Resonance Triadic Quantum Switch

This research investigates a number of problems, related to Stokes flow and to heat flow. The Stokes flow is inspired by glass flow in the process of making bottles or jars. The heat flow is related to a heat conduction model problem, and a problem about hot-spots formation in the microwave heating. We will discuss the first problem. There are two phases during the industrial process of making glass, viz. the pressing phase and the blowing phase. We consider some mathematical aspects of the pressing phase. The motion of glass at temperatures above 6000C can be described by the Navier-Stokes equations. Since glass is a highly viscous fluid, those equations can be simplified to the Stokes equations. We use two different methods to solve these equations, viz. perturbation and operator methods. The perturbation method is based on the geometry being slowly varying. As a result, we obtain the velocity analytically. This result has a good agreement with numerical results based on finite element modelling. Using the velocity obtained we derive the formula for the force on the plunger. Next, we consider the operator method. Using this method, the Stokes equations can be transformed into an operator equation on the boundary ??? with a tangent vector field a on the boundary ??? as unknown. Solving this operator equation shows, that the solutions of the Stokes equations can be parameterized by aH, the harmonic extension of a to the interior of the domain ??. As an application, we present some full explicit solutions of the Stokes equations for several domains such as the interior and exterior of the unit ball and of the unit disk, an infinite strip, a half space, and a wedge. In the second problem, we consider the heat conduction problem inside two types of geometry, viz. slowly and slightly varying geometry. Using this problem, we show the difference between those geometries. An example that involves the boundary layers at the ends is presented. Finally, we consider a simplified model of the microwave heating of a one-dimensional unit slab. This slab consists of three layers that have different thermal conductivities. We consider only the steady state problem with Dirichlet boundary conditions and continuity of heat flux across the layers. Using a fundamental-mode approximation of eigenfunction expansion, we investigate the effect of thermal conductivity on the formation of hot-spots where the temperature increases catastrophically as a function of d, the amplitude of the applied electric field. First, we consider a unit slab geometry. In this geometry, we find the critical value dcr, for which slight changes in d yields a sudden jump to another stable solution, now with a much higher temperature. Next, we consider a unit slab consisting of three layers of material with different thermal conductivity (µ). We assume the inner layer has the smallest value of µ. We find the temperature in this layer is much higher than that in other layers. Then, we consider only the inner layer. For a given value of d and changing values of µ, we get a temperature jump near some values of µ. This jump shows that there is a critical value of µ and signifies the formation of a hot-spot.

Range and magnitude of electric fields at biomolecular interfaces and their fluctuations in a time window down to the subpicosecond regime have remained controversial, calling for electric-field mapping in space and time. Here, we trace fluctuating electric fields at the surface of native salmon DNA via their interactions with backbone vibrations in a wide range of hydration levels by building the water shell layer by layer. Femtosecond two-dimensional infrared spectroscopy and ab initio based theory establish water molecules in the first two layers as the predominant source of interfacial electric fields, which fluctuate on a 300 fs time scale with an amplitude of 25 MV/cm due to thermally excited water motions. The observed subnanometer range of these electric interactions is decisive for biochemical structure and function.

The effect of an external electric field on the quark matter is an important question due to the presence of strong electric fields in heavy ion collisions. In the lattice QCD approach, the case of a real electric field suffers from the `sign problem', and a classical electric field is often used similar as the case of chemical potential. Interestingly, in axial gauge a uniform classical electric field actually can correspond to an inhomogeneous imaginary chemical potential that varies with coordinate. On the other hand, with imaginary chemical potential, Roberge-Weiss~(R-W) phase transition occurs. In this work, the case of a uniform classical electric field is studied by using lattice QCD approach, with the emphasis on the properties of the R-W phase. Novel phenomena show up at high temperatures. It is found that, the chiral condensation oscillates with $z$ at high temperatures, and so is the absolute value of the Polyakov loop. It is verified that the charge density also oscillates with $z$ at high temperatures. The Polyakov loop can be described by an ansatz $A_p+\sum _{q=u,d} C_q\exp\left(L_τ Q_q iazeE_z\right)$, where $A_p$ is a complex number and $C_d>0,C_u\geq 0$ are real numbers that are fitted for different temperatures and electric field strengths. As a consequence, the behavior of the phase of Polyakov loop is different depending on whether the Polyakov loop encloses the origin, which implies a possible phase transition.

