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26203 results in Theoretical Physics and Mathematical Physics

Page 44 of 1311

Theory of Liquids
  • From Excitations to Thermodynamics
  • Kostya Trachenko
  • Published online:
    01 September 2023
    Print publication:
    17 August 2023
  • Of the three basic states of matter, liquid is perhaps the most complex. While its flow properties are described by fluid mechanics, its thermodynamic properties are often neglected, and for many years it was widely believed that a general theory of liquid thermodynamics was unattainable. In recent decades that view has been challenged, as new advances have finally enabled us to understand and describe the thermodynamic properties of liquids. This book explains the recent developments in theory, experiment and modelling that have enabled us to understand the behaviour of excitations in liquids and the impact of this behaviour on heat capacity and other basic properties. Presented in plain language with a focus on real liquids and their experimental properties, this book is a useful reference text for researchers and graduate students in condensed matter physics and chemistry as well as for advanced courses covering the theory of liquids.

Fundamentals of Particle Physics
  • Understanding the Standard Model
  • Pascal Paganini
  • Published online:
    31 August 2023
    Print publication:
    14 September 2023
  • This text is a modern introduction to the Standard Model of particle physics for graduate students and advanced undergraduate students. Assuming only prior knowledge of special relativity and non-relativistic quantum mechanics, it presents all aspects of the field, including step-by-step explanations of the theory and the most recent experimental results. Taking a pedagogical, first-principles approach, it demonstrates the essential tools for students to process and analyse experimental particle physics data for themselves. While relatively short compared to other texts, it provides enough material to be covered comfortably in a two-semester course. Some of the more technical details are given in optional supplementary boxes, while problems are provided at the end of each chapter. Written as a bridge between basic descriptive books and purely theoretical works, this text offers instructors ample flexibility to meet the needs of their courses.

Condensed Matter Field Theory
  • 3rd edition
  • Alexander Altland, Ben Simons
  • Published online:
    24 August 2023
    Print publication:
    14 September 2023
  • The methods of quantum field theory underpin many conceptual advances in contemporary condensed matter physics and neighbouring fields. This book provides a praxis-oriented and pedagogical introduction to quantum field theory in many-particle physics, emphasizing the application of theory to real physical systems. This third edition is organized into two parts: the first half of the text presents a streamlined introduction, elevating readers to a level where they can engage with contemporary research literature, from the introduction of many-body techniques and functional integration to renormalization group methods, and the second half addresses a range of advanced topics including modern aspects of gauge theory, topological and relativistic quantum matter, and condensed matter physics out of thermal equilibrium. At all stages, the text seeks a balance between methodological aspects of quantum field theory and practical applications. Extended problems with worked solutions provide a bridge between formal theory and a research-oriented approach.

  • Equidistribution of exponential sums indexed by a subgroup of fixed cardinality

  • Part of
  • THÉO UNTRAU
  • Journal:
    Mathematical Proceedings of the Cambridge Philosophical Society / Volume 176 / Issue 1 / January 2024
    Published online by Cambridge University Press:
    24 August 2023, pp. 65-94
    Print publication:
    January 2024
    • Article
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  • We consider families of exponential sums indexed by a subgroup of invertible classes modulo some prime power q. For fixed d, we restrict to moduli q so that there is a unique subgroup of invertible classes modulo q of order d. We study distribution properties of these families of sums as q grows and we establish equidistribution results in some regions of the complex plane which are described as the image of a multi-dimensional torus via an explicit Laurent polynomial. In some cases, the region of equidistribution can be interpreted as the one delimited by a hypocycloid, or as a Minkowski sum of such regions.

  • On the values taken by slice torus invariants

  • PETER FELLER, LUKAS LEWARK, ANDREW LOBB
  • Journal:
    Mathematical Proceedings of the Cambridge Philosophical Society / Volume 176 / Issue 1 / January 2024
    Published online by Cambridge University Press:
    23 August 2023, pp. 55-63
    Print publication:
    January 2024
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  • We study the space of slice torus invariants. In particular we characterise the set of values that slice torus invariants may take on a given knot in terms of the stable smooth slice genus. Our study reveals that the resolution of the local Thom conjecture implies the existence of slice torus invariants without having to appeal to any explicit construction from a knot homology theory.

Page 44 of 1311