Statistisk fysik

This book provides a captivating journey through the realms of classical and quantum systems as it unravels the profound influence that noise may have on their static and dynamic properties. The first part of the book offers succinct yet enlightening discussions on foundational topics related to noise. The second part focuses on a variety of applications, where a diverse spectrum of noise effects in physical systems comes to life, meticulously presented and thoughtfully analyzed. Whether you are a curious student or a dedicated researcher, this book is your key to gaining invaluable insights into noise effects in physical systems. ¿The book has the merit of presenting several topics scattered in the literature and could become a very useful reference.¿ Giovanni Jona-Lasinio, Sapienza ¿ Università di Roma, Italy

This thesis makes significant advances in the use of microspheres in optical traps as highly precise sensing platforms. While optically trapped microspheres have recently proven their dominance in aqueous and vacuum environments, achieving state-of-the-art measurements of miniscule forces and torques, their sensitivity to perturbations in air has remained relatively unexplored. This thesis shows that, by uniquely operating in air and measuring its thermally-fluctuating instantaneous velocity, an optically trapped microsphere is an ultra-sensitive probe of both mass and sound. The mass of the microsphere is determined with similar accuracy to competitive methods but in a fraction of the measurement time and all while maintaining thermal equilibrium, unlike alternative methods. As an acoustic transducer, the air-based microsphere is uniquely sensitive to the velocity of sound, as opposed to the pressure measured by a traditional microphone. By comparison to state-of-the-art commercially-available velocity and pressure sensors, including the world¿s smallest measurement microphone, the microsphere sensing modality is shown to be both accurate and to have superior sensitivity at high frequencies. Applications for such high-frequency acoustic sensing include dosage monitoring in proton therapy for cancer and event discrimination in bubble chamber searches for dark matter. In addition to reporting these scientific results, the thesis is pedagogically organized to present the relevant history, theory, and technology in a straightforward way.

This book addresses research challenges in the rapidly developing area of nonequilibrium thermodynamics and fluctuation kinetics. This cross-disciplinary field comprises various topics, ranging from fundamental problems of nonequilibrium statistical mechanics and thermodynamics to multiple applications in plasma, fluid mechanics, nonlinear science, systems of dissipative particles, and high-Q resonators. The purpose of this book is to bring together world-leading experts in the above fields to initiate a cross-fertilization among these active research areas. The book is dedicated to and honours the memory of Professor Slava Belyi who passed away unexpectedly on May 20, 2020. He was pioneering the theory of nonequilibrium fluctuations, in particular the application of the Callen-Welton fluctuation-dissipation theorem to nonequilibrium systems and its generalization. This and related problems also feature in the book.

This book covers recent developments in the understanding, quantification, and exploitation of entanglement in spin chain models from both condensed matter and quantum information perspectives. Spin chain models are at the foundation of condensed matter physics and quantum information technologies and elucidate many fundamental phenomena such as information scrambling, quantum phase transitions, and many-body localization. Moreover, many quantum materials and emerging quantum devices are well described by spin chains. Comprising accessible, self-contained chapters written by leading researchers, this book is essential reading for graduate students and researchers in quantum materials and quantum information.  The coverage is comprehensive, from the fundamental entanglement aspects of quantum criticality, non-equilibrium dynamics, classical and quantum simulation of spin chains through to their experimental realizations, and beyond into machine learning applications.

This book offers the reader a journey through the counterintuitive nature of Brownian motion under confinement. Diffusion is a universal phenomenon that controls a wide range of physical, chemical, and biological processes. The transport of spatially-constrained molecules and small particles is ubiquitous in nature and technology and plays an essential role in different processes. Understanding the physics of diffusion under conditions of confinement is essential for a number of biological phenomena and potential technological applications in micro- and nanofluidics, among others. Studies on diffusion under confinement are typically difficult to understand for young scientists and students because of the extensive background on diffusion processes, physics, and mathematics that is required. All of this information is provided in this book, which is essentially self-contained as a result of the authors¿ efforts to make it accessible to an audience of students from avariety of different backgrounds. The book also provides the necessary mathematical details so students can follow the technical process required to solve each problem. Readers will also find detailed explanations of the main results based on the last 30 years of research devoted to studying diffusion under confinement. The authors approach the physical problem from various angles and discuss the role of geometries and boundary conditions in diffusion. This textbook serves as a comprehensive and modern overview of Brownian motion under confinement and is intended for young scientists, graduate students, and advanced undergraduates in physics, physical chemistry, biology, chemistry, chemical engineering, biochemistry, bioengineering, and polymer and material sciences.

