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Books on the topic 'Hamiltonian operators'

Author: Grafiati

Published: 4 June 2021

Last updated: 14 March 2023

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1

Alber, Mark. Energy dependent Schrödinger operators and complex Hamiltonian systems on Riemann surfaces. Hewlett Packard, 1996.

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2

Systèmes intégrables semi-classiques: Du local au global. Société Mathématique de France, 2006.

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3

Green's function estimates for lattice Schrödinger operators and applications. Princeton University Press, 2005.

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4

Boutet de Monvel-Berthier, Anne, 1948- and Georgescu V. 1947-, eds. C₀-groups, commutator methods, and spectral theory of N-Body Hamiltonians. Birkhäuser Verlag, 1996.

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5

Nonlinear integrable equations: Recursion operators, group theoretical and Hamiltonian structures of soliton equations. Springer-Verlag, 1987.

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6

Analysis of Hamiltonian PDEs. Oxford University Press, 2000.

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7

Nonlinear oscillations of Hamiltonian PDEs. Birkhauser, 2007.

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8

Wachsmuth, Jakob. Effective Hamiltonians for constrained quantum systems. American Mathematical Society, 2013.

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9

Lombardi, Olimpia. Introduction to the modal-Hamiltonian interpretation of quantum mechanics. Nova Science Publishers, 2010.

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10

Lombardi, Olimpia. Introduction to the modal-Hamiltonian interpretation of quantum mechanics. Nova Science Publishers, 2011.

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11

Boutet, Monvel Anne, and Georgescu Vladimir, eds. C 0-Groups, Commutator Methods and Spectral Theory of N-Body Hamiltonians. Birkhäuser Basel, 1996.

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12

Eduardo, Friedman, Mantoiu Marius, and SpringerLink (Online service), eds. Spectral Analysis of Quantum Hamiltonians: Spectral Days 2010. Springer Basel, 2012.

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13

Jacob, Birgit. Linear Port-Hamiltonian Systems on Infinite-dimensional Spaces. Springer Basel, 2012.

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14

Lazutkin, V. F. KAM theory and semiclassical approximations to eigenfunctions. Springer-Verlag, 1993.

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15

author, Winternitz Pavel, ed. Classification and identification of Lie algebras. American Mathematical Society, 2014.

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16

Müller-Kirsten, H. J. W. Classical mechanics and relativity. World Scientific, 2008.

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17

Sardella, Edson. Elastic properties of the Abrikosov flux line lattice for anisotropic superconductors and some applications of the projection operator method to phenomenological and exact Hamiltonian systems. University of Manchester, 1993.

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18

Dzhamay, Anton, Christopher W. Curtis, Willy A. Hereman, and B. Prinari. Nonlinear wave equations: Analytic and computational techniques : AMS Special Session, Nonlinear Waves and Integrable Systems : April 13-14, 2013, University of Colorado, Boulder, CO. American Mathematical Society, 2015.

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19

(Dietmar), Salamon D., ed. J-holomorphic curves and symplectic topology. 2nd ed. American Mathematical Society, 2012.

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20

Mathematical foundations of quantum field theory and perturbative string theory. American Mathematical Society, 2011.

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21

Cauchy Problem for Noneffectively Hyperbolic Operators. Mathematical Society of Japan, 2013.

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22

Baaquie, Belal E. Path Integrals and Hamiltonians: Principles and Methods. Cambridge University Press, 2014.

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23

Path Integrals and Hamiltonians: Principles and Methods. Cambridge University Press, 2014.

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24

Baaquie, Belal E. Path Integrals and Hamiltonians: Principles and Methods. Cambridge University Press, 2014.

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25

Raines, Allen Crawford. Hamiltonian-symplectic methods for solving the quadratic regulator problem. 1993.

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26

Hurtubise, Vincent. Formal properties, computational aspects, and electronic structure applications of effective operators. 1993.

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27

Konopelchenko, Boris G. Nonlinear Integrable Equations: Recursion Operators, Group-Theoretical and Hamiltonian Structures of Soliton Equations. Springer Berlin / Heidelberg, 2013.

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28

Horing, Norman J. Morgenstern. Identical Particles and Second Quantization: Occupation Number Representation. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0002.

