Over the last twenty years quantum field theory has become not only the framework for the discussion of all fundamental interactions except gravity, but also for the understanding of second-order phase transitions in statistical mechanics. This advanced text is based on graduate courses and summer schools given by the author over a number of years. It approaches the subject in terms of path and functional intergrals, adopting a Euclidean metric and using the language of partition and correlation functions. Renormalization and the renormalization group are examined, as are critical phenomena and the role of instantons. Changes for this edition 1. Extensive revision to eliminate a few bugs that had survived the second edition and (mainly) to improve the pedagogical presentation, as a result of experience gathered by lecturing. 2. Additional new topics; holomorphic or coherent state path integral; functional integral and representation of the field theory S-matrix in the holomorphic formalis; non-relativistic limit of massive quantization and brief discussion of non-renormalization of quantum gravity based on Info rmat io n Discussio n (0 ) Files Ho ldings Search Submit Help CERN Document Server

Quantum Field Theory And Critical Phenomena

Solitons, Introduction to.

In this article, we have presented an innovative formulation of nonlinear element of block cipher. The suggested construction is chaos based, where we used a Duffing chaotic system. We have investigated various characteristics of our proposed nonlinear component. The outcomes of the investigation validate that the designed cryptosystem is consistent for secure communication.

A construction of novel chaos base nonlinear component of block cipher

In this article, we present a brief overview of some of the recent progress made in identifying and generating finite dimensional integrable nonlinear dynamical systems, exhibiting interesting oscillatory and other solution properties, including quantum aspects. Particularly we concentrate on Lienard type nonlinear oscillators and their generalizations and coupled versions. Specific systems include Mathews-Lakshmanan oscillators, modified Emden equations, isochronous oscillators and generalizations. Nonstandard Lagrangian and Hamiltonian formulations of some of these systems are also briefly touched upon. Nonlocal transformations and linearization aspects are also discussed.

Generating finite dimensional integrable nonlinear dynamical systems

The classical and quantum-mechanical correspondence for constant mass settings is used, along with some point canonical transformation, to find the position-dependent mass (PDM) classical and quantum Hamiltonians. The comparison between the resulting quantum PDM-Hamiltonian and the von Roos PDM-Hamiltonian implied that the ordering ambiguity parameters of von Roos are strictly determined. Eliminating, in effect, the ordering ambiguity associated with the von Roos PDM-Hamiltonian. This, consequently, played a vital role in the construction and identification of the PDM-momentum operator. The same recipe is followed to identify the form of the minimal coupling of electromagnetic interactions for the classical and quantum PDM-Hamiltonians. It turned out that whilst the minimal coupling may very well inherit the usual form in classical mechanics (i.e., $p_{j} (\vec{x}) \rightarrow p_{j}(\vec{x}) -e A_{j}(\vec{x})$
 , where $p_{j}(\vec{x})$
 is the j-th component of the classical PDM-canonical-momentum), it admits a necessarily different and vital form in quantum mechanics (i.e., $\hat{p}_{j}(\vec{x})/\sqrt{m(\vec{x})} \rightarrow (\hat{p}_{j}(\vec{x})$
 $ -e A_{j}(\vec{x}))/\sqrt{m(\vec{x})}$
 , where $ \hat{p}_{j}(\vec{x})$
 is the j-th component of the quantum PDM-momentum operator). Under our point transformation settings, only one of the two commonly used vector potentials (i.e., $\vec{A} (\vec{x}) \sim (-x_{2}, x_{1}, 0)$
 ) is found eligible and is considered for our Illustrative examples.

Position-dependent mass momentum operator and minimal coupling: point canonical transformation and isospectrality

We examine some nontrivial consequences that emerge from interpreting a position-dependent mass (PDM)-driven Duffing oscillator in the presence of a quartic potential. The propagation dynamics is numerically studied and the sensitivity to the PDM-index is noted. Remarkable transitions from a limit cycle to chaos through period doubling and from a chaotic to a regular motion through intermediate periodic and chaotic routes are demonstrated.

http://iopscience.iop.org/article/10.1088/1751-8113/46/3/032001/pdf

Nonlinear dynamics of a position-dependent mass-driven Duffing-type oscillator

We examine some nontrivial consequences that emerge from interpreting a position-dependent mass (PDM) driven Duffing oscillator in the presence of a quartic potential. The propagation dynamics is studied numerically and sensi- tivity to the PDM-index is noted. Remarkable transitions from a limit cycle to chaos through period doubling and from a chaotic to a regular motion through intermediate periodic and chaotic routes are demonstrated.

Nonlinear Dynamics of a position-dependent mass driven Duffing-type oscillator

In this work, an extended elliptic function method is proposed and applied to the generalized shallow water wave equation. We systematically investigate on how to classify new exact travelling wave solutions expressible in terms of quasi-periodic elliptic integral functions and doubly periodic Jacobian elliptic functions. The derived new solutions include rational, periodic, singular and solitary wave solutions. An interesting comparison with the canonical procedure is provided. In some cases the obtained elliptic solution has singularity at a certain region in the whole space. For such solutions we have computed the effective region where the obtained solution is free from such a singularity.

https://iopscience.iop.org/article/10.1088/0031-8949/82/02/025003/pdf

New exact solutions of a generalized shallow water wave equation

Effect of CeO2 on the sintering behaviour of zirconia–alumina composite

In response to the comment of Mustafa (2013 J. Phys. A: Math. Theor. 46 368001) we justify our stand of considering an extended Lagrange equation involving a non-conservative force term when the particle mass varies with position. As has been known for some time, such an extended form not only takes into account the principle of virtual work applied to D’Alembert’s principle but yields precisely the form of Newton’s equation expected for a particle possessing a position-dependent mass.

Supratim Das

Papers

Nonlinear dynamics of a position-dependent mass-driven Duffing-type oscillator

Nonlinear Dynamics of a position-dependent mass driven Duffing-type oscillator

New exact solutions of a generalized shallow water wave equation

Effect of CeO2 on the sintering behaviour of zirconia–alumina composite

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