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Books on the topic 'Many-particle system'

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Published: 4 June 2021
Last updated: 16 February 2022

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1

Henri, Orland, ed. Quantum many-particle systems. Reading, MA: Perseus Books, 1998.

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2

Henri, Orland, ed. Quantum many-particle systems. Redwood City, Calif: Addison-Wesley Pub. Co., 1988.

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3

Bazarov, I. P. Theory of many-particle systems. New York: American Institute of Physics, 1989.

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4

Arkeryd, Leif, Pierre-Louis Lions, Peter A. Markowich, and Srinivasa R. S. Varadhan. Nonequilibrium Problems in Many-Particle Systems. Edited by Carlo Cercignani and Mario Pulvirenti. Berlin, Heidelberg: Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/bfb0090926.

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5

Cabra, Daniel C., Andreas Honecker, and Pierre Pujol, eds. Modern Theories of Many-Particle Systems in Condensed Matter Physics. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-10449-7.

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6

Modern theories of many-particle systems in condensed matter physics. Heidelberg: Springer, 2012.

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7

Endres, Manuel. Probing Correlated Quantum Many-Body Systems at the Single-Particle Level. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-05753-8.

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8

Patil, S. H. Asymptotic methods in quantum mechanics: Application to atoms, molecules, and nuclei. Berlin: Springer, 2000.

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9

(Editor), J. Ullrich, and V. P. Shevelko (Editor), eds. Many-Particle Quantum Dynamics in Atomic and Molecular Fragmentation (Springer Series on Atomic, Optical, and Plasma Physics). Springer, 2003.

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10

Horing, Norman J. Morgenstern. Equations of Motion with Particle–Particle Interactions and Approximations. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0008.

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Starting with the equation of motion for the field operator ψ(x,t) of an interacting many-particle system, the n-particle Green’s function (Gn) equation of motion is developed, with interparticle interactions generating an infinite chain of equations coupling it to (n+1)- and (n−1)-particle Green’s functions (Gn+1 and Gn−1, respectively). Particularly important are the one-particle Green’s function equation with its coupling to the two-particle Green’s function and the two-particle Green’s function equation with its coupling to the three-particle Green’s function. To develop solutions, it is necessary to introduce non-correlation decoupling procedures involving the Hartree and Hartree-Fock approximations for G2 in the G1 equation; and a similar factorization “ansatz” for G3 in the G2 equation, resulting in the Sum of Ladder Diagrams integral equation for G2, with multiple Born iterates and finite collisional lifetimes. Similar treatment of the G11-equation for the joint propagation of one-electron and one-hole subject to mutual Coulomb attraction leads to bound electron-hole exciton states having a discrete hydrogen like spectrum of energy eigenstates. Its role in single-particle propagation is also discussed in terms of one-electron self-energy Σ‎ and the T-matrix
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11

Boudreau, Joseph F., and Eric S. Swanson. Many body dynamics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198708636.003.0018.

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Specialized techniques for solving the classical many-body problem are explored in the context of simple gases, more complicated gases, and gravitating systems. The chapter starts with a brief review of some important concepts from statistical mechanics and then introduces the classic Verlet method for obtaining the dynamics of many simple particles. The practical problems of setting the system temperature and measuring observables are discussed. The issues associated with simulating systems of complex objects form the next topic. One approach is to implement constrained dynamics, which can be done elegantly with iterative methods. Gravitational systems are introduced next with stress on techniques that are applicable to systems of different scales and to problems with long range forces. A description of the recursive Barnes-Hut algorithm and particle-mesh methods that speed up force calculations close out the chapter.
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12

Quantum Many-Particle Systems. Addison-Wesley Pub Co, 1988.

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13

Negele, John W., and Henri Orland. Quantum Many-Particle Systems. CRC Press, 2018. http://dx.doi.org/10.1201/9780429497926.

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14

Kolanoski, Hermann, and Norbert Wermes. Particle Detectors. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198858362.001.0001.

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The book describes the fundamentals of particle detectors in their different forms as well as their applications, presenting the abundant material as clearly as possible and as deeply as needed for a thorough understanding. The target group for the book are both, students who want to get an introduction or wish to deepen their knowledge on the subject as well as lecturers and researchers who intend to extent their expertise. The book is also suited as a preparation for instrumental work in nuclear, particle and astroparticle physics and in many other fields (addressed in chapter 2). The detection of elementary particles, nuclei and high-energetic electromagnetic radiation, in this book commonly designated as ‘particles’, proceeds through interactions of the particles with matter. A detector records signals originating from the interactions occurring in or near the detector and (in general) feeds them into an electronic data acquisition system. The book describes the various steps in this process, beginning with the relevant interactions with matter, then proceeding to their exploitation for different detector types like tracking detectors, detectors for particle identification, detectors for energy measurements, detectors in astroparticle experiments, and ending with a discussion of signal processing and data acquisition. Besides the introductory and overview chapters (chapters 1 and 2), the book is divided into five subject areas: – fundamentals (chapters 3 to 5), – detection of tracks of charged particles (chapters 6 to 9), – phenomena and methods mainly applied for particle identification (chapters 10 to 14), – energy measurement (accelerator and non-accelerator experiments) (chapters 15, 16), – electronics and data acquisition (chapters 17 and 18). Comprehensive lists of literature, keywords and abbreviations can be found at the end of the book.
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15

Quantum Theory of Many-Particle Systems. Dover Publications, 2003.

