Dynamics Of One Dimensional Quantum Systems
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Author | : Yoshio Kuramoto |
Publisher | : Cambridge University Press |
Total Pages | : 487 |
Release | : 2009-08-06 |
Genre | : Mathematics |
ISBN | : 0521815983 |
A concise and accessible account of the dynamical properties of one-dimensional quantum systems, for graduate students and new researchers.
Author | : Fabio Franchini |
Publisher | : Springer |
Total Pages | : 186 |
Release | : 2017-05-25 |
Genre | : Science |
ISBN | : 3319484877 |
This book introduces the reader to basic notions of integrable techniques for one-dimensional quantum systems. In a pedagogical way, a few examples of exactly solvable models are worked out to go from the coordinate approach to the Algebraic Bethe Ansatz, with some discussion on the finite temperature thermodynamics. The aim is to provide the instruments to approach more advanced books or to allow for a critical reading of research articles and the extraction of useful information from them. We describe the solution of the anisotropic XY spin chain; of the Lieb-Liniger model of bosons with contact interaction at zero and finite temperature; and of the XXZ spin chain, first in the coordinate and then in the algebraic approach. To establish the connection between the latter and the solution of two dimensional classical models, we also introduce and solve the 6-vertex model. Finally, the low energy physics of these integrable models is mapped into the corresponding conformal field theory. Through its style and the choice of topics, this book tries to touch all fundamental ideas behind integrability and is meant for students and researchers interested either in an introduction to later delve in the advance aspects of Bethe Ansatz or in an overview of the topic for broadening their culture.
Author | : Vladimir M. Akulin |
Publisher | : Springer Science & Business Media |
Total Pages | : 477 |
Release | : 2005-09-13 |
Genre | : Science |
ISBN | : 3540210520 |
Coherent Dynamics of Complex Quantum Systems is aimed at senior-level undergraduate students in the areas of atomic, molecular, and laser physics, physical chemistry, quantum optics and quantum informatics. It should help them put particular problems in these fields into a broader scientific context and thereby take advantage of the well-elaborated technique of the adjacent fields.
Author | : Tim Langen |
Publisher | : Springer |
Total Pages | : 154 |
Release | : 2015-05-22 |
Genre | : Science |
ISBN | : 3319185640 |
This work presents a series of experiments with ultracold one-dimensional Bose gases, which establish said gases as an ideal model system for exploring a wide range of non-equilibrium phenomena. With the help of newly developed tools, like full distributions functions and phase correlation functions, the book reveals the emergence of thermal-like transient states, the light-cone-like emergence of thermal correlations and the observation of generalized thermodynamic ensembles. This points to a natural emergence of classical statistical properties from the microscopic unitary quantum evolution, and lays the groundwork for a universal framework of non-equilibrium physics. The thesis investigates a central question that is highly contested in quantum physics: how and to which extent does an isolated quantum many-body system relax? This question arises in many diverse areas of physics, and many of the open problems appear at vastly different energy, time and length scales, ranging from high-energy physics and cosmology to condensed matter and quantum information. A key challenge in attempting to answer this question is the scarcity of quantum many-body systems that are both well isolated from the environment and accessible for experimental study.
Author | : Elliott H. Lieb |
Publisher | : Academic Press |
Total Pages | : 580 |
Release | : 2013-09-17 |
Genre | : Science |
ISBN | : 1483218562 |
Mathematical Physics in One Dimension: Exactly Soluble Models of Interacting Particles covers problems of mathematical physics with one-dimensional analogs. The book discusses classical statistical mechanics and phase transitions; the disordered chain of harmonic oscillators; and electron energy bands in ordered and disordered crystals. The text also describes the many-fermion problem; the theory of the interacting boson gas; the theory of the antiferromagnetic linear chains; and the time-dependent phenomena of many-body systems (i.e., classical or quantum-mechanical dynamics). Physicists and mathematicians will find the book invaluable.
Author | : Minoru Takahashi |
Publisher | : Cambridge University Press |
Total Pages | : 268 |
Release | : 1999-03-28 |
Genre | : Science |
ISBN | : 9780521551434 |
Exactly solvable models are very important in physics from a theoretical point of view and also from the experimentalist's perspective, because in such cases theoretical results and experimental results can be compared without ambiguity. This is a book about an important class of exactly solvable models in physics. The subject area is the Bethe-ansatz approach for a number of one-dimensional models, and the setting up of equations within this approach to determine the thermodynamics of these systems. It is a topic that crosses the boundaries among condensed matter physics, mathematics and field theory. The derivation and application of thermodynamic Bethe-ansatz equations for one-dimensional models are explained in detail. This technique is indispensable for physicists studying the low-temperature properties of one-dimensional substances. Written by the originator of much of the work in the subject, this book will be of great interest to theoretical condensed matter physicists.
