Higher Dimensional SUSY Quantum Mechanics

Higher dimensional supersymmetric quantum mechanics is studied. General properties of the two dimensional case are presented. For three spatial dimesions or higher, a spin structure is shown to arise naturally from the nonrelativistic supersymmetry algebra.Comment: 8 pages, Late

On the Divergence of Perturbation Theory: Steps Towards a Convergent Series

The mechanism underlying the divergence of perturbation theory is exposed. This is done through a detailed study of the violation of the hypothesis of the Dominated Convergence Theorem of Lebesgue using familiar techniques of Quantum Field Theory. That theorem governs the validity (or lack of it) of the formal manipulations done to generate the perturbative series in the functional integral formalism. The aspects of the perturbative series that need to be modified to obtain a convergent series are presented. Useful tools for a practical implementation of these modifications are developed. Some resummation methods are analyzed in the light of the above mentioned mechanism

Quantum transport on small-world networks: A continuous-time quantum walk approach

We consider the quantum mechanical transport of (coherent) excitons on small-world networks (SWN). The SWN are build from a one-dimensional ring of N nodes by randomly introducing B additional bonds between them. The exciton dynamics is modeled by continuous-time quantum walks and we evaluate numerically the ensemble averaged transition probability to reach any node of the network from the initially excited one. For sufficiently large B we find that the quantum mechanical transport through the SWN is, first, very fast, given that the limiting value of the transition probability is reached very quickly; second, that the transport does not lead to equipartition, given that on average the exciton is most likely to be found at the initial node.Comment: 8 pages, 8 figures (high quality figures available upon request

Waveguide integrated superconducting single-photon detectors with high internal quantum efficiency at telecom wavelengths

Superconducting nanowire single-photon detectors (SNSPDs) provide high efficiency for detecting individual photons while keeping dark counts and timing jitter minimal. Besides superior detection performance over a broad optical bandwidth, compatibility with an integrated optical platform is a crucial requirement for applications in emerging quantum photonic technologies. Here we present SNSPDs embedded in nanophotonic integrated circuits which achieve internal quantum efficiencies close to unity at 1550 nm wavelength. This allows for the SNSPDs to be operated at bias currents far below the critical current where unwanted dark count events reach milli-Hz levels while on-chip detection efficiencies above 70% are maintained. The measured dark count rates correspond to noise-equivalent powers in the 10-19 W/Hz-1/2 range and the timing jitter is as low as 35 ps. Our detectors are fully scalable and interface directly with waveguide-based optical platforms

Functional changes in the lower extremity after non-immersive virtual reality and physiotherapy following stroke

Objective: To analyse the effect of virtual reality (VR) therapy combined with conventional physiotherapy on balance, gait and motor functional disturbances, and to determine whether there is an influence on motor recovery in the subacute (< 6 months) or chronic (> 6 months) phases after stroke. Methods: A total of 59 stroke inpatients (mean age 60.3 years (standard deviation (SD) 14.8); 14.0 months (SD 25.7) post-stroke) were stratified into 2 groups: subacute (n = 31) and chronic (n = 28). Clinical scales (Fugl-Meyer lower extremity (FM LE); Functional Independence Measure (FIM); Berg Balance Scale (BBS); Functional Ambulation Category (FAC); modified Ashworth scale (MAS); 10-metre walk test (10MWT); and kinematic parameters during specific motor tasks in sitting and standing position (speed; time; jerk; spatial error; length) were applied before and after treatment. The VR treatment lasted for 15 sessions, 5 days/week, 1 h/day. Results: The subacute group underwent significant change in all variables, except MAS and length. The chronic group underwent significant improvement in clinical scales, except MAS and kinematics. Motor impairment improved in the severe = 19 FM LE points, moderate 20-28 FM LE points, mild = 29 FM LE points. Neither time since stroke onset nor affected hemisphere differed significantly between groups. The correlations were investigated between the clinical scales and the kinematic parameters of the whole sample. Moreover, FM LE, BBS, MAS, and speed showed high correlations (R2> 0.70) with independent variables. Conclusion: VR therapy combined with conventional physiotherapy can contribute to functional improvement in the subacute and chronic phases after stroke

Frequency and phase noise of ultra-high Q silicon nitride nanomechanical resonators

We describe the measurement and modeling of amplitude noise and phase noise in ultra-high Q nanomechanical resonators made from stoichiometric silicon nitride. With quality factors exceeding 2 million, the resonators' noise performance is studied with high precision. We find that the amplitude noise can be well described by the thermomechanical model, however, the resonators exhibit sizable extra phase noise due to their intrinsic frequency fluctuations. We develop a method to extract the resonator frequency fluctuation of a driven resonator and obtain a noise spectrum with dependence, which could be attributed to defect motion with broadly distributed relaxation times