We study the adiabatic evolution of a two-level model in the presence of an external classical electric field. The coupling between the quantum model and the classical field is taken in the electric dipole approximation. In this regime, we show the absence of geometric phases in the interacting two-level model in the presence of any periodic real time-dependent classical electric field. We obtain a conservative scalar potential in the calculation of Berry's phases of the instantaneous eigenstates of the model. For complex electric fields, we recover the existence of geometric phases. In particular, the geometric phases of the instantaneous eigenstates of the model in the presence of a positive or of a negative frequency component of the monochromatic electric field differ by an overall sign. As a check on our results, we map this interacting two-level model onto a spin-1/2 model under the action of a classical magnetic field. We confirm that the first one acquires Berry's phase only in the rotating wave approximation [RWA].

The aim of this paper is to establish the asymptotic expansion of the eigenvalues of the Stark Hamiltonian, with a strong uniform electric field and Dirichlet boundary conditions on a smooth bounded domain of [Formula: see text], [Formula: see text]. This work aims at generalizing the recent results of Cornean, Krejčiřik, Pedersen, Raymond, and Stockmeyer in dimension 2. More precisely, in dimension N, in the strong electric field limit, we derive, under certain local convexity conditions, a full asymptotic expansion of the low-lying eigenvalues. To establish our main result, we perform the construction of quasi-modes. The “optimality” of our constructions is then established thanks to a reduction to model operators and localization estimates.

In the present note we give a simpler proof of the recent result of Hedenmalm that the Green function for the weighted biharmonic operator ∆|z| 2α ∆, α > -1, on the unit disc D with the Dirichlet boundary conditions is positive.The main ingredient, which in the special case of the unweighted biharmonic operator ∆ 2 is due to Loewner and which is of an independent interest, is a lemma characterizing, for a positive C 2 weight function w, the second-order linear differential operators which take any function u satisfying ∆w -1 ∆u = 0 into a harmonic function.Another application of this lemma concerning positivity of the Poisson kernels for the biharmonic operator ∆ 2 is also given.

The Hénon problem with large exponent in the disc

Controllability of a 2D quantum particle in a time-varying disc with radial data

It is theoretically proved that the excited wave in two-valley semiconductors is growing. It is indicated that the directions of external fields play an essential role for the appearance of growing waves in the sample. It is shown that oscillations can occur at certain values of the sample dimensions L ,L ,L x y z Analytical formulas for the frequency of the growing waves are obtained. The interval of variation of the external electric field in a strong magnetic field μH>>c has been determined. The paper takes into account that the time of transition from the lower valley to the upper valley differs from the time of transition from the upper valley to the lower valley. It means τ12≠τ21 In the sample, the total concentration is constant, and therefore, n0=na+nb=const. The changes in the corresponding concentrations are equal to each other and have na'=-nb'. It is taken into account that at critical values of the electric and magnetic fields and the corresponding concentrations they change as a monochromatic wave. And the change in these quantities differs little from their equilibrium value. For simplicity of mathematical calculations, the external electric and magnetic fields are directed in the same way, i.e. in x direction. Since the current oscillations in one direction (for example, along x) are studied in the experiment, the following equalities were taken into account jy'=0, jz'=0. In the vicinity of the critical field at the beginning of the current oscillation in the sample, the current oscillation frequency is ϖ=ϖ0+iϖ1, ϖ1<<ϖ0. In addition, the magnitude of the critical electric field, at which the current fluctuation changes depending on the magnetic field as follows .

A matrix-free Chimera approach based on Dirichlet–Dirichlet coupling for domain composition purposes