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16

Negele, J. W., and Henri Orland. Quantum Many-particle Systems (Frontiers in Physics). Perseus Books,U.S., 1994.

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17

The Flow Equation Approach to Many-Particle Systems. Springer, 2006.

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18

Kehrein, Stefan. The Flow Equation Approach to Many-Particle Systems. Springer, 2010.

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19

The Flow Equation Approach to Many-Particle Systems. Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/3-540-34068-8.

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20

Bishop, R. F., D. Mukherjee, Uzi Kaldor, and Hermann Kummel. The Coupled Cluster Approach to Quantum Many-Particle Systems. Springer-Verlag, 2003.

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21

Kato, Tosio. On the Eigenfunctions of Many-particle Systems in Quantum Mechanics. Franklin Classics, 2018.

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22

Cabra, Daniel C., Andreas Honecker, and Pierre Pujol. Modern Theories of Many-Particle Systems in Condensed Matter Physics. Springer, 2012.

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23

Kuzemsky, Alexander Leonidovich. Statistical Mechanics and the Physics of Many-Particle Model Systems. World Scientific Publishing Co Pte Ltd, 2017.

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24

Horing, Norman J. Morgenstern. Schwinger Action Principle and Variational Calculus. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0004.

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Chapter 4 introduces the Schwinger Action Principle, along with associated particle and potential sources. While the methods described here originally arose in the relativistic quantum field theory of elementary particle physics, they have also profoundly advanced our understanding of non-relativistic many-particle physics. The Schwinger Action Principle is a quantum-mechanical variational principle that closely parallels the Hamilton Principle of Least Action of classical mechanics, generalizing it to include the role of quantum operators as generalized coordinates and momenta. As such, it unifies all aspects of quantum theory, incorporating Hamilton equations of motion for those operators and the Heisenberg equation, as well as producing the canonical equal-time commutation/anticommutation relations. It yields dynamical coupled field equations for the creation and annihilation operators of the interacting many-body system by variational differentiation of the Hamiltonian with respect to the field operators. Also, equations for the development of matrix elements (underlying Green’s functions) are derived using variations with respect to particle and potential “sources” (and coupling strength). Variational calculus, involving impressed potentials, c-number coordinates and fields, also quantum operator coordinates and fields, is discussed in full detail. Attention is given to the introduction of fermion and boson particle sources and their use in variational calculus.
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25

Morawetz, Klaus. Multiple Impurity Scattering. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797241.003.0005.

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Furnished with basic ideas about the scattering on a single impurity, the motion of a particle scattered by many randomly distributed impurities is approached. In spite of having a single particle only, this system already belongs to many-body physics as it combines randomising effects of high-angle collisions with mean-field effects due to low-angle collisions. The averaged wave function leads to the Dyson equation. Various approximations are systematically introduced and discussed ranging from Born, averaged T-matrix to coherent potential approximation. The effective medium and the effective mass as wave function renormalisations are discussed and the various approximations are accurately compared.
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26

Morawetz, Klaus. Scattering on a Single Impurity. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797241.003.0004.

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Evolution of a many-body system consists of permanent collisions among particles. Looking at the motion of a single particle, one can identify encounters by which a particle abruptly changes the direction of flight, these are seen as true collisions, and small-angle encounters, which in sum act as an applied force rather than randomising collisions. The scattering on impurities is used to introduce the mentioned mechanisms and, in particular, to show how they affect each other. Point impurities are assumed, i.e. impurities the potential of which is restricted to a single atomic site of the crystal lattice. In this case interaction potentials never overlap and many-body effects are due to nonlocal character of the quantum particle. To introduce elementary components of the formalism, in this chapter we first describe the interaction of an electron with a single impurity. Lippman–Schwinger equations are derived and the physics behind the collision delay, dissipativeness and optical theorems is explored.
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27

Probing Correlated Quantum Many-Body Systems at the Single-Particle Level. Springer, 2014.

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28

Rau, Jochen. Quantum Theory. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780199595068.003.0002.

