have compared our results with available experimental ones and with other theoretical results. We give also new values of Stark shifts.

The spectrum of cesium was recorded in the 300–1250 Å on a 3 m normal incidence spectrograph using a triggered spark source. The 5s²5p³ (6d + 7s) configurations in Cs IV spectrum were investigated. 41 out of 47 levels of two configurations have been established on the basis of 76 lines in the 344 Å–949 Å region. The observed spectrum was interpreted satisfactorily by carrying out Hartree–Fock (HF) and least-squares-fitting (LSF) calculations using Cowan Code.

We have presented an investigation on the characteristics of a laser beam, which is a mixture of two degenerate modes (TEM₀₀ and TEM₀₁), that is propagating through cubic quintic nonlinear media. Employing WKBJ method and paraxial ray approximation we have derived a pair of dynamical equations for the beam widths of the mixture of two modes. These equations are identical to two coupled nonlinear oscillators of mass unity. We have found that in the absence of quintic nonlinearity, stable propagation is possible for certain values of intensity ratio of two modes, whereas for other intensity ratios only quasi steady propagation is allowed. In the presence of quintic nonlinearity, stable propagation is allowed irrespective of the value of intensity ratio of two modes. Bound as well as unbound oscillatory regions have been identified. It has been found that, higher values of quintic nonlinearity and the intensity of TEM₀₁ mode reduce the amplitude of oscillations.

A relativistic short laser pulse is modeled having amplitude modulation in time and Gaussian profile of intensity distribution transverse to the direction of laser propagation. The relativistic laser exerts a ponderomotive force on the electrons imparting them an oscillatory velocity. When the plasma has a density gradient perpendicular to this ponderomotive force, a quasistatic magnetic field is produced. The magnetic field lasts for duration of the laser pulse. At plasma resonance (ω_p ≈ Ω/2), the magnetic field is enhanced significantly.

A theoretical investigation has been made of electrostatic acoustic modes and associated instabilities and dampings in a uniform partially ionized, self-gravitating dusty plasma taking into account the effects of ionization, ion-drag, ion-neutral and neutral dust friction. It is found that the ionization and ion-drag force play important roles in stabilizing or destabilizing the dust ion-acoustic modes. In a weak self-gravitational field, when the electron to ion temperature ratio exceeds the threshold value the ion-drag force destabilizes the dust acoustic modes. It is also found that the gravitational collapse can not be stopped by any value of the collision frequencies.

A dispersion relation of Langmuir wave in a dusty plasma with grain charge fluctuations is derived from the moment equations of a kinetic equation which takes into account the grain charging collisions with a simple Bhatnagar-Gross-Krook model. The resulting dispersion relation is analyzed with the aid of a Nyquist diagram to obtain the criterion of instability. It is found that the grain charging collisions always damp the high frequency Langmuir wave. The cubic dispersion relation is analyzed in detail to obtain the real frequency and the damping rate.

Stark widths (W) of 23 doubly ionized oxygen (O III) spectral lines belonging to the ten highest multiplets in the 3s3p and 3p3d transitions have been measuredin the optically thin oxygen plasma created in a linear, low-pressure, pulsed arc discharge at a 42 000 K electron temperature and 1.65 × 10²³ m^-3 electron density. They are not measured before and four (295.969, 311.567, 312.163 and 313.279 nm) of them in the two multiplets (3p ¹P – 3d ¹D^o and 3p ³S – 3d ³P^o) are the first data in this field. In four multiplets (3p ¹P – 3d ¹D^o, 3p ³S – 3d ³P^o, 3p ⁵D^o – 3d ⁵F and 3s ⁵P – 3p ⁵S^o) our W are the first measured data.

Thin film CuInSe₂ chalcopyrite semiconductors have been prepared on glass substrates by means of two-stage process. The structural properties and atomic compositions of films were determined by energy-dispersive analysis of x-rays (EDAX) and x-ray diffraction (XRD) measurements. Reflectance and transmittance measurements were performed on the films in the photon wavelength range of 300–2200 nm. The samples used in the measurements have different Cu/In ratios. The reflectance and transmittance spectra were analyzed on the basis of multiple reflection model considering the absorbing film on a non-absorbing substrate and then complex refractive-index n*(E) = n(E) + ik(E) and complex dielectric constant ε*(E) = ε₁(E) + iε₂(E) were determined. It has been concluded that the films having higher Cu/In ratios show stronger absorption at low photon energy region than those having lower Cu/In ratios.

