Breakup of a multisoliton state of the linearly damped nonlinear Schrödinger equation

We address the breakup (splitting) of multisoliton solutions of the nonlinear Schrödinger equation (NLSE), occurring due to linear loss. Two different approaches are used for the study of the splitting process. The first one is based on the direct numerical solution of the linearly damped NLSE and the subsequent analysis of the eigenvalue drift for the associated Zakharov-Shabat spectral problem. The second one involves the multisoliton adiabatic perturbation theory applied for studying the evolution of the solution parameters, with the linear loss taken as a small perturbation. We demonstrate that in the case of strong nonadiabatic loss the evolution of the Zakharov-Shabat eigenvalues can be quite nontrivial. We also demonstrate that the multisoliton breakup can be correctly described within the framework of the adiabatic perturbation theory and can take place even due to small linear loss. Eventually we elucidate the occurrence of the splitting and its dependence on the phase mismatch between the solitons forming a two-soliton bound state. © 2007 The American Physical Society.

Non-Gaussian error probability in optical soliton transmission

We find the probability distribution of the fluctuating parameters of a soliton propagating through a medium with additive noise. Our method is a modification of the instanton formalism (method of optimal fluctuation) based on a saddle-point approximation in the path integral. We first solve consistently a fundamental problem of soliton propagation within the framework of noisy nonlinear Schrödinger equation. We then consider model modifications due to in-line (filtering, amplitude and phase modulation) control. It is examined how control elements change the error probability in optical soliton transmission. Even though a weak noise is considered, we are interested here in probabilities of error-causing large fluctuations which are beyond perturbation theory. We describe in detail a new phenomenon of soliton collapse that occurs under the combined action of noise, filtering and amplitude modulation. © 2004 Elsevier B.V. All rights reserved.

Free energy functional expansion as the generalized approach to the equation of state of dense fluids

A version of the thermodynamic perturbation theory based on a scaling transformation of the partition function has been applied to the statistical derivation of the equation of state in a highpressure region. Two modifications of the equations of state have been obtained on the basis of the free energy functional perturbation series. The comparative analysis of the experimental PV T- data on the isothermal compression for the supercritical fluids of inert gases has been carried out. © 2012.

Optimisation of random DFB Raman laser amplifier

We numerically optimise 2nd-order random DFB Raman laser amplifiers for transmission for the first time. Optical signal to noise ratio, nonlinear phase shift, signal power variation and the impact of the reflectivity of FBG are investigated in the links from 10 - 120 km.

Channel model and lower capacity bound for the transmission based on nonlinear Fourier transform

The integrability of the nonlinear Schräodinger equation (NLSE) by the inverse scattering transform shown in a seminal work [1] gave an interesting opportunity to treat the corresponding nonlinear channel similar to a linear one by using the nonlinear Fourier transform. Integrability of the NLSE is in the background of the old idea of eigenvalue communications [2] that was resurrected in recent works [3{7]. In [6, 7] the new method for the coherent optical transmission employing the continuous nonlinear spectral data | nonlinear inverse synthesis was introduced. It assumes the modulation and detection of data using directly the continuous part of nonlinear spectrum associated with an integrable transmission channel (the NLSE in the case considered). Although such a transmission method is inherently free from nonlinear impairments, the noisy signal corruptions, arising due to the ampli¯er spontaneous emission, inevitably degrade the optical system performance. We study properties of the noise-corrupted channel model in the nonlinear spectral domain attributed to NLSE. We derive the general stochastic equations governing the signal evolution inside the nonlinear spectral domain and elucidate the properties of the emerging nonlinear spectral noise using well-established methods of perturbation theory based on inverse scattering transform [8]. It is shown that in the presence of small noise the communication channel in the nonlinear domain is the additive Gaussian channel with memory and signal-dependent correlation matrix. We demonstrate that the effective spectral noise acquires colouring", its autocorrelation function becomes slow decaying and non-diagonal as a function of \frequencies", and the noise loses its circular symmetry, becoming elliptically polarized. Then we derive a low bound for the spectral effiency for such a channel. Our main result is that by using the nonlinear spectral techniques one can significantly increase the achievable spectral effiency compared to the currently available methods [9]. REFERENCES 1. Zakharov, V. E. and A. B. Shabat, Sov. Phys. JETP, Vol. 34, 62{69, 1972. 2. Hasegawa, A. and T. Nyu, J. Lightwave Technol., Vol. 11, 395{399, 1993. 3. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4312{4328, 2014. 4. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4329{4345 2014. 5. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4346{4369, 2014. 6. Prilepsky, J. E., S. A. Derevyanko, K. J. Blow, I. Gabitov, and S. K. Turitsyn, Phys. Rev. Lett., Vol. 113, 013901, 2014. 7. Le, S. T., J. E. Prilepsky, and S. K. Turitsyn, Opt. Express, Vol. 22, 26720{26741, 2014. 8. Kaup, D. J. and A. C. Newell, Proc. R. Soc. Lond. A, Vol. 361, 413{446, 1978. 9. Essiambre, R.-J., G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, J. Lightwave Technol., Vol. 28, 662{701, 2010.