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From the outset statistical mechanics will be framed in the language of quantum theory. The typical macroscopic system is composed of multiple constituents, and hence described in some many-particle Hilbert space. In general, not much is known about such a system, certainly not the precise preparation of all its microscopic details. Thus, its description requires a more general notion of a quantum state, a so-called mixed state. This chapter begins with a brief review of the basic axioms of quantum theory regarding observables, pure states, measurements, and time evolution. Particular attention is paid to the use of projection operators and to the most elementary quantum system, a two-level system. The chapter then motivates the introduction of mixed states and examines in detail their mathematical representation and properties. It also dwells on the description of composite systems, introducing, in particular, the notions of statistical independence and correlations.
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29

Horing, Norman J. Morgenstern. Quantum Statistical Field Theory. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.001.0001.

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The methods of coupled quantum field theory, which had great initial success in relativistic elementary particle physics and have subsequently played a major role in the extensive development of non-relativistic quantum many-particle theory and condensed matter physics, are at the core of this book. As an introduction to the subject, this presentation is intended to facilitate delivery of the material in an easily digestible form to students at a relatively early stage of their scientific development, specifically advanced undergraduates (rather than second or third year graduate students), who are mathematically strong physics majors. The mechanism to accomplish this is the early introduction of variational calculus with particle sources and the Schwinger Action Principle, accompanied by Green’s functions, and, in addition, a brief derivation of quantum mechanical ensemble theory introducing statistical thermodynamics. Important achievements of the theory in condensed matter and quantum statistical physics are reviewed in detail to help develop research capability. These include the derivation of coupled field Green’s function equations of motion for a model electron-hole-phonon system, extensive discussions of retarded, thermodynamic and non-equilibrium Green’s functions, and their associated spectral representations and approximation procedures. Phenomenology emerging in these discussions includes quantum plasma dynamic, nonlocal screening, plasmons, polaritons, linear electromagnetic response, excitons, polarons, phonons, magnetic Landau quantization, van der Waals interactions, chemisorption, etc. Considerable attention is also given to low-dimensional and nanostructured systems, including quantum wells, wires, dots and superlattices, as well as materials having exceptional conduction properties such as superconductors, superfluids and graphene.
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30

Wigmans, Richard. Analysis and Interpretation of Test Beam Data. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786351.003.0009.

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This chapter describes some of the many pitfalls that may be encountered when developing the calorimeter system for a particle physics experiment. Several of the examples chosen for this chapter are based on the author’s own experience. Typically, the performance of a new calorimeter is tested in a particle beam provided by an accelerator. The potential pitfalls encountered in correctly assessing this performance both concern the analysis and the interpretation of the data collected in such tests. The analysis should be carried out with unbiased event samples. Several consequences of violating this principle are illustrated with practical examples. For the interpretation of the results, it is very important to realize that the conditions in a testbeam are fundamentally different than in practice. This has consequences for the meaning of the term “energy resolution”. It is shown that the way in which the results of beam tests are quoted may create a misleading impression of the quality of the tested instrument.
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31

Davidson, Sacha, Paolo Gambino, Mikko Laine, Matthias Neubert, and Christophe Salomon, eds. Effective Field Theory in Particle Physics and Cosmology. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198855743.001.0001.

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Effective field theory (EFT) is a general method for describing quantum systems with multiple-length scales in a tractable fashion. It allows us to perform precise calculations in established models (such as the standard models of particle physics and cosmology), as well as to concisely parametrize possible effects from physics beyond the standard models. EFTs have become key tools in the theoretical analysis of particle physics experiments and cosmological observations, despite being absent from many textbooks. This volume aims to provide a comprehensive introduction to many of the EFTs in use today, and covers topics that include large-scale structure, WIMPs, dark matter, heavy quark effective theory, flavour physics, soft-collinear effective theory, and more.
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32

Morawetz, Klaus. Interacting Systems far from Equilibrium. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797241.001.0001.

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In quantum statistics based on many-body Green’s functions, the effective medium is represented by the selfenergy. This book aims to discuss the selfenergy from this point of view. The knowledge of the exact selfenergy is equivalent to the knowledge of the exact correlation function from which one can evaluate any single-particle observable. Complete interpretations of the selfenergy are as rich as the properties of the many-body systems. It will be shown that classical features are helpful to understand the selfenergy, but in many cases we have to include additional aspects describing the internal dynamics of the interaction. The inductive presentation introduces the concept of Ludwig Boltzmann to describe correlations by the scattering of many particles from elementary principles up to refined approximations of many-body quantum systems. The ultimate goal is to contribute to the understanding of the time-dependent formation of correlations. Within this book an up-to-date most simple formalism of nonequilibrium Green’s functions is presented to cover different applications ranging from solid state physics (impurity scattering, semiconductor, superconductivity, Bose–Einstein condensation, spin-orbit coupled systems), plasma physics (screening, transport in magnetic fields), cold atoms in optical lattices up to nuclear reactions (heavy-ion collisions). Both possibilities are provided, to learn the quantum kinetic theory in terms of Green’s functions from the basics using experiences with phenomena, and experienced researchers can find a framework to develop and to apply the quantum many-body theory straight to versatile phenomena.
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33

Arkeryd, L., P. A. Markovich, and P. L. Lions. Nonequilibrium Problems in Many-Particle Systems: Lectures Given at the 3rd Session of the Centro Internazionale Matematico Estivo (Lecture Notes in Mathematics). Springer, 1993.