Microwave breast hyperthermia is a noninvasive treatment method for breast cancer that utilizes microwave energy (ME) sources to raise tissue temperatures above 42 , inducing tumor cell necrosis. The efficiency of ME deposition depends on the electric field magnitude and tissue conductivity, with antenna phase and amplitude adjustments used to maximize the electric field magnitude within tumors. Achieving precise ME focusing in the complex and heterogeneous breast tissue is challenging and can lead to unwanted hot spots in normal tissue. This study presents a novel method for optimizing ME focusing on the center of target tumors, using a simplified calculation of antenna phases, heuristic optimization for antenna amplitudes, and realistic breast phantoms for performance evaluation. In this work, we propose an approach to optimize the microwave hyperthermia system, employing phase and amplitude modulation techniques to concentrate the electric field at the center of a malignant tumor within a breast medium. The approach uses line sources arranged in a circular pattern around realistic breast models. The method begins by determining the phase, followed by adjusting the amplitudes of each source in order to maximize the total electric field at the tumor's center. The goal is to maximize the electric field at the tumor center while minimizing the optimization cost andcomplexity. Simulations are performed at 4 GHz frequency using two different types of digital breast phantoms (fatty and dense breasts) as test beds. The algorithm is tested by using three quantities; that is, the electric field distribution, the power density distribution, and the temperature distribution inside the whole breast region. The electric field and power density are calculated using an in-house method of moments (MoM) algorithm, while the temperature distributions are obtained with computer simulation technology (CST) software. To further evaluate the method with quantitative measures of success, thermal indices are calculated for each phantom andmethod. The specific absorbtion rate (SAR) results and corresponding temperature distributions for each breast type and optimization demonstrate that effective focusing is achieved in both cases. However, the combined phase-amplitude optimization provides more precise focusing by eliminating hot spots. Among thermal indices, the TC75 and T90 values obtained from the phase-amplitude combined optimization for both breast types outperform the results found in the literature. The T50 values obtained using the combined optimization are above 42 . This study presents an optimization method for focusing ME within breast tissue, performed in two steps: first phase optimization, followed by amplitude optimization. The electric field calculations are performed using both the MoM and Finite Difference Time Domain methods. The technique is numerically tested on two realistic breast models, with thermal indices calculated for each phantom and optimization process. Results show T90 values exceeding 40 and T50 values above 42 . While the study employs a 2D applicator, it provides a strong foundation for future development in 3Dapplications.

In this work, we develop a new technique for the numerical study of quantum field theory. The procedure, borrowed from non-relativistic quantum mechanics, is that of finding the eigenvalues of a finite Hamiltonian matrix. The matrix is created by evaluating the matrix elements of the Hamiltonian operator on a finite basis of states. The eigenvalues and eigenvectors of the finite dimensional matrix become an accurate approximation to those of the physical system as the finite basis of states is extended to become more complete. We study a model of scalars coupled to fermions in 0+1 dimensions as a simple field theory to consider in the course of developing the technique. We find in the course of studying this model a change of basis which diagonalizes the Hamiltonian in the large coupling limit. The importance of this transformation is that it can be generalized to higher dimensional field theories involving a trilinear coupling between a Bose and a Fermi field. Having developed the numerical and analytical techniques, we consider a Fermi field coupled to a Bose field in 1+1 dimensions with the Yukawa coupling λΨΨΨ. We extend the large coupling limit basis of the 0+1 dimensional model to this case using a Bogoliubov transformation on the fermions. Although we do not use this basis in the numerical work due to its complexity, it provides a handle on the behavior of the system in the large coupling limit. In this model we consider the effects of renormalization and the generation of bound states.

In this study, we investigate the scope of molybdenum disulfide (MoS2) as an electric field sensor. We show that MoS2 sensors can be used to identify the polarity as well as to detect the magnitude of the electric field. The response of the sensor is recorded as the change in the drain current when the electric field is applied. The sensitivity, defined as the percentage change in the drain current, reveals that it has a linear relation with the magnitude of the electric field. Furthermore, the sensitivity is highly dependent on the layer thickness, with the single-layer device being highly sensitive and the sensitivity decreasing with the thickness. We have also compared the electric field sensitivity of MoS2 devices to that of previously studied graphene devices and found the former to be exceptionally sensitive than the latter for a given electric field magnitude.

We consider the grand canonical partition function for the ordered one-dimensional, two-component plasma at fugacityζ in an applied electric fieldE with Dirichlet boundary conditions. The system has a phase transition from a low-coupling phase with equally spaced particles to a high-coupling phase with particles clustered into dipolar pairs. An exact expression for the partition function is developed. In zero applied field the zeros in theζ plane occupy the imaginary axis from −i∞ to −iζc and iζc to i∞ for some ζc. They also occupy the diamond shape of four straight lines from ±iζc to ζc and from ±iζc to −ζc. The fugacityζ acts like a temperature or coupling variable. The symmetry-breaking field is the applied electric fieldE. A finite-size scaling representation for the partition in scaled coupling and scaled electric field is developed. It has standard mean field form. When the scaled coupling is real, the zeros in the scaled field lie on the imaginary axis and pinch the real scaled field axis as the scaled coupling increases. The scaled partition function considered as a function of two complex variables, scaled coupling and scaled field, has zeros on a two-dimensional surface in a domain of four real variables. A numerical discussion of some of the properties of this surface is presented.

Electric fields in the ionosphere and the excitation of the red lines of atomic oxygen