This second edition of Dynamics, Information and Complexity in Quantum Systems widens its scope by focussing more on the dynamics of quantum correlations and information in microscopic and mesoscopic systems, and their use for metrological and machine learning purposes. The book is divided into three parts:Part One: Classical Dynamical SystemsAddresses classical dynamical systems, classical dynamical entropy, and classical algorithmic complexity.Includes a survey of the theory of simple perceptrons and their storage capacity.Part Two: Quantum Dynamical SystemsFocuses on the dynamics of entanglement under dissipative dynamics and its metrological use in finite level quantum systems.Discusses the quantum fluctuation approach to large-scale mesoscopic systems and their emergent dynamics in quantum systems with infinitely many degrees of freedom.Introduces a model ofquantum perceptron whose storage capacity is computed and compared with the classical one.Part Three: Quantum Dynamical Entropies and ComplexitiesDevoted to quantum dynamical entropies and algorithmic complexities.This book is meant for advanced students, young and senior researchers working in the fields of quantum statistical mechanics, quantum information, and quantum dynamical systems. It is self-contained, and the only prerequisites needed are a standard knowledge of statistical mechanics, quantum mechanics, and linear operators on Hilbert spaces.

Community detection is one of the most important methodological fields of network science, and one which has attracted a significant amount of attention over the past decades. This area deals with the automated division of a network into fundamental building blocks, with the objective of providing a summary of its large-scale structure. Despite its importance and widespread adoption, there is a noticeable gap between what is arguably the state-of-the-art and the methods which are actually used in practice in a variety of fields. The Elements attempts to address this discrepancy by dividing existing methods according to whether they have a 'descriptive' or an 'inferential' goal. While descriptive methods find patterns in networks based on context-dependent notions of community structure, inferential methods articulate a precise generative model, and attempt to fit it to data. In this way, they are able to provide insights into formation mechanisms and separate structure from noise. This title is also available as open access on Cambridge Core.

This book offers an interdisciplinary theoretical approach based on non-equilibrium statistical thermodynamics and control theory for mathematically modeling shock-induced out-of-equilibrium processes in condensed matter. The book comprises two parts. The first half of the book establishes the theoretical approach, reviewing fundamentals of non-equilibrium statistical thermodynamics and control theory of adaptive systems. The latter half applies the presented approach to a problem on shock-induced plane wave propagation in condensed matter. The result successfully reproduces the observed feature of waveform propagation in experiments, which conventional continuous mechanics cannot access. Further, the consequent stress-strain relationships derived with relaxation and inertia effect in elastic-plastic transition determines material properties in transient regimes.

Von der Physik bis zur Informationstheorie und Kosmologie, von der Struktur tierischer Gesellschaften bis zur linguistischen Analyse der menschlichen Schrift zeigen Systeme, die aus vielen interagierenden Bestandteilen bestehen, oft ein kollektives Verhalten, das sich nicht aus der Interaktion der einzelnen Bestandteile vorhersagen lässt. In Mehr als die Summe der Teile befasst sich Helmut Satz mit verschiedenen Formen dieses komplexen Verhaltens, die erst in den letzten Jahrzehnten gründlich untersucht worden sind. Obwohl diese Studien ihren Ursprung in der Physik haben, erweist sich das Verhalten als universell und reicht von der Struktur des frühen Universums über die Bildung von Vogelschwärmen bis hin zur Häufigkeit von Wörtern in literarischen Texten. Die Komplexität wird somit zu einem immer wichtigeren interdisziplinären Bereich für die künftige wissenschaftliche Forschung.Auf konzeptionelle und nicht-technische Weise erschließt Satz dieses spannende Gebiet für eine allgemeine Leserschaft und für Studierende aller naturwissenschaftlichen Fächer.

This brief book introduces the Poisson-Boltzmann equation in three chapters that build upon one another, offering a systematic entry to advanced students and researchers. Chapter one formulates the equation and develops the linearized version of Debye-Hückel theory as well as exact solutions to the nonlinear equation in simple geometries and generalizations to higher-order equations. Chapter two introduces the statistical physics approach to the Poisson-Boltzmann equation. It allows the treatment of fluctuation effects, treated in the loop expansion, and in a variational approach. First applications are treated in detail: the problem of the surface tension under the addition of salt, a classic problem discussed by Onsager and Samaras in the 1930s, which is developed in modern terms within the loop expansion, and the adsorption of a charged polymer on a like-charged surface within the variational approach. Chapter three finally discusses the extension of Poisson-Boltzmann theory to explicit solvent. This is done in two ways: on the phenomenological level of nonlocal electrostatics and with a statistical physics model that treats the solvent molecules as molecular dipoles. This model is then treated in the mean-field approximation and with the variational method introduced in Chapter two, rounding up the development of the mathematical approaches of Poisson-Boltzmann theory. After studying this book, a graduate student will be able to access the research literature on the Poisson-Boltzmann equation with a solid background.

