This book discusses the properties of quantized vortex lines in superfluid helium-4 in the light of research on vortices in modern fluid mechanics, and gives the first comprehensive treatment of the problem. The author begins with a review of the knowledge of classical fluid dynamics which is relevant to the main topics of the book. This is followed by a presentation of basic material on helium II and quantized vortices. The following chapters deal with various different aspects of the subject, and the book concludes with substantial introductions to two currently active topics, namely superfluid turbulence and the nucleation of quantized vortices. Both quantum tunnelling and thermal activation nucleation processes are also discussed, including the Kosterlitz-Thouless transition in thin films. The author's comprehensive approach will make this book invaluable for students taking advanced undergraduate or graduate courses, and for all those involved in research on classical and quantum vortices.

This volume gives an up-to-date, systematic account of the microscopic theory of Bose-condensed fluids developed since the late 1950s. In contrast to the usual phenomenological discussions of superfluid 4He, the present treatment is built on the pivotal role of the Bose broken symmetry and a Bose condensate. The many-body formalism is developed, with emphasis on the one- and two-particle Green's functions and their relation to the density response function. These are all coupled together by the Bose broken symmetry, which provides the basis for understanding the elementary excitations and response functions in the hydrodynamic and collisionless regions. It also explains the difference between excitations in the superfluid and normal phases. Chapter 4 gives the first critical assessment of the experimental evidence for a Bose condensate in liquid 4He, based on high-momentum neutron scattering data.

Nature is inherently noisy and nonlinear. It is noisy in the sense that all macroscopic systems are subject to the fluctuations of their environments and also to internal fluctuations. It is nonlinear in the sense that the restoring force on a system displaced from equilibrium does not usually vary linearly with the size of the displacement. To calculate the properties of stochastic (noisy) nonlinear systems is in general extremely difficult, although considerable progress has been made in the past. The three volumes that make up Noise in Nonlinear Dynamical Systems comprise a collection of specially written authoritative reviews on all aspects of the subject, representative of all the major practitioners in the field. The first volume deals with the basic theory of stochastic nonlinear systems. It includes an historical overview of the origins of the field, chapters covering some developed theoretical techniques for the study of coloured noise, and the first English-language translation of the landmark 1933 paper by Pontriagin, Andronov and Vitt.

Nature is inherently noisy and nonlinear. It is noisy in the sense that all macroscopic systems are subject to the fluctuations of their environments and also to internal fluctuations. It is nonlinear in the sense that the restoring force on a system displaced from equilibrium does not usually vary linearly with the size of the displacement. To calculate the properties of stochastic (noisy) nonlinear systems is in general extremely difficult, although considerable progress has been made in the past. The three volumes that make up Noise in Nonlinear Dynamical Systems comprise a collection of specially written authoritative reviews on all aspects of the subject, representative of all the major practitioners in the field. The second volume applies the theory of Volume 1 to the calculation of the influence of noise in a variety of contexts. These include quantum mechanics, condensed matter, noise induced transitions, escape processes and transition probabilities, systems with periodic potentials, discrete nonlinear systems, symmetry-breaking transition, and optics.

Nature is inherently noisy and nonlinear. It is noisy in the sense that all macroscopic systems are subject to the fluctuations of their environments and also to internal fluctuations. It is nonlinear in the sense that the restoring force on a system displaced from equilibrium does not usually vary linearly with the size of the displacement. To calculate the properties of stochastic (noisy) nonlinear systems is in general extremely difficult, although considerable progress has been made in the past. The three volumes that make up Noise in Nonlinear Dynamical Systems comprise a collection of specially written authoritative reviews on all aspects of the subject, representative of all the major practitioners in the field. The third volume deals with experimental aspects of the study of noise in nonlinear dynamical systems. It covers noise-driven phenomena in superfluid helium, liquid crystals, lasers and optical bistability as well as the solution of stochastic equations by digital simulation and analogue experiment.