Author | : Lampros A A Nikolopoulos |
Publisher | : Morgan & Claypool Publishers |
Total Pages | : 195 |
Release | : 2019-03-29 |
Genre | : Science |
ISBN | : 168174712X |
The dynamics of quantum systems exposed to ultrafast (at the femtosecond time-scale) and strong laser radiation has a highly non-linear character, leading to a number of new phenomena, outside the reach of traditional spectroscopy. The current laser technology makes feasible the probing and control of quantum-scale systems with fields that are as strong as the interatomic Coulombic interactions and time resolution that is equal to (or less than) typical atomic evolution times. It is indispensable that any theoretical description of the induced physical processes should rely on the accurate calculation of the atomic structure and a realistic model of the laser radiation as pulsed fields. This book aims to provide an elementary introduction of theoretical and computational methods and by no means is anywhere near to complete. The selection of the topics as well as the particular viewpoint is best suited for early-stage students and researchers; the included material belongs in the mainstream of theoretical approaches albeit using simpler language without sacrificing mathematical accuracy. Therefore, subjects such as the Hilbert vector-state, density-matrix operators, amplitude equations, Liouville equation, coherent laser radiation, free-electron laser, Dyson-chronological operator, subspace projection, perturbation theory, stochastic density-matrix equations, time-dependent Schrödinger equation, partial-wave analysis, spherical-harmonics expansions, basis and grid wavefunction expansions, ionization, electron kinetic-energy and angular distributions are presented within the context of laser-atom quantum dynamics.
Author | : Ángel Rivas |
Publisher | : Springer Science & Business Media |
Total Pages | : 103 |
Release | : 2011-10-01 |
Genre | : Science |
ISBN | : 3642233546 |
In this volume the fundamental theory of open quantum systems is revised in the light of modern developments in the field. A unified approach to the quantum evolution of open systems is presented by merging concepts and methods traditionally employed by different communities, such as quantum optics, condensed matter, chemical physics and mathematical physics. The mathematical structure and the general properties of the dynamical maps underlying open system dynamics are explained in detail. The microscopic derivation of dynamical equations, including both Markovian and non-Markovian evolutions, is also discussed. Because of the step-by-step explanations, this work is a useful reference to novices in this field. However, experienced researches can also benefit from the presentation of recent results.
Author | : Berthold-Georg Englert |
Publisher | : World Scientific |
Total Pages | : 234 |
Release | : 2006 |
Genre | : Science |
ISBN | : 9812569707 |
Note: ?The three volumes are not sequential but rather independent of each other and largely self-contained.Basic Matters is a first introduction to quantum mechanics that does not assume any prior knowledge of the subject. The emphasis is on the general structure as the necessary foundation of any understanding. Starting from the simplest quantum phenomenon, the Stern-Gerlach experiment with its choice between two discrete outcomes, and ending with one-dimensional continuous systems, the physical concepts and notions as well as the mathematical formalism of quantum mechanics are developed in successive, manageable steps. The presentation is modern inasmuch as the natural language of the trade -- Dirac's kets and bras and so on -- is introduced early, and the temporal evolution is dealt with in a picture-free manner, with SchrOdinger's and Heisenberg's equations of motion side by side and on equal footing.The reader of Simple Systems is not expected to be familiar with the material in Basic Matters, but should have the minimal knowledge of a standard brief introduction to quantum mechanics with its typical emphasis on one-dimensional position wave functions. The step to Dirac's more abstract and much more powerful formalism is taken immediately, followed by reviews of quantum kinematics and quantum dynamics. The important standard examples (force-free motion, constant force, harmonic oscillator, hydrogen-like atoms) are then treated in considerable detail, whereby a nonstandard perspective is offered wherever it is deemed feasible and useful. A final chapter is devoted to approximation methods, from the Hellmann-Feynman theorem to the WKB quantization rule.Perturbed Evolution has a closer link to Simple Systems than that volume has to Basic Matters, but any reader familiar with the subject matter of a solid introduction to quantum mechanics -- such as Dirac's formalism of kets and bras, SchrOdinger's and Heisenberg's equations of motion, and the standard examples that can be treated exactly, with harmonic oscillators and hydrogen-like atoms among them -- can cope with the somewhat advanced material of this volume. The basics of kinematics and dynamics are reviewed at the outset, including discussions of Bohr's principle of complementarity and Schwinger's quantum action principle. The Born series, the Lippmann-Schwinger equation, and Fermi's golden rule are recurring themes in the treatment of the central subject matter -- the evolution in the presence of perturbing interactions for which there are no exact solutions as one has them for the standard examples in Simple Systems. The scattering by a localized potential is regarded as a perturbed evolution of a particular kind and is dealt with accordingly. The unique features of the scattering of indistinguishable quantum objects illustrate the nonclassical properties of bosons and fermions and prepare the groundwork for a discussion of multi-electron atoms.
Author | : Christian Miniatura |
Publisher | : OUP Oxford |
Total Pages | : 663 |
Release | : 2011-05-05 |
Genre | : Science |
ISBN | : 019162179X |
In recent years, there has been much synergy between the exciting areas of quantum information science and ultracold atoms. This volume, as part of the proceedings for the XCI session of Les Houches School of Physics (held for the first time outside Europe in Singapore) brings together experts in both fields. The theme of the school focused on two principal topics: quantum information science and ultracold atomic physics. The topics range from Bose Einstein Condensates to Degenerate Fermi Gases to fundamental concepts in Quantum Information Sciences, including some special topics on Quantum Hall Effects, Quantum Phase Transition, Interactions in Quantum Fluids, Disorder and Interference Phenomenoma, Trapped Ions and Atoms, and Quantum Optical Devices.