Adiabatic Perturbation Theory in Quantum Dynamics by Stefan Teufel

By Stefan Teufel

Separation of scales performs a primary function within the realizing of the dynamical behaviour of complicated structures in physics and different typical sciences. A well-known instance is the Born-Oppenheimer approximation in molecular dynamics. This booklet specializes in a contemporary method of adiabatic perturbation thought, which emphasizes the function of powerful equations of movement and the separation of the adiabatic restrict from the semiclassical restrict. an in depth advent provides an summary of the topic and makes the later chapters obtainable additionally to readers much less accustomed to the cloth. even if the final mathematical concept in keeping with pseudodifferential calculus is gifted intimately, there's an emphasis on concrete and correct examples from physics. functions variety from molecular dynamics to the dynamics of electrons in a crystal and from the quantum mechanics of in part limited platforms to Dirac debris and nonrelativistic QED.

Show description

Read or Download Adiabatic Perturbation Theory in Quantum Dynamics PDF

Best quantum physics books

Quantum noise: A Handbook of Markovian and Non-Markovian Quantum Stochastic Methods with Applications to Quantum Optics

This ebook bargains a scientific and accomplished exposition of the quantum stochastic equipment which have been constructed within the box of quantum optics. It comprises new remedies of photodetection, quantum amplifier conception, non-Markovian quantum stochastic methods, quantum input-output concept, and optimistic P-representations.

Two Dimensional Quantum Gravity and Random Surfaces: Jerusalem Winter School for Theoreticalphysic S, Jerusalem, Israel, 27 Dec, 90-4 Jan, 91

Some time past few years there was a lot learn of random two-dimensional surfaces. those supply uncomplicated types of string theories with a number of levels of freedom, in addition to toy versions of quantum gravity. they've got attainable purposes to the statistical mechanics of section barriers and to the advance of an efficient string description of QCD.

Quantum Theory: A Two-Time Success Story: Yakir Aharonov Festschrift

Yakir Aharonov is among the prime figures within the foundations of quantum physics. His contributions variety from the prestigious Aharonov-Bohm impact (1959), to the newer idea of susceptible measurements (whose experimental confirmations have been lately ranked because the most vital result of physics in 2011).

Additional resources for Adiabatic Perturbation Theory in Quantum Dynamics

Example text

A severe drawback of the derivation of the T-BMT equation via the time-adiabatic theorem is that, even at higher orders, it is impossible to see a back-reaction of the spin-dynamics on the translational motion. This is because we must a priori prescribe the classical trajectory of the particle along which we choose to compute the evolution of its spin. Such a simple minded adiabatic approximation thus will never explain why an electron beam is split in a Stern-Gerlach magnet because of spin. 2, is solved once we switch to the space-adiabatic setting.

Since ∇x He ∈ L(H), a short calculation shows that [H ε , ε∇x ⊗ 1] = O(ε) in L(H 1,ε ⊗ He , H). Hence we obtain for G = F · (ε∇x ⊗ 1) that [ H ε , G ] = [ H ε , F ] · (ε∇x ⊗ 1) + F · [ H ε , ε∇x ⊗ 1 ] = P∗⊥ (∇x P∗ ) P∗ · (ε∇x ⊗ 1) + O(ε) with O(ε) in the norm of L(H 2,ε ⊗ He , H). 41) dt ε ε = eiH t/ε P∗⊥ (∇x P∗ ) P∗ · (ε∇x ⊗ 1) e−iH t/ε + O ε(1 + |t|)2 , where O(ε(1 + |t|)2 ) holds in the norm of L(H 2,ε ⊗ He , H). e. the kinetic energy of the nuclei may grow in time. 42) in L(H 1,ε ⊗ He , H) follows from (ε∇x ⊗ 1) e−iH ε t/ε ψ ≤ (εDA ⊗ 1) e−iH ≤ (εDA ⊗ 1) ψ + ε t/ε ψ + (εA ⊗ 1) e−iH (εDA ⊗ 1), e−iH ε t/ε ε t/ε ψ ψ +C ψ ≤ (ε∇x ⊗ 1) ψ + C |t| ψ + 2 C ψ for ψ ∈ H 1 ⊗ He .

As in the time-adiabatic case we define A(t) = −i ε eiH ε t/ε G e−iH ε t/ε , such that ε ε ε ε t d i ε A(t) = eiH t/ε [ H ε , G ] e−iH t/ε = eiH t/ε Hod e−iH ε + O(ε) . 21) and integrate by parts, e−iH ε t/ε − e−iHdiag t/ε = ε t d A(t ) dt 0 ≤ A(t) + A(0) dt = t dt A(t ) + 0 = O(ε(1 + |t|)) . 22). 3 Time-dependent Born-Oppenheimer theory: Part I The physical background of the time-dependent Born-Oppenheimer approximation was already discussed in the Introduction. In the present section we apply the first-order space-adiabatic scheme, which was developed in the previous section, to the full molecular Hamiltonian for l nuclei and k electrons: Hmol = 1 2mn l −i ∇xn + A(xn ) 2 + n=1 1 2me k −i ∇yn − A(yn ) 2 n=1 + Ve (y) + Ven (x, y) + Vn (x) .

Download PDF sample

Rated 4.84 of 5 – based on 48 votes