Non-Reciprocal gain in non-Hermitian time-Floquet Systems

We explore the unconventional wave scattering properties of non-Hermitian systems in which amplification or damping are induced by time-periodic modulation. These non- Hermitian time-Floquet systems are capable of non-reciprocal operations in the frequency domain, which can be exploited to induce novel physical phenomena such as unidirectional wave amplification and perfect non-reciprocal response with zero or even negative insertion losses. This unique behavior is obtained by imparting a specific low-frequency time-periodic modulation to the coupling between lossless resonators, promoting only upward frequency conversion, and leading to non-reciprocal parametric gain. We provide a full-wave demonstration of our findings in a one-way microwave amplifier, and establish the potential of non-Hermitian time-Floquet devices for insertion-loss free microwave isolation and unidirectional parametric amplification.Comment: 15 pages, 4 figure

Thin shell implies spectral gap up to polylog via a stochastic localization scheme

We consider the isoperimetric inequality on the class of high-dimensional isotropic convex bodies. We establish quantitative connections between two well-known open problems related to this inequality, namely, the thin shell conjecture, and the conjecture by Kannan, Lovasz, and Simonovits, showing that the corresponding optimal bounds are equivalent up to logarithmic factors. In particular we prove that, up to logarithmic factors, the minimal possible ratio between surface area and volume is attained on ellipsoids. We also show that a positive answer to the thin shell conjecture would imply an optimal dependence on the dimension in a certain formulation of the Brunn-Minkowski inequality. Our results rely on the construction of a stochastic localization scheme for log-concave measures.Comment: 33 page

Parametric amplification and bidirectional invisibility in PT-symmetric time-Floquet systems

Parity-Time (PT) symmetric wave devices, which exploit balanced interactions between material gain and loss, exhibit extraordinary properties, including lasing and flux-conserving scattering processes. In a seemingly different research field, periodically driven systems, also known as time-Floquet systems, have been widely studied as a relevant platform for reconfigurable active wave control and manipulation. In this article, we explore the connection between PT-symmetry and parametric time-Floquet systems. Instead of relying on material gain, we use parametric amplification by considering a time-periodic modulation of the refractive index at a frequency equal to twice the incident signal frequency. We show that the scattering from a simple parametric slab, whose dynamics follow Mathieu equation, can be described by a PT-symmetric scattering matrix, whose PT-breaking threshold corresponds to the Mathieu instability threshold. By combining different parametric slabs modulated out-of-phase, we create PT-symmetric time-Floquet systems that feature exceptional scattering properties, such as CPA/Laser operation and bidirectional invisibility. These bidirectional properties, rare for regular PT-symmetric systems, are related to a compensation of parametric amplification due to multiple scattering between two parametric systems modulated with a phase difference

Resuming motor vehicle driving following orthopaedic surgery or limb trauma.

Following elective orthopaedic surgery or the treatment of a fracture, patients are temporarily unable to drive. This loss of independence may have serious social and economic consequences for the patient. It is therefore essential to know when it is safe to permit such patients to return to driving. This article, based upon a review of the current literature, proposes recommendations of the time period after which patients may safely return to driving. Practical decisions are made based upon the type of surgical intervention or fracture. Swiss legislation is equally approached so as to better define the decision

A model of gravitation with global U(1)-symmetry

It is shown that an embedding of the general relativity $4-$space into a flat $12-$space gives a model of gravitation with the global $U(1)-$symmetry and the discrete $D_{1}-$one. The last one may be transformed into the $SU(2)-$symmetry of the unified model, and the demand of independence of $U(1)-$ and $SU(2)-$transformations leads to the estimate $\sin^{2}\theta_{min}=0,20$ where $\theta_{min}$ is an analog of the Weinberg angle of the standard model.Comment: 7 page

Do metals exist in two dimensions? A study of many-body localisation in low density electron gas

Using a combination of ground state quantum Monte-Carlo and finite size scaling techniques, we perform a systematic study of the effect of Coulomb interaction on the localisation length of a disordered two-dimensional electron gas. We find that correlations delocalise the 2D system. In the absence of valley degeneracy (as in GaAs heterostructures), this delocalization effect corresponds to a finite increase of the localization length. The delocalisation is much more dramatic in the presence of valley degeneracy (as in Si MOSFETSs) where the localization length increases drastically. Our results suggest that a rather simple mechanism can account for the main features of the metallic behaviour observed in high mobility Si MOSFETs. Our findings support the claim that this behaviour is indeed a genuine effect of the presence of electron-electron interactions, yet that the system is not a ``true'' metal in the thermodynamic sense.Comment: 5 pages 4 figure