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Focusing on systems of many identical particles, Chapter 2 introduces appropriate operators to describe their properties in terms of Schwinger’s “measurement symbols.” The latter are then factorized into “creation” and “annihilation” operators, whose fundamental properties and commutation/anticommutation relations are derived in conjunction with the Pauli exclusion principle. This leads to “second quantization” with the Hamiltonian, number, linear and angular momentum operators expressed in terms of the annihilation and creation operators, as well as the occupation number representation. Final

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29

Konopelchenko, Boris G. Nonlinear Integrable Equations: Recursion Operators, Group-Theoretical and Hamiltonian Structures of Soliton Equations (Lecture Notes in Physics). Springer, 1987.

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30

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 un

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31

Horing, Norman J. Morgenstern. Q. M. Pictures; Heisenberg Equation; Linear Response; Superoperators and Non-Markovian Equations. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0003.

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Three fundamental and equivalent mathematical frameworks (“pictures”) in which quantum theory can be lodged are exhibited and their relations and relative advantages/disadvantages are discussed: (1) The Schrödinger picture considers the dynamical development of the overall system state vector as a function of time relative to a fixed complete set of time-independent basis eigenstates; (2) The Heisenberg picture (convenient for the use of Green’s functions) embeds the dynamical development of the system in a time-dependent counter-rotation of the complete set of basis eigenstates relative to th

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32

Berti, Massimiliano. Nonlinear Oscillations of Hamiltonian PDEs. Springer, 2008.

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33

Georgescu, Vladimir, Werner O. Amrein, and Anne Boutet de Monvel. C0-Groups, Commutator Methods and Spectral Theory of N-Body Hamiltonians. Springer Basel AG, 2013.

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34

Georgescu, Vladimir, Werner O. Amrein, and Anne Boutet de Monvel. C0-Groups, Commutator Methods and Spectral Theory of N-Body Hamiltonians. Birkhauser Verlag, 2013.

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35

Spectral Analysis Of Quantum Hamiltonians Spectral Days 2010. Springer Basel, 2012.

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36

Jacob, Birgit, and Hans J. Zwart. Linear Port-Hamiltonian Systems on Infinite-Dimensional Spaces. Birkhäuser Boston, 2014.

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37

Benguria, Rafael, Eduardo Friedman, and Marius Mantoiu. Spectral Analysis of Quantum Hamiltonians: Spectral Days 2010. Birkhäuser, 2015.

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38

Benguria, Rafael, Eduardo Friedman, and Marius Mantoiu. Spectral Analysis of Quantum Hamiltonians: Spectral Days 2010. Springer, 2012.

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39

Leon, Manuel De, Modesto Salgado-Seco, Silvia Vilarino-Fernandez, and Manuel De Leon. Methods of Differential Geometry in Classical Field Theories: K-Symplectic and K-Cosymplectic Approaches. World Scientific Publishing Co Pte Ltd, 2015.

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40

Linear PortHamiltonian Systems on InfiniteDimensional Spaces Operator Theory Advances and Applications Linear Operator. Birkh User, 2012.

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41

Kvapil, Jaroslav, Antonin Dvorak, Otto Schenk, Laurie Feldman, and Barbara Willis Sweete. Rusalka. 2015.

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42

Zabrodin, Anton. Quantum spin chains and classical integrable systems. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797319.003.0013.

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This chapter is a review of the recently established quantum-classical correspondence for integrable systems based on the construction of the master T-operator. For integrable inhomogeneous quantum spin chains with gl(N)-invariant R-matrices in finite-dimensional representations, the master T-operator is a sort of generating function for the family of commuting quantum transfer matrices depending on an infinite number of parameters. Any eigenvalue of the master T-operator is the tau-function of the classical modified KP hierarchy. It is a polynomial in the spectral parameter which is identifie

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43

Rajeev, S. G. Fluid Mechanics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805021.001.0001.

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Starting with a review of vector fields and their integral curves, the book presents the basic equations of the subject: Euler and Navier–Stokes. Some solutions are studied next: ideal flows using conformal transformations, viscous flows such as Couette and Stokes flow around a sphere, shocks in the Burgers equation. Prandtl’s boundary layer theory and the Blasius solution are presented. Rayleigh–Taylor instability is studied in analogy with the inverted pendulum, with a digression on Kapitza’s stabilization. The possibility of transients in a linearly stable system with a non-normal operator

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44

Nonlinear Dirac Equation: Spectral Stability of Solitary Waves. American Mathematical Society, 2020.

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