Search

We study the spectral problem in deformed supersymmetric quantum mechanics with polynomial superpotential by using the exact WKB method and the TBA equations. We apply the ODE/IM correspondence to the Schrödinger equation with an effective potential deformed by integrating out the fermions, which admits a continuous deformation parameter. We find that the TBA equations are described by the ℤ4-extended ones. For cubic superpotential corresponding to the symmetric double-well potential, the TBA system splits into the two D3-type TBA equations. We investigate in detail this example based on the TBA equations and their analytic continuation as well as the massless limit. We find that the energy spectrum obtained from the exact quantization condition is in good agreement with the diagonalization approach of the Hamiltonian. [ABSTRACT FROM AUTHOR]

The angular momentum of any quantum system should be unambiguously quantized. We show that such a quantization fails for a pure Dirac monopole due to a previously overlooked field angular momentum from the monopole-electric charge system coming from the magnetic field of the Dirac string and the electric field of the charge. Applying the point-splitting method to the monopole-charge system yields a total angular momentum which obeys the standard angular momentum algebra, but which is gauge variant. In contrast it is possible to properly quantize the angular momentum of a topological 't Hooft–Polyakov monopole plus charge. This implies that pure Dirac monopoles are not viable – only 't Hooft–Polyakov monopoles are theoretically consistent with angular momentum quantization and gauge invariance. [ABSTRACT FROM AUTHOR]

A Digital-to-Time Converter based (DTC-based) fractional- N digital phase-locked loop (DPLL) using probability-density-shaping (PDS) spur immunity and quantization phase (Q-noise) reduction techniques is presented. PDS-DSM is used to generate a loop spur immunity control code for DTC. A diff type dither is proposed to further suppress the fractional spur. The loop nonlinearity will not cause fractional spurs if certain conditions are obeyed. Moreover, to reduce the quantization noise, a configurable Phase Interpolator (PI) with 0.125/0.25/0.5/1.0 division step is integrated with a multi-module divider (MMDIV), leading to an 18-dB Q-noise suppression. A reference doubler with duty-cycle correction is adopted to further reduce phase noise. The fractional spurs are greatly mitigated by combining the PDS-DSM and phase interpolator. A DPLL prototype using the aforementioned techniques was designed in a 40-nm standard CMOS process, occupying a 0.99 mm2 silicon area. At a near-integer- N frequency, i.e., near 2.23 GHz, with PDS turned on and off, the post-layout simulated fractional spur is −59 dBc and −20 dBc, respectively. The RMS jitter of the whole chip is 4.218 ps, corresponding to a figure of merit (FOM) of −220.5 dB. [ABSTRACT FROM AUTHOR]