Manabu Machida

Temperature Dependence of ESR Intensity for the Nanoscale Molecular Magnet V15

The electron spin resonance (ESR) of nanoscale molecular magnet V 15 is studied. Since the Hamiltonian of V 15 has a large Hilbert space and numerical calculations of the ESR signal evaluating the Kubo formula with exact diagonalization method is difficult, we implement the formula with the help of the random vector technique and the Chebyshev polynominal expansion, which we name the double Chebyshev expansion method. We calculate the temperature dependence of the ESR intensity of V 15 and compare it with the data obtained in experiment. As another complementary approach, we also implement the Kubo formula with the subspace iteration method taking only important low-lying states into account. We study the ESR absorption curve below 100 K by means of both methods. We find that side peaks appear due to the Dzyaloshinsky-Moriya interaction and these peaks grows as temperature decreases.

Temporal Oscillation of Conductances in Quantum Hall Effect of Bloch Electrons

We study a nonadiabatic effect on the conductances in the quantum Hall effect of two-dimensional electrons with a periodic potential. We found that the Hall and longitudinal conductances oscillate in time with very large frequencies due to quantum fluctuation.

Frequency dependence of quantum localization in a periodically driven system

We study the quantum localization phenomena for a random matrix model belonging to the Gaussian orthogonal ensemble (GOE). An oscillating external field is applied on the system. After the transien...

Transient Oscillation of Currents in Quantum Hall Effect of Bloch Electrons

We consider the quantum Hall effect of two-dimensional electrons with a periodic potential and study the time dependence of the Hall and longitudinal currents when the electric field is applied abruptly. We find that the currents oscillate in time with very large frequencies because of quantum fluctuation and the oscillations eventually vanish, for their amplitudes decay as 1=t. atomic gas trapped by a rotating optical lattice. We calcu- late the resulting current with the Kubo formula. 21-24) The linear response theory for an abruptly applied dc field was particularly investigated by Greenwood. 24) We here follow Greenwoods formulation of the linear response theory. An interesting feature of our finding is an observation of fluctuation around the quantized conductivity, which is normally considered a very rigid quantity; we find that the Hall current has a time-dependent correction to the Chern-number term in the TKNN theory. The Hall current jx and the longitudinal current jy oscillate in time with large frequencies because of quantum fluctuation, or oscilla- tion between different subbands. The oscillation eventually ceases and the time-dependent Hall current converges to the Chern-number term of the TKNN theory. The amplitude of the oscillation decays as 1=t. In the previous paper, 20) we already reported the existence of time-dependent correction terms. In the present paper, we present additional calcu- lations particularly on the long-time behavior and on the time-dependent fields under an applied current. This paper is organized as follows. In §2, we derive the currents in the x and y directions following Greenwoods formulation of the linear response theory. We derive the same results as in our previous paper, but under a different gauge. We also mention the correspondence between elec- tron gases in a magnetic field and rotating cold atomic gases. In §3, we show that the time-dependent oscillation of the currents decays as 1=t and eventually ceases, and the Hall current approaches to a certain value obtained from the TKNN theory. Finally we give conclusions. In Appendix, we calculate electric fields under an applied current instead of currents under an applied field. We show that the voltages have similar time dependence.

ESR Intensity and Anisotropy of the Nanoscale Molecular Magnet V15

The low temperature ESR intensity of the nanoscale molecular magnet V15 is studied theoretically. First we numerically obtain the temperature dependence of the intensity. Then we analytically explore the effect of the Dzyaloshinsky‐Moriya interaction on the intensity at zero temperature using the triangle model.