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34

Eckle, Hans-Peter. Models of Quantum Matter. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780199678839.001.0001.

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This book focuses on the theory of quantum matter, strongly interacting systems of quantum many–particle physics, particularly on their study using exactly solvable and quantum integrable models with Bethe ansatz methods. Part 1 explores the fundamental methods of statistical physics and quantum many–particle physics required for an understanding of quantum matter. It also presents a selection of the most important model systems to describe quantum matter ranging from the Hubbard model of condensed matter physics to the Rabi model of quantum optics. The remaining five parts of the book examines appropriate special cases of these models with respect to their exact solutions using Bethe ansatz methods for the ground state, finite–size, and finite temperature properties. They also demonstrate the quantum integrability of an exemplary model, the Heisenberg quantum spin chain, within the framework of the quantum inverse scattering method and through the algebraic Bethe ansatz. Further models, whose Bethe ansatz solutions are derived and examined, include the Bose and Fermi gases in one dimension, the one–dimensional Hubbard model, the Kondo model, and the quantum Tavis–Cummings model, the latter a model descendent from the Rabi model.
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35

Arkeryd, L. Nonequilibrium Problems in Many-Particle Systems: Lectures Given at the 3rd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) Held in (NATO ... Series F, Computer and Systems Sciences). Springer, 1993.

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36

Horing, Norman J. Morgenstern. Quantum Mechanical Ensemble Averages and Statistical Thermodynamics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0006.

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Chapter 6 introduces quantum-mechanical ensemble theory by proving the asymptotic equivalence of the quantum-mechanical, microcanonical ensemble average with the quantum grand canonical ensemble average for many-particle systems, based on the method of Darwin and Fowler. The procedures involved identify the grand partition function, entropy and other statistical thermodynamic variables, including the grand potential, Helmholtz free energy, thermodynamic potential, Gibbs free energy, Enthalpy and their relations in accordance with the fundamental laws of thermodynamics. Accompanying saddle-point integrations define temperature (inverse thermal energy) and chemical potential (Fermi energy). The concomitant emergence of quantum statistical mechanics and Bose–Einstein and Fermi–Dirac distribution functions are discussed in detail (including Bose condensation). The magnetic moment is derived from the Helmholtz free energy and is expressed in terms of a one-particle retarded Green’s function with an imaginary time argument related to inverse thermal energy. This is employed in a discussion of diamagnetism and the de Haas-van Alphen effect.
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37

Zinn-Justin, Jean. Quantum Field Theory and Critical Phenomena. 5th ed. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780198834625.001.0001.

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Introduced as a quantum extension of Maxwell's classical theory, quantum electrodynamic (QED) has been the first example of a quantum field theory (QFT). Eventually, QFT has become the framework for the discussion of all fundamental interactions at the microscopic scale except, possibly, gravity. More surprisingly, it has also provided a framework for the understanding of second order phase transitions in statistical mechanics. In fact, as hopefully this work illustrates, QFT is the natural framework for the discussion of most systems involving an infinite number of degrees of freedom with local couplings. These systems range from cold Bose gases at the condensation temperature (about ten nanokelvin) to conventional phase transitions (from a few degrees to several hundred) and high energy particle physics up to a TeV, altogether more than twenty orders of magnitude in the energy scale. Therefore, although excellent textbooks about QFT had already been published, I thought, many years ago, that it might not be completely worthless to present a work in which the strong formal relations between particle physics and the theory of critical phenomena are systematically emphasized. This option explains some of the choices made in the presentation. A formulation in terms of field integrals has been adopted to study the properties of QFT. The language of partition and correlation functions has been used throughout, even in applications of QFT to particle physics. Renormalization and renormalization group (RG) properties are systematically discussed. The notion of effective field theory (EFT) and the emergence of renormalizable theories are described. The consequences for fine-tuning and triviality issue are emphasized. This fifth edition has been updated and fully revised.
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38

Nonequilibrium problems in many-particle systems: Lectures given at the 3rd Session of the Centro internazionale matematico estivo (C.I.M.E.) held in Montecatini, Italy, June 15-27, 1992. Berlin: Springer, 1993.

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39

Tang, K. T., and S. H. Patil. Asymptotic Methods in Quantum Mechanics: Applications to Atoms, Molecules, and Nuclei (Springer Series in Chemical Physics). Springer, 2000.

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