Table of contents

I study persistent current and low-field magnetic susceptibility of one-dimensional normal metal mesoscopic rings and Möbius strips threaded by slowly varying magnetic flux ϕ. In strictly one-channel perfect rings, current shows saw-tooth-like variation with ϕ for the cases where the rings contain odd and even number of electrons N_e respectively. But in disordered rings, current shows a continuous variation with ϕ. In these systems current has only ϕ₀ flux-quantum periodicity. Now in Möbius strips, the motion of the electrons in the transverse direction has an important factor on persistent current and also on low-field magnetic response. If the electrons are unable to hop in the transverse direction then an electron encircles the system twice before returning to its initial position and current obtains ϕ₀/2 flux-quantum periodicity unlike ϕ₀ flux-quantum periodicity in strictly one-channel rings or multi-channel cylinders. The sign of the low-field currents in one-channel mesoscopic rings can be predicted exactly, even in the presence of impurity in these systems. For perfect rings current has only diamagnetic behaviour in the limit of zero field irrespective of the total number of electrons N_e. On the other hand, in dirty rings, current shows paramagnetic and diamagnetic signs respectively for the rings with even and odd N_e. In Möbius strips for zero hopping strength of the electrons in the transverse direction we get exactly the same behaviour as in strictly one-channel rings, but for nonzero transverse hopping strength the sign of the low-field currents cannot be predicted since it strongly depends on N_e and the specific realization of disorder configuration of the systems.

In this study, a cluster variation theory for the Maier–Saupe model of the nematic–isotropic phase transition is generalized by using non-extensive thermostatistics. The variation of long-range order parameter with temperature is investigated and the effect of the possible generalization is shown for some values of the entropic index. The critical value of the long-range order parameter at the nematic–isotropic transition temperature versus the entropic index is also compared with Monte Carlo simulation values and experimental data.

We study the effects of non-universal extra dimensions on the decay widths of the lepton flavour violating (LFV) processes, t→c l_i⁻l_j⁺ and H⁰→h⁰(A⁰)l_i⁻l_j⁺ in the general two Higgs doublet model. We consider that the extra dimensions are accessible to the standard model gauge fields and the new Higgs doublet. We observe that the LFV H⁰→h⁰(τ⁺μ⁻+τ⁻μ⁺) and H⁰→A⁰(τ⁺μ⁻+τ⁻μ⁺) Higgs decays are sensitive to the extra dimensions, especially in the case of two spatial ones. This result may ensure a test to determine the compactification scale and the possible number of extra dimensions with the accurate experimental measurements.

A new algorithm for approximating numerical solutions of Burgers' equation in a modified B-polynomial basis is presented. The desired solutions are expanded in terms of a set of continuous polynomials over the entire interval for the spatial part with only the time variable requiring discretization. The algorithm makes use of the Galerkin method to determine the expansion coefficients to construct initial values for expansion coefficients. Matrix formulation is used to construct system of equations in time variable which are solved using a fourth-order Runge–Kutta method. The accuracy of the solutions is dependent on the size of the B-polynomial basis set. The current algorithm is implemented in solving two cases of homogeneous and non-homogeneous boundary conditions. Excellent agreement is found between exact and approximate solutions. This procedure has great potential to be implemented in more complex systems of differential equations where no exact solution is available.

We study the exact statistical mechanics of Lamé solitons using a transfer matrix method. This requires a knowledge of the first forbidden band of the corresponding Schrödinger equation with the periodic Lamé potential. Since the latter is a quasi-exactly solvable system, an analytical evaluation of the partition function can be done only for a few temperatures. We also study approximately the finite temperature thermodynamics using the ideal kink gas phenomenology. The zero-temperature 'thermodynamics' of the soliton lattice solutions is also addressed. Moreover, in appropriate limits our results reduce to that of the sine-Gordon problem.