Nonlinear refraction in optical lattices induced by the wave-soliton interference

In the framework of 1D Nonlinear Shrödinger Equation (NSE) we demonstrate how one can control the refractive angle of a fundamental soliton beam passing through an optical lattice, by adjusting either the shape of an individual waveguide or the relative positions of waveguides. Even for a single scatterer its shape has a nontrivial effect on the refraction direction. In the case of shallow modulation we provide an analytical description based of the effect on the soliton perturbation theory. When one considers a lattice of scatterers, there emanates an additional form factor in the radiation density (RD) of emitted waves referring to the wave-soliton beating and interference inside the lattice. We concentrate on the results for two cases: periodic lattice and disordered lattice of scattering shapes. © 2011 IEEE.

Nonlinear quantum transport in low-dimensional electronic devices

The study of transport processes in low-dimensional semiconductors requires a rigorous quantum mechanical treatment. However, a full-fledged quantum transport theory of electrons (or holes) in semiconductors of small scale, applicable in the presence of external fields of arbitrary strength, is still not available. In the literature, different approaches have been proposed, including: (a) the semiclassical Boltzmann equation, (b) perturbation theory based on Keldysh's Green functions, and (c) the Quantum Boltzmann Equation (QBE), previously derived by Van Vliet and coworkers, applicable in the realm of Kubo's Linear Response Theory (LRT). ^ In the present work, we follow the method originally proposed by Van Wet in LRT. The Hamiltonian in this approach is of the form: H = H 0(E, B) + λV, where H0 contains the externally applied fields, and λV includes many-body interactions. This Hamiltonian differs from the LRT Hamiltonian, H = H0 - AF(t) + λV, which contains the external field in the field-response part, -AF(t). For the nonlinear problem, the eigenfunctions of the system Hamiltonian, H0(E, B), include the external fields without any limitation on strength. ^ In Part A of this dissertation, both the diagonal and nondiagonal Master equations are obtained after applying projection operators to the von Neumann equation for the density operator in the interaction picture, and taking the Van Hove limit, (λ → 0, t → ∞, so that (λ2 t)n remains finite). Similarly, the many-body current operator J is obtained from the Heisenberg equation of motion. ^ In Part B, the Quantum Boltzmann Equation is obtained in the occupation-number representation for an electron gas, interacting with phonons or impurities. On the one-body level, the current operator obtained in Part A leads to the Generalized Calecki current for electric and magnetic fields of arbitrary strength. Furthermore, in this part, the LRT results for the current and conductance are recovered in the limit of small electric fields. ^ In Part C, we apply the above results to the study of both linear and nonlinear longitudinal magneto-conductance in quasi one-dimensional quantum wires (1D QW). We have thus been able to quantitatively explain the experimental results, recently published by C. Brick, et al., on these novel frontier-type devices. ^

Nonlinear quantum transport in low-dimensional electronic devices

The study of transport processes in low-dimensional semiconductors requires a rigorous quantum mechanical treatment. However, a full-fledged quantum transport theory of electrons (or holes) in semiconductors of small scale, applicable in the presence of external fields of arbitrary strength, is still not available. In the literature, different approaches have been proposed, including: (a) the semiclassical Boltzmann equation, (b) perturbation theory based on Keldysh's Green functions, and (c) the Quantum Boltzmann Equation (QBE), previously derived by Van Vliet and coworkers, applicable in the realm of Kubo's Linear Response Theory (LRT). In the present work, we follow the method originally proposed by Van Vliet in LRT. The Hamiltonian in this approach is of the form: H = H°(E, B) + λV, where H0 contains the externally applied fields, and λV includes many-body interactions. This Hamiltonian differs from the LRT Hamiltonian, H = H° - AF(t) + λV, which contains the external field in the field-response part, -AF(t). For the nonlinear problem, the eigenfunctions of the system Hamiltonian, H°(E, B) , include the external fields without any limitation on strength. In Part A of this dissertation, both the diagonal and nondiagonal Master equations are obtained after applying projection operators to the von Neumann equation for the density operator in the interaction picture, and taking the Van Hove limit, (λ → 0 , t → ∞ , so that (λ2 t)n remains finite). Similarly, the many-body current operator J is obtained from the Heisenberg equation of motion. In Part B, the Quantum Boltzmann Equation is obtained in the occupation-number representation for an electron gas, interacting with phonons or impurities. On the one-body level, the current operator obtained in Part A leads to the Generalized Calecki current for electric and magnetic fields of arbitrary strength. Furthermore, in this part, the LRT results for the current and conductance are recovered in the limit of small electric fields. In Part C, we apply the above results to the study of both linear and nonlinear longitudinal magneto-conductance in quasi one-dimensional quantum wires (1D QW). We have thus been able to quantitatively explain the experimental results, recently published by C. Brick, et al., on these novel frontier-type devices.

