text.skipToContent text.skipToNavigation

Mathematical Physics of Quantum Mechanics

  • Verlag: Springer, Berlin
eBook (PDF)
94,95 €
inkl. gesetzl. MwSt.
Sofort per Download lieferbar

Online verfügbar

Mathematical Physics of Quantum Mechanics

QMath9 is a meeting for young scientists to learn about the state of the art in the Mathematical Physics of Quantum Systems. This selection of outstanding articles written in pedagocical style has six sections that cover new techniques and recent results on spectral theory, statistical mechanics, Bose-Einstein condensation, random operators, magnetic Schrödinger operators and much more. For postgraduate students this book can be used as a useful introduction to the research literature. For more expert researcher this book will be a concise and modern source of reference.
Written for: Postdocs and researchers in mathematical and quantum physics
quantum chaos
quantum dynamics
random operators
spectral theory


    Format: PDF
    Kopierschutz: AdobeDRM
    Seitenzahl: 485
    Sprache: Englisch
    ISBN: 9783540342731
    Verlag: Springer, Berlin
    Serie: Lecture Notes in Physics Vol.690
    Größe: 5151kBytes
Weiterlesen weniger lesen

Mathematical Physics of Quantum Mechanics

Part I Quantum Dynamics and Spectral Theory (p. 3-4)
Different aspects of the solution of a long-standing major problem in mathematical physics are reported in the contributions of Avila, Jitomirskaya and Puig. It had been conjectured for about thirty years by physicists and mathematicians that the problem of electrons confined to a plane under the influence of a periodic potential and a perpendicular magnetic field exhibits fractal spectral properties. Experimental evidence of Hofstadters butterflylike energy spectrum was found about five years ago.
Here the mathematical physicists Avila, Jitomirskaya and Puig report on the proof that the spectrum of a related operator is a Cantor set. Their proofs rely much on recent techniques in classical dynamical systems.We mention that the mathematical model still has fascinating unsolved aspects which are important to physics and especially the quantum hall effect for example the question whether the spectral gaps are open. Building Micron-size robots which move much faster than bacteria is one of the visions of small scale physics. Y. Avron gave an introduction on recent results on the problem of designing an optimal micro-swimmer.
These have been obtained using methods from geometry and linear response theory. V. Betz and S. Teufel report on their progress in the old Landau?Zener problem. For a time dependent two state problem which is asymptotically constant, a detailed approximate solution which takes into account the adiabatic transitions is obtained for all times. It describes both the exponential smallness of the transition probability and the time scale over which it takes place. The theory of transport in mesoscopic systems is addressed in two contributions. Büttiker and Moskalets treat quantum pumping. If the system is driven by several internal parameters oscillating slowly, a direct current may result.
It can be calculated to leading order in terms of stationary scattering matrices. To take account the energy exchange with the environment the full time dependent scattering matrix is developed to next order. A mathematical proof of the formula relating conductance and transmittance has been given by H.D. Cornean, A. Jensen, V. Moldoveanu in the case of an adiabatically switched on external potential. The formula is applied numerically to a model.
Geometry meets physics again in the contribution of P. Exner who presents a conjecture about an interesting isoperimetric problem arising from the spectral analysis of a quantum model with point interactions. S. Glazek discusses examples of renormalization group analysis applied to Schrödinger operators and in particular the occurrence of a limit cycle as a critical attractor instead of a fixed point.

Weiterlesen weniger lesen