Energy splittings of 53 fine-structure levels as well as oscillator strengths and radiative decay rates for all electric-dipole-allowed and intercombination transitions among the (1s²2s²2p⁶)3s²(¹S), 3s3p(^1,3P⁰), 3s3d(^1,3D), 3s4s(^1,3S), 3s4p(^1,3P⁰), 3s4d(^1,3D), 3s4f(^1,3F⁰), 3p²(¹S,³P,¹D), 3p3d(^1,3P⁰,^1,3D⁰, ^1,3F⁰), 3p4s(^1,3P⁰) and 3d²(¹S,³P,¹D,³F,¹G) states of Kr XXV are calculated using very extensive configuration-interaction (CI) wavefunctions. These wavefunctions are obtained using the CIV3 computer code of Hibbert. The important relativistic effects in intermediate coupling are incorporated by means of the Breit–Pauli Hamiltonian. In order to keep our calculated energy splittings as close as possible to the experimental values, we have made small adjustments to the diagonal elements of the Hamiltonian matrices. Our excitation energies, including their ordering, are in excellent agreement with the available experimental results. The enormous mixing among several fine-structure levels makes it very difficult to identify them correctly with the result that their positions in other calculations are interchanged compared to our results and the experimental values. From our transition probabilities, we have also calculated radiative lifetimes of some fine-structure levels. Our calculated oscillator strengths, radiative decay rates and the lifetimes are found to be in good agreement with the experimental and other theoretical results (wherever available). In this calculation, we also predict new data for several fine-structure levels where no other theoretical and/or experimental results are available. We believe that the new oscillator strengths reported in this paper will be useful in many astrophysical applications and in technical plasma modelling.

The multiconfiguration Dirac–Fock method is used to systematically calculate the energy levels, wavelengths and oscillator strengths for transitions among the levels of the terms belonging to the 3s², 3s3p, 3s3d, 3s4s, 3s4p, 3s4d, 3p², 3p3d, 3p4s, 3p4p, 3p4d, 3d4s, 3d4p, 3d4d and 3d² configurations for the elements of the magnesium isoelectronic sequence from high nuclear charge Z = 53 to 58 by taking into account main correlation relativistic effects. Another wavelength region λ = 6–11 Å from n = 3–4 transitions and the corresponding oscillator strengths are for the first time extensively reported. The trends of wavelengths and oscillator strengths along the isoelectronic sequence are discussed. Many strong configuration mixings and level-crossings in particular between the two states 3p3d ³F₃⁰ and 3p3d ³D₃⁰ in Mg-like La and Ce ions are investigated.

A quantized fermion is represented by a scalar particle encircling a magnetic flux line. It has a spinor structure which can be constructed from quantum gates and qubits. We have studied here the role of Berry phase in removing dynamical phase during one qubit rotation of a quantized fermion. The entanglement of two qubits inserting spin-echo to one of them allows the trapped Berry phase to measure entanglement. Some effort is given to study the effect of noise on the Berry phase of spinors and their entangled states.

Dynamics of macro-particles forming two-dimensional (2d)-fluid-like structures is numerically studied for pair potentials of Yukawa type. The parameters responsible for the phase state and transport processes are determined and investigated. Comparison of obtained results with data of numerical investigations for 3d Yukawa systems is presented.

By means of a two-step unitary transformation, the exact quantum mechanical solution of two-dimensional mesoscopic circuit coupled via inductance is derived. The wavefunction, propagator and expectation value of Hamiltonian are evaluated. The fluctuations of charges and currents are calculated and uncertainty products between charges and their conjugate currents are obtained. We apply our results to the system with special cases of the power source such as the sinusoidal and the sawtooth power source and show that the probability densities oscillate with time due to the power source.

The one-dimensional (1D) modified complex Ginzburg–Landau (MCGL) equation for travelling wave systems is analytically studied. We investigate soliton solutions of this equation and find solutions with fixed amplitude, arbitrary amplitude as well as chirp-free solitons. All these solutions are written in explicit form in terms of the parameters of the MCGL equation.