This book discusses the properties of quantized vortex lines in superfluid helium-4 in the light of research on vortices in modern fluid mechanics, and gives the first comprehensive treatment of the problem. The author begins with a review of the knowledge of classical fluid dynamics which is relevant to the main topics of the book. This is followed by a presentation of basic material on helium II and quantized vortices. The following chapters deal with various different aspects of the subject, and the book concludes with substantial introductions to two currently active topics, namely superfluid turbulence and the nucleation of quantized vortices. Both quantum tunnelling and thermal activation nucleation processes are also discussed, including the Kosterlitz-Thouless transition in thin films. The author's comprehensive approach will make this book invaluable for students taking advanced undergraduate or graduate courses, and for all those involved in research on classical and quantum vortices.

This volume gives an up-to-date, systematic account of the microscopic theory of Bose-condensed fluids developed since the late 1950s. In contrast to the usual phenomenological discussions of superfluid 4He, the present treatment is built on the pivotal role of the Bose broken symmetry and a Bose condensate. The many-body formalism is developed, with emphasis on the one- and two-particle Green's functions and their relation to the density response function. These are all coupled together by the Bose broken symmetry, which provides the basis for understanding the elementary excitations and response functions in the hydrodynamic and collisionless regions. It also explains the difference between excitations in the superfluid and normal phases. Chapter 4 gives the first critical assessment of the experimental evidence for a Bose condensate in liquid 4He, based on high-momentum neutron scattering data.

Nature is inherently noisy and nonlinear. It is noisy in the sense that all macroscopic systems are subject to the fluctuations of their environments and also to internal fluctuations. It is nonlinear in the sense that the restoring force on a system displaced from equilibrium does not usually vary linearly with the size of the displacement. To calculate the properties of stochastic (noisy) nonlinear systems is in general extremely difficult, although considerable progress has been made in the past. The three volumes that make up Noise in Nonlinear Dynamical Systems comprise a collection of specially written authoritative reviews on all aspects of the subject, representative of all the major practitioners in the field. The first volume deals with the basic theory of stochastic nonlinear systems. It includes an historical overview of the origins of the field, chapters covering some developed theoretical techniques for the study of coloured noise, and the first English-language translation of the landmark 1933 paper by Pontriagin, Andronov and Vitt.

Nature is inherently noisy and nonlinear. It is noisy in the sense that all macroscopic systems are subject to the fluctuations of their environments and also to internal fluctuations. It is nonlinear in the sense that the restoring force on a system displaced from equilibrium does not usually vary linearly with the size of the displacement. To calculate the properties of stochastic (noisy) nonlinear systems is in general extremely difficult, although considerable progress has been made in the past. The three volumes that make up Noise in Nonlinear Dynamical Systems comprise a collection of specially written authoritative reviews on all aspects of the subject, representative of all the major practitioners in the field. The second volume applies the theory of Volume 1 to the calculation of the influence of noise in a variety of contexts. These include quantum mechanics, condensed matter, noise induced transitions, escape processes and transition probabilities, systems with periodic potentials, discrete nonlinear systems, symmetry-breaking transition, and optics.

Nature is inherently noisy and nonlinear. It is noisy in the sense that all macroscopic systems are subject to the fluctuations of their environments and also to internal fluctuations. It is nonlinear in the sense that the restoring force on a system displaced from equilibrium does not usually vary linearly with the size of the displacement. To calculate the properties of stochastic (noisy) nonlinear systems is in general extremely difficult, although considerable progress has been made in the past. The three volumes that make up Noise in Nonlinear Dynamical Systems comprise a collection of specially written authoritative reviews on all aspects of the subject, representative of all the major practitioners in the field. The third volume deals with experimental aspects of the study of noise in nonlinear dynamical systems. It covers noise-driven phenomena in superfluid helium, liquid crystals, lasers and optical bistability as well as the solution of stochastic equations by digital simulation and analogue experiment.