Influence of the grain size on the effective carrier mobility (μ_eff) and transfer characteristics of a polycrystalline silicon thin-film transistor (poly-Si TFT) has been theoretically investigated by developing an analytical model. The dependence of μ_eff is studied as function of doping concentration and gate voltage for different values of grain size. It is observed that at low as well as at high doping concentrations, the effective carrier mobility (μ_eff) increases with increasing grain size, whereas the observed dip at the intermediate doping concentration is confirmed. The effect of the grain size on transfer characteristics of poly-Si TFT in its linear region is also presented. It is found that at low gate voltages, μ_eff and I_D increase rapidly with the increase in V_G for all grain sizes due to the grain boundary barrier lowering effect. At high gate voltage the grain boundary barrier lowering effect becomes insignificant and causes the saturation of μ_eff and I_D. The model was found to account correctly for the experimentally observed mobility variation and yield a reasonably good agreement.

In recent years methods have been proposed to extend classical game theory into the quantum domain. In a previous publication the nature of several non-cummutative games was briefly analyzed.

Here we give an analysis of the simplest non-commutative quantum game, which is a gambling game much like simple heads or tails. The quantum game displays strategies which, though non direct-product strategies, allow for correlations between the players pay-off.

After a brief historical introduction, we dwell on two recent experiments in the low-temperature, monoclinic phase of V₂O₃: K-edge resonant x-ray scattering and non-reciprocal linear dichroism, whose interpretations are in conflict, as they require incompatible magnetic space groups. Such a conflict is critically reviewed, in the light of the present literature, and new experimental tests are suggested, in order to determine unambiguously the magnetic group. We then focus on the correlated, non-local nature of the ground-state wave function, that is at the basis of some drawbacks of the LDA + U approach: we singled out the physical mechanism that makes LDA + U unreliable, and indicate the way out for a possible remedy. Finally we explain, by means of a symmetry argument related to the molecular wave function, why the magnetic moment lies in the glide plane, even in the absence of any local symmetry at vanadium sites.

The synchrotron x-ray diffraction studies of magnetic materials under extreme conditions performed at the beam-line BL19LXU at SPring-8 are reviewed. After a description of the experimental setup, we report recent results of non-resonant x-ray magnetic and charge scattering measurements on some antiferromagnets obtained in high magnetic fields and low temperatures. The first result is the observation of the spin-flop transition in the prototypical uniaxial antiferromagnet MnF₂ and we find that the intensity of the magnetic x-ray diffraction depends on the angle the magnetic moment in the sample makes with the scattering vector. The second result is the synchrotron x-ray diffraction measurement of the high field phase of a spin-Peierls system. We have measured the x-ray diffraction by CuGeO₃ in magnetic field, H, up to 15 T. We find that the temperature, T, dependence of the incommensurate peak is quite different at lower H from that at higher H. At magnetic fields slightly above the critical field, H_SP, for the commensurate to incommensurate transition, the incommensurability, δl, depends much on T, whereas at H well above H_SP, δl is almost independent of T. We interpret this finding as due to a stabilization of the incommensurate state by a strong magnetic field which suppresses thermal fluctuations. The third one is the synchrotron x-ray diffraction measurement at a very low temperature. We have observed a jump in the lattice constant of the ladder-like compound Cu₂(C₅H₁₂N₂)₂Cl₄ at about 40 mK associated with the field induced magnetic ordering from the non-magnetic spin-liquid state. This is the first experimental confirmation of the theoretical prediction on the generalized spin-Peierls phenomenon in quantum magnets.

Quantum-mechanical correlations, or the quantum entanglement, of nuclear spin and spatial degrees of freedom can be observed with neutron scattering. The underlying concepts in quantum mechanics are discussed in the context of two recent experiments, which utilize the total scattering and the Compton scattering of neutrons.

We describe, using the Mean Field Theory, a detailed analysis of the magnetic contribution to the molar heat capacity C_mag for ferromagnetic systems. This calculation is designed to be used as a teaching homework problem for physics undergraduates. The description emphasises that C_mag at the transition temperature T_C is characterised by the existence of a simple jump discontinuity anomaly, but when the temperature is lowered down to 0 K the shape of C_mag depends strongly on the magnitude of the spin S. In fact, the appearance of a shoulder in C_mag for S > 3/2 is expected. The origin of this shoulder could be understood as a Schottky-like anomaly in the ordered state. These physical results are in good agreement with those from real systems, and give the student a valuable insight into the behaviour of the thermodynamical response of a ferromagneticmaterial.