W. Apel

Publications (6)0 Total impact

• Chapter: On Deriving Relaxation Equations for Nuclear Spins

  W. Apel, Yu. A. Bychkov
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  ABSTRACT: We review the microscopic derivation of the relaxation equations for a nuclear spin I that is weakly coupled to a quantum mechanical environment. Our derivation holds within the adiabatic approximation for a general stationary non-equilibrium state of the environment and also for an arbitrary value of I. The system of coupled relaxation equations contains two independent characteristic times. The stationary solution of the equations is the correct equilibrium distribution for given spin I, if the environment is assumed to be in the equilibrium state. The slowest relaxation rate towards the stationary solution can be faster, by a factor of up to 2I, than that determined perturbatively for use in the Bloch equations. KeywordsNuclear Magnetic Relaxation
  06/2011: pages 223-234;
• Source

  Available from: arxiv.org

  Article: Fractional minima in the conductivity of the quantum-Hall-system under microwaves

  W. Apel, Yu. A. Bychkov, M. Weyrauch
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  ABSTRACT: We analyse theoretically the conductivity of a quantum Hall system exposed to microwave radiation. We find that whenever microwave frequency and cyclotron frequency are commensurate, there is a {\em resonance} in the longitudinal conductivity. This resonance has the form of the derivative of a Lorentz function; precisely at the center of the resonance, the microwave induced conductivity vanishes. Between the resonances there are maxima and minima, the depths and precise positions of which depend on the microwave amplitude and the scattering rate of the impurities. We demonstrate the existence of these resonances by a microscopic, analytical calculation of the conductivity in lowest order in the microwave intensity and show here that the conductivity is independent of the microwave polarization, linear or circular. We then discuss the general case and predict minima in the longitudinal conductivity corresponding to fractional values of the microwave frequency divided by the cyclotron frequency.
  01/2006;
• Source

  Available from: arxiv.org

  Article: Nuclear Spin Relaxation for Higher Spin

  W. Apel, Yu. A. Bychkov
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  ABSTRACT: We study the relaxation of a spin I that is weakly coupled to a quantum mechanical environment. Starting from the microscopic description, we derive a system of coupled relaxation equations within the adiabatic approximation. These are valid for arbitrary I and also for a general stationary non--equilibrium state of the environment. In the case of equilibrium, the stationary solution of the equations becomes the correct Boltzmannian equilibrium distribution for given spin I. The relaxation towards the stationary solution is characterized by a set of relaxation times, the longest of which can be shorter, by a factor of up to 2I, than the relaxation time in the corresponding Bloch equations calculated in the standard perturbative way. Comment: 4 pages, Latex, 2 figures
  06/2000;
• Source

  Available from: arxiv.org

  Article: Spin relaxation in quantum Hall systems

  W. Apel, Yu. A. Bychkov
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  ABSTRACT: We study the spin relaxation in an interacting two--dimensional electron gas in a strong magnetic field for the case that the electron density is close to filling just one Landau sub--level of one spin projection, i.e., for filling factor near one. Assuming the relaxation to be caused by scattering with phonons, we derive the kinetic equations for the electron's spin--density which replace the Bloch equations in our case. These equations are non--linear and their solution depends crucially on the filling factor and on the temperature of the phonon bath. In the limit of zero temperature and for filling factor 1, the solution relaxes asymptotically with a power law inversely proportional to time, instead of following the conventional exponential behavior. Comment: 4 pages, 1 figure
  11/1998;
• Source

  Available from: arxiv.org

  Article: Hopf term and the effective Lagrangian for the Skyrmions in a two-dimensional electron gas at small g-factor

  W. Apel, Yu. A. Bychkov
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  ABSTRACT: We study interacting electrons in two dimensions moving in the lowest Landau level under the condition that the Zeeman energy is much smaller than the Coulomb energy and the filling factor is one. In this case, Skyrmion quasiparticles play an important role. Here, we present a simple and transparent derivation of the corresponding effective Lagrangian. In its kinetic part, we find a non-zero Hopf term the prefactor of which we determine rigorously. In the Hamiltonian part, we calculate, by means of a gradient expansion, the Skyrmion-Skyrmion interaction completely up to fourth order in spatial derivatives. Comment: 4 pages, Latex
  10/1996;
• Article: Reply: Apel and Bychkov

  W. Apel, Yu. A. Bychkov