It is generally believed that collisions of particles reduce the self-diffusion coefficient. In this book, Erik Kalz shows that in classical systems under the effect of Lorentz force, which are characterized by diffusion tensors with antisymmetric elements, collisions surprisingly can enhance self-diffusion. In these systems, due to an inherent curving effect, the motion of particles is facilitated, instead of hindered by collisions. Consistent with this the author finds that the collective diffusion remains unaffected. Using a geometric model, he theoretically predicts a magnetic field governed crossover from a reduced to an enhanced self-diffusion. The physical interpretation is quantitatively supported by the force autocorrelation function, which turns negative with increasing the magnetic field. Using Brownian-dynamics simulations, he validates the predictions.

This textbook presents the fundamental concepts and theories in thermal physics and elementary statistical mechanics in a very simple, systematic and comprehensive way. This book is written in a way that it presents the topics in a holistic manner with end-of-chapter exercises and examples where concepts are supported by numerous solved examples and multiple-choice questions to aid self-learning. The textbook also contains illustrated diagrams for better understanding of the concepts. The book will benefit students who are taking introductory courses in thermal physics, thermodynamics and statistical mechanics.

The importance of thermodynamics, particularly its Second Principle, to all branches of science in which systems with very large numbers of particles are involved cannot be overstated. This book offers a panoramic view of non-equilibrium thermodynamics. Perhaps the two most attractive aspects of thermodynamic equilibrium are its stability and its independence from the specifics of the particular system involved. Does an equivalent exist for non-equilibrium thermodynamics? Many researchers have tried to describe such stability in the same way that the Second Principle describes the stability of thermodynamic equilibrium - and failed. Most of them invoked either entropy, or its production rate, or some modified version of it. In their efforts, however, those researchers have found a lot of useful stability criteria for far-from-equilibrium states. These criteria usually take the form of variational principles, in terms of the minimization or maximization of some quantity. The aim of this book is to discuss these variational principles by highlighting the role of macroscopic quantities. This book is aimed at a wider audience than those most often exposed to the criteria described, i.e., undergraduates in STEM, as well as the usual interested and invested professionals. 

The book discusses a class of discrete time stochastic growth processes for which the growth rate is proportional to the exponential of a Gaussian Markov process. These growth processes appear naturally in problems of mathematical finance as discrete time approximations of stochastic volatility models and stochastic interest rates models such as the Black-Derman-Toy and Black-Karasinski models. These processes can be mapped to interacting one-dimensional lattice gases with long-range interactions. The book gives a detailed discussion of these statistical mechanics models, including new results not available in the literature, and their implication for the stochastic growth models. The statistical mechanics analogy is used to understand observed non-analytic dependence of the Lyapunov exponents of the stochastic growth processes considered, which is related to phase transitions in the lattice gas system. The theoretical results are applied to simulations of financial models and are illustrated with Mathematica code. The book includes a general introduction to exponential stochastic growth with examples from biology, population dynamics and finance. The presentation does not assume knowledge of mathematical finance. The new results on lattice gases can be read independently of the rest of the book. The book should be useful to practitioners and academics studying the simulation and application of stochastic growth models.

This book deals with certain important problems in Classical and Quantum Information Theory and will be very helpful for students of Undergraduate and Postgraduate Courses in Electronics, Communication and Signal Processing.

The first monograph to treat topological, group-theoretic, and geometric problems of ideal hydrodynamics and magnetohydrodynamics from a unified point of view. It describes the necessary preliminary notions both in hydrodynamics and pure mathematics with numerous examples and figures. The book is accessible to graduates as well as pure and applied mathematicians working in hydrodynamics, Lie groups, dynamical systems, and differential geometry.

This is the first monograph devoted to investigation of the most complex physical processes of soft systems, including a wide class of solutions. It blends modern theoretical understanding and experimental results, proposing new methods and models for the description of several soft systems.

The aim of this book is to provide the fundamentals of statistical physics and its application to condensed matter.