Semi-relativistic calculations are carried out for the photoionization of neutral argon from its ground state 3s²3p⁶¹S₀ and the lowest three excited levels 3s²3p⁵(2P⁰)4s³P⁰₂, 3s²3p⁵(²P⁰)4s  ³P⁰₁ and 3s²3p⁵(²P⁰)4s ³P⁰₀, using the semi-relativistic Breit–Pauli approximation. Configuration interaction (CI) wavefunctions are used to represent the lowest 12 target states of the Ar II ion retained in the R-matrix expansion. The Rydberg series 3s3p^6 2S_1/2{np[1/2]₁, np[3/2]1}, J=1° of autoionizing resonances formed in the photoionization process of ground state 3s²3p⁶¹S₀, just below 3s3p⁶²S_1/2 threshold of Ar II, are identified and their resonance positions and effective quantum numbers are reported. Excellent agreement with previously published resonance positions and effective quantum numbers is observed. Further, new results for photoionization cross-sections from excited states of Ar, involving clusters of Feshbach resonances converging to different thresholds of Ar II, are predicted.

Relativistic configuration interaction calculations have been performed for Mo VI 4p⁵ 4d²J=5/2 and nf ²F_5/2 (n=4–6) wavefunctions. Level energies and E1 oscillator strengths for transitions between these states and the nd²D (n=4–6) states have been obtained. The calculated LS compositions of all 11 levels of 4p⁵ 4d²J=5/2 have been found to be in good agreement with other designations. While most calculated level energies agree well with the most recent experimental work, large discrepancies in a few (upper) levels do exist. The oscillator strength of all 84 transitions are computed, and 36 of the largest (f > 0.001) are presented here. Most of the oscillator strengths are computed for the first time.

The Sn IX–Sn XII spectra excited in a vacuum spark have been analysed in the 130–160 Å wavelength region. The analysis was based on the energy parameter extrapolation in the isonuclear Sn VI–VIII and Sn XIII–XIV sequence. 266 spectral lines belonging to the 4d^m–(4d^m−14f+4p⁵4d^m+1) (m=6–3) transition arrays were classified in the Sn IX–Sn XII spectra for the first time. All 18 level energies of the 4d³ configuration and 39 level energies of the strongly interacting 4d²4f and 4p⁵4d⁴ configurations were established in the Sn XII spectrum. The energy differences between the majority of the 4d^m levels and about 40 levels of the 4d^m−14f+4p⁵4d^m+1 configurations were determined in each of the Sn IX, Sn X and Sn XI spectra (m=6–4). As a result, all intense lines were classified in the 130–140 Å region relevant to the extreme ultraviolet (EUV) lithography. It was shown that the most of the intense lines in the 2% bandwidth at 135 Å belong to the transitions in the Sn XI–Sn XIII spectra.

This paper inspects more closely the problem of the momentum and energy of a bound (non-radiative) electromagnetic (EM) field. It has been shown that for an isolating system of non-radiative non-relativistic mechanically free charged particles, a transformation of mechanical to EM momentum and vice versa occurs in accordance with the requirement =const, where is the canonical momentum (N>1 is the number of particles, q is the charge, is the vector potential, is the mechanical momentum of the system). Then represents the self-force, acting on this isolating system due to violation of Newton's third law in EM interaction. This equation is not applicable to an isolated charged particle, and the problems of its self-action and its own EM momentum have been examined. Analysing the systems of non-radiative particles, where the retardation is not negligible ('dynamical' systems in our definition) it has been found that the total momentum is the same at the initial and final stationary states of such systems, but it varies with time during the dynamical processes. It means a violation of continuous conservation of the total momentum, if the bound EM field spreads at the light velocity c. Finally, the compatibility of the energy conservation law and the Lentz rule for retarded non-radiative EM field has been examined. It has been shown that for dynamical systems the energy conservation law comes into a certain contradiction with the finite (light) spread velocity for the bound EM field.

A recently developed simple approach for the exact/approximate solution of Schrödinger equations with constant/position-dependent mass, in which the potential is considered as in the perturbation theory, is shown to be equivalent to the one leading to the construction of exactly solvable potentials via the solution of second-order differential equations in terms of known special functions. The formalism in the former solves difficulties encountered in the latter in revealing the corrections explicitly to the unperturbed piece of the solutions whereas the other obviates cumbersome procedures used in the calculations of the former.

