The critical values of coupling strength of the non-self-dual Ising lattices under decimation transformation

In this work, the values of critical coupling strengths of the Ising lattices which are changing their lattice structure (or non-self-dual) under decimation transformations, such as the honeycomb, the triangular and the body centered cubic Ising lattices, are obtained by a modified real space renormalization group approach (RSRG). This modification is necessary to obtain a proper relation between the coupling strengths of the original and the decimated lattices. Indeed, we have achieved to obtain a proper renormalized coupling strength relation for honeycomb and triangular lattices readily, since the decimation transformation of the honeycomb lattice produces the triangular lattice or vice versa. Here, the problem of having physically untractable interactions between degrees of freedom in the renormalized Hamiltonian, which leads eventually to inevitable approximations in the treatment, except for the 1D Ising chain, has been solved with a proper approximation. Especially for the 3D Ising lattices, the physically untractable interactions appearing in the renormalized Hamiltonian make the mathematical treatment too cumbersome. As a result, there is not enough research dealing with the 3D Ising lattices using RG theory. Our approximation is based on using the simple relation [Formula: see text], which is, of course, a very relevant first-order approximation, if [Formula: see text]. With the help of this approximation, decimation transformation process produces only pairwise interactions in the renormalized Hamiltonian instead of having four spins, six spins, or even eight spin interactions which appear naturally if all the terms are kept in the renormalized Hamiltonians of the Ising lattices in 2D and higher dimensions. Without this approximation, one cannot apply analytic RG treatment feasibly to even simple cubic lattice, let alone applying it to the body centered cubic lattice. Using this modified RG approach, the values of critical coupling strengths of the honeycomb, the triangular and the body centered cubic Ising lattices are obtained analytically as [Formula: see text], [Formula: see text] and [Formula: see text] respectively. Apparently, these estimations are really close to the results obtained from cumbersome exact treatments which are [Formula: see text], [Formula: see text] and [Formula: see text] for the honeycomb, the triangular and the body centered cubic lattices.

Critically coupled Fabry–Perot cavity with high signal contrast for refractive index sensing

Perfect absorption at a resonance wavelength and extremely low absorption at the wavelength range of off-resonance in a one-port optical cavity is required for refractive index (RI) sensing with high signal contrast. Here, we propose and analyze an absorption-enhanced Fabry–Perot (MAFP) cavity based on a critical coupling condition in a near-infrared wavelength range. For a one-port cavity, a thick bottom Au is used as a mirror and an absorber. To achieve the critical coupling condition, a top dielectric metasurface is employed and tailored to balance the radiation coupling and the absorption coupling rates, and the one-port cavity is theoretically analyzed using temporal coupled-mode theory. We investigate two types of MAFP structures for gas and liquid. The gas MAFP cavity shows a sensitivity of ~ 1388 nm/RIU and a full-width at half-maximum of less than 0.7 nm. This MAFP cavity resolves the RI change of 5 × 10−4 with a reflectance signal margin of 50% and achieves a signal contrast of ~ 100%. The liquid MAFP cavity shows a sensitivity of ~ 996 nm/RIU when RI of liquid changes from 1.30 to 1.38. With tailoring the period of the metasurface maintaining its thickness, a signal contrast of ~ 100% is achieved for each specific RI range.

About theory of extended interaction klystron and drift space in the form of medium with complex permittivity

Purpose of this work is to construct a theory of extended interaction klystron with ordinary distributed resonators, but with a drift space in the form of medium with complex permittivity. Methods. For this, a hybrid of extended interaction klystron and an amplifier with a complex permittivity is considered in the framework of the weak signal approximation. Two types of configurations of a extended interaction klystron were considered: with two and three distributed resonators. For a two-resonator klystron with distributed interaction, two cases are considered: without reflections from the ends of distributed resonators and the case when the input binder is fully matched to the external transmission line, and for the second distributed resonator, the so-called condition of critical coupling of the “hot” resonator with the transmission line is satisfied. For a three-resonator klystron with distributed interaction, the case is considered without reflections from the ends of distributed resonators. Results and conclusion. According to the results of the developed theory of a weak signal in a extended interaction klystron with ordinary distributed resonators and a drift space with a complex dielectric constant, by choosing the parameters, it is possible to achieve a greater gain at a length that is shorter than in a conventional extended interaction klystron, all other things being equal. In addition, the presence of an intermediate distributed resonator makes it possible to increase the gain while maintaining the full length of the device.

Dielectric Coupler for General Purpose Q-Band EPR Cavity

Here, we report on a robust and efficient mechanism for tuning the microwave coupling of a Q-band (34 GHz), general purpose, cylindrical EPR cavity operating in the TE011 mode. This novel mechanism allows for both the adjustment of the cavity’s coupling over a wide frequency range, as well as its bandwidth from that of a high-Q cavity (about 10 MHz), to a broadband cavity (above 1 GHz). The coupling element consists of a dielectric plate fixed onto a movable waveguide short that allows for two modes of operation. In the first mode, the dielectric plate does not influence the resonance properties of the coupling iris and allows for precise, critical coupling of the high-Q cavity. In the second mode, the dielectric plate is positioned in front of the coupling iris, varying the iris’ resonance properties and allowing very strong overcoupling to be achieved. This mechanism can be generalized for other types of EPR cavities, in particular at high microwave frequencies.

High-Q-Factor Tunable Silica-Based Microring Resonators

A high-Q-factor tunable silica-based microring resonator (MRR) is demonstrated. To meet the critical-coupling condition, a Mach–Zehnder interferometer (MZI) as the tunable coupler was integrated with a racetrack resonator. Then, 40 mW electronic power was applied on the microheater on the arm of MZI, and a maximal notch depth of about 13.84 dB and a loaded Q factor of 4.47 × 106 were obtained. The proposed MRR shows great potential in practical application for optical communications and integrated optics.

Critical behavior of the 2d scalar theory: resumming the N8LO perturbative mass gap

We apply the optimized perturbation theory (OPT) to resum the perturbative series describing the mass gap of the bidimensional ϕ4 theory in the ℤ2 symmetric phase. Already at NLO (one loop) the method is capable of generating a quite reasonable non-perturbative result for the critical coupling. At order-g7 we obtain gc = 2.779(25) which compares very well with the state of the art N8LO result, gc = 2.807(34). As a novelty we investigate the supercritical region showing that it contains some useful complimentary information that can be used in extrapolations to arbitrarily high orders.

Deciphering the spectral collapse in two-photon Rabi model

In this communication, based upon a squeezed-state trial wave function, we have performed a simple variational study of the spectral collapse of the two-photon Rabi model. Our analysis indicates that the light-matter interaction and the spin-flipping effectively constitute two competing impacts upon the radiation mode. Whilst the former tries to decrease the radiation mode frequency, the latter may counteract or reinforce it, contingent upon the state of the atomic system. The light–matter interaction appears to dominate the frequency modulation as its coupling strength goes beyond the critical value, leading to the emergence of the spectral collapse. However, at the critical coupling the dominance of the light–matter interaction is not complete, and incomplete spectral collapse appears. The extent of incomplete spectral collapse is found to depend upon the energy difference between the two atomic levels as well.