A new SOS-DFPT approximation for NMR shielding calculations : the Loc.3 correction applied to the catalytic mechanism of Serine Proteases

Thèse numérisée par la Direction des bibliothèques de l'Université de Montréal.

First-principles calculation of carrier-phonon scattering in n-type Si1−xGex alloys

First-principles electronic structure methods are used to find the rates of inelastic intravalley and intervalley n-type carrier scattering in Si1-xGex alloys. Scattering parameters for all relevant Delta and L intra- and intervalley scattering are calculated. The short-wavelength acoustic and the optical phonon modes in the alloy are computed using the random mass approximation, with interatomic forces calculated in the virtual crystal approximation using density functional perturbation theory. Optical phonon and intervalley scattering matrix elements are calculated from these modes of the disordered alloy. It is found that alloy disorder has only a small effect on the overall inelastic intervalley scattering rate at room temperature. Intravalley acoustic scattering rates are calculated within the deformation potential approximation. The acoustic deformation potentials are found directly and the range of validity of the deformation potential approximation verified in long-wavelength frozen phonon calculations. Details of the calculation of elastic alloy scattering rates presented in an earlier paper are also given. Elastic alloy disorder scattering is found to dominate over inelastic scattering, except for almost pure silicon (x approximate to 0) or almost pure germanium (x approximate to 1), where acoustic phonon scattering is predominant. The n-type carrier mobility, calculated from the total (elastic plus inelastic) scattering rate, using the Boltzmann transport equation in the relaxation time approximation, is in excellent agreement with experiments on bulk, unstrained alloys..

A new SOS-DFPT approximation for NMR shielding calculations : the Loc.3 correction applied to the catalytic mechanism of Serine Proteases

Thèse numérisée par la Direction des bibliothèques de l'Université de Montréal.

Effect of dipole polarizability on positron binding by strongly polar molecules

A model for positron binding to polar molecules is considered by combining the dipole potential outside the molecule with a strongly repulsive core of a given radius. Using existing experimental data on binding energies leads to unphysically small core radii for all of the molecules studied. This suggests that electron–positron correlations neglected in the simple model play a large role in determining the binding energy. We account for these by including the polarization potential via perturbation theory and non-perturbatively. The perturbative model makes reliable predictions of binding energies for a range of polar organic molecules and hydrogen cyanide. The model also agrees with the linear dependence of the binding energies on the polarizability inferred from the experimental data (Danielson et al 2009 J. Phys. B: At. Mol. Opt. Phys. 42 235203). The effective core radii, however, remain unphysically small for most molecules. Treating molecular polarization non-perturbatively leads to physically meaningful core radii for all of the molecules studied and enables even more accurate predictions of binding energies to be made for nearly all of the molecules considered.

Estudo do comportamento biomecânico de aneurismas cerebrais

Os aneurismas cerebrais são dilatações patológicas das artérias cerebrais e são conhecidos como um dos eventos cerebrovasculares mais comuns e graves. A maioria dos aneurismas cerebrais não provocam sintomas até que se tornem grandes, começando a vazar sangue ou a romperem-se. O principal objetivo deste trabalho é a caracterização do comportamento biomecânico de aneurismas, tendo em consideração diferentes parâmetros geométricos e fisiológicos, de forma a analisar o comportamento da parede de um vaso sanguíneo aquando a formação de um aneurisma. O estudo numérico foi efetuado considerando diferentes modelos constitutivos híper-elásticos, que é o caso dos vasos sanguíneos, com intuito de verificar qual o que melhor se adequa a este tipo de estudos e de analisar e calcular os deslocamentos e as deformações ocorridas no aneurisma cerebral. Os diferentes modelos constitutivos foram aproximados por uma curva de tensão/deformação que contém valores experimentais de um ensaio de tração até à rutura de uma mucosa vaginal. Foram utilizados dois módulos do software Ansys®, sendo estes o Fluent e o Static Structural. O primeiro utilizou-se determinar a pressão exercida pelo fluido na parede interior do canal, sendo este resultado exportado para o Static Structural, permitindo assim fazer o estudo estrutural do canal com aneurisma. Concluiu-se que a nível qualitativo, qualquer modelo constitutivo estudado pode ser utilizado, pois todos mostram o mesmo tipo de distribuição de deslocamentos e deformações. No entanto, os modelos mais fiáveis a nível quantitativo é o modelo de Mooney-Rivlin 5 Parameter e o Polynomial 2nd Order, pois apresentam os mesmos resultados.

Equivalence of quantum field theories related by the θ-exact Seiberg-Witten map

The equivalence of the noncommutative U(N) quantum field theories related by the θ-exact Seiberg-Witten maps is, in this paper, proven to all orders in the perturbation theory with respect to the coupling constant. We show that this holds for super Yang-Mills theories with N=0, 1, 2, 4 supersymmetry. A direct check of this equivalence relation is performed by computing the one-loop quantum corrections to the quadratic part of the effective action in the noncommutative U(1) gauge theory with N=0, 1, 2, 4 supersymmetry.