The dynamics of intense laser pulses in plasmas are investigated both theoretically and numerically. The linear growth and nonlinear saturation of relativistic stimulated Raman scattering of plasmons are investigated by means of a nonlinear dispersion relation and via direct Vlasov simulations. We observe acceleration of electrons up to ultra-relativistic energies by a positive electrostatic potential that is created by intense short laser pulses.

It is demonstrated how the right-hand sides of the Lorentz transformation equations may be written, in a Lorentz-invariant manner, as 4-vector scalar products. This implies the existence of invariant length intervals analogous to invariant proper time intervals. An important distinction between the physical meanings of the space–time and energy–momentum 4-vectors is pointed out. The formalism is shown to provide a short derivation of the Lorentz force law of classical electrodynamics, and the conventional definition of the magnetic field, in terms of spatial derivatives of the 4-vector potential, as well as the Faraday–Lenz law and the Gauss law for magnetic fields. The connection between the Gauss law for the electric field and the electrodynamic Ampère law, due to the 4-vector character of the electromagnetic potential, is also pointed out.

The influence of details of an international thermonuclear experimental reactor (ITER)-like geometry on drift wave stability is studied. The eigenvalue problem for electrostatic electron drift waves is solved numerically by following the ballooning mode formalism and using a standard shooting technique. The real frequencies and growth rates of the most unstable modes and their eigenfunctions are calculated for two specific magnetic flux surfaces. For the equilibrium under investigation, the modes are found to be unstable for peak density profiles and their stability is found to be strongly affected by the local magnetic shear (LMS). The presence of positive LMS is found to be destabilizing on the magnetic surface where global magnetic shear is reverse. The stability behaviour is however different for a positive magnetic shear surface where the effect of large positive LMS is found to be stabilizing. The eigenfunctions are more localized in the regions where normal curvature is bad and magnetic field is weak.

New approaches to nonlinear force-free field equations are presented and new exact solutions are found analytically. Examples are given and some implications of the results to astrophysical solar plasmas as well as tokamak plasmas are discussed.

An intense short pulse laser propagating through a plasma undergoes filamentation instability under the combined effects of relativistic mass variation and ponderomotive force-induced electron density depression. These two nonlinearities superimpose each other. In a tenuous plasma, the filament size scales as where ω _p is the plasma frequency, a₀ is the normalized laser amplitude and γ ₀ is the relativistic gamma factor.

The new and improved treatment of η-meson exchange diagrams turns out to be essential in order to fully describe both total cross-sections and, in particular, the challenging pp invariant mass distributions. Contrary to other approaches, the η-meson contribution in our model is comparable with the leading π-meson exchange term, and using the phenomenological final state interaction we have no need to include other mesons, like ρ and ω, in order to obtain good agreement with experiment.

In this paper, a method for solving multipoint boundary value problems is presented. The main idea behind this work is the use of the well-known Adomian decomposition method. In this technique, the solution is found in the form of a rapid convergent series. Using this method, it is possible to obtain the solution of the general form of multipoint boundary value problems. The Adomian decomposition method is not affected by computation round off errors and one is not faced with the necessity of large computer memory and time. To show the efficiency of the developed method, numerical results are presented.

After a unitary transformation, exact wavefunctions of the time-dependent two-dimensional harmonic oscillator in a time-dependent magnetic field are written in the form of the product of two one-dimensional time-dependent harmonic oscillators in the (x, p_y) representation. Applying the Heisenberg correspondence principle (HCP) to the system, the exact classical solution is obtained from the quantum matrix elements. Meanwhile, the coherent state is discussed.

A simple model wavefunction, consisting of a linear combination of two free-particle Gaussians, describes many of the observed features seen in the interactions of two isolated Bose–Einstein condensates (BECs) as they expand, overlap and interfere. It is shown that a simple extension of this idea can be used to predict the qualitative time-development of a single expanding BEC produced near an infinite wall boundary, giving similar interference phenomena. Other possible time-dependent behaviours of single BECs in restricted geometries, such as wave packet revivals are also briefly discussed.

We provide a summary of the physics reported at the 37th EGAS conference. Advances in attosecond science, atomic antimatter, cold atom physics and contemporary spectroscopy are among the topics surveyed.