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I review the four mechanisms of bound states in the continuum (BICs) in the application of microwave and acoustic cavities open to directional waveguides. The most simple are symmetry-protected BICs, which are localized inside the cavity because of the orthogonality of the eigenmodes to the propagating modes of waveguides. However, the most general and interesting is the Friedrich-Wintgen mechanism, when the BICs are the result of the fully destructive interference of outgoing resonant modes. The third type of BICs, Fabry-Perot BICs, occurs in a double resonator system when each resonator can serve as an ideal mirror. Finally, the accidental BICs can be realized in the open cavities with no symmetry like the open Sinai billiard in which the eigenmode of the resonator can become orthogonal to the continuum of the waveguide accidentally due to a smooth deformation of the eigenmode. We also review the one-dimensional systems in which the BICs occur owing to the fully destructive interference of two waves separated by spin or polarization or by paths in the Aharonov-Bohm rings. We make broad use of the method of effective non-Hermitian Hamiltonian equivalent to the coupled mode theory, which detects BICs by finding zero-width resonances.
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Coupling of two dielectric wires with a rectangular cross section gives rise to bonding and anti-bonding resonances. The latter is featured by extremal narrowing of the resonant width for variation of the aspect ratio of the cross section and distance between wires. A plane wave resonant to this anti-bonding resonance gives rise to unprecedent enhancement of the optical forces up to several nano Newtons per micrometer length of the wires. The forces oscillate with the angle of incidence of the plane wave but always try to repel the wires. If the wires are fixed at the ends, the light power 1.5mW/µm2 bends wires with length 50 µm by order 100 nm.
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A non-coaxial waveguide composed of a cylindrical resonator of radius R and cylindrical waveguides with the radii r1 and r2, respectively, is considered. The radii satisfy the inequality r1
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We consider reflection of the Laguerre-Gaussian light beams by a dielectric slab. In view of the unified operator approach, the higher-order Laguerre-Gaussian beams represent a parametric family with the transverse beam profile given by an arbitrary generating parameter. Relying on the Fourier expansion in the focal plane of the beam, we compute the Goos-Hänchen and the Imbert-Fedorov shifts for light beams with non-zero order and azimuthal index. It is demonstrated that both shifts exhibit resonant behavior as functions of the angle of incidence due to the interference between the waves reflected from the upper and lower interfaces. The centroid shifts strongly depend on the order and azimuthal index of the beam. Most interestingly, it is found that the generating parameter of the higher-order beam families strongly affects the shifts. Thus, reshaping of the incident wavefront with fixed order and azimuthal index changes the linear Goos-Hänchen shift up to one half of the beam radius, both negative and positive.
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We present propagating Bloch bound states in the radiation continuum with orbital angular momentum in an infinite linear periodical array of dielectric spheres. The bound states in the continuum demonstrate a giant Poynting vector spiraling around the array. They can be excited by a plane wave with incident linear polarization with a small tilt relative to the axis of the array.
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We study wave transmission through a Fabry-Perot resonator (FPR) loaded with point-like impurities. We show both analytically in the framework of the coupled mode theory and numerically that there are two different regimes for transmission dependent on the quality of the FPR mirrors. For low quality, we obtain transmittance very similar to the clean FPR with slightly shifted Lorentz peaks. However, for good quality, the transmittance peaks are strongly reduced and substituted with Gaussian peaks because of multiple scattering of waves by each impurity. As a side effect, we observe the angular (channel) conversion in the disordered FPR. We demonstrate that the resonant peaks are dependent on the concentration of impurities to pave a way for resonant measurement of the concentration.
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We consider the trapping of electrons with a definite spin polarization by bound states in the continuum (BSC) in the open Aharonov-Bohm rings in the presence of the Rashba spin-orbit interaction (RSOI). Neglecting the Zeeman term we show the existence of BSCs in the one-dimensional ring when the eigenstates of the closed ring are doubly degenerate. With account of the Zeeman term BSCs occur only at the points of threefold degeneracy. The BSCs are found in the parametric space of flux and RSOI strength in close pairs with opposite spin polarization. Thereby the spin polarization of electrons transmitted through the ring can be altered by minor variation of magnetic or electric field at the vicinity of these pairs. Numerical simulations of the two-dimensional open ring show similar results for the BSCs. Encircling the BSC points in the parametric space of the flux and the RSOI constant gives rise to a geometric phase.
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We consider quantum transmission through double-bend [Formula: see text]- and Z-shaped waveguides controlled by the finger gate potential. Using the effective non-Hermitian Hamiltonian approach we explain the resonances in transmission. We show a difference in transmission in the short waveguides that is the result of different chirality in Z and [Formula: see text] waveguides. We demonstrate that the potential selectively affects the resonant widths resulting in the occurrence of bound states in the continuum.
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We consider a system of two or four nonlinear sites coupled with binary chain waveguides. When a monochromatic wave is injected into the first (symmetric) propagation channel, the presence of cubic nonlinearity can lead to symmetry breaking, giving rise to emission of antisymmetric wave into the second (antisymmetric) propagation channel of the waveguides. We found that in the case of nonlinear plaquette, there is a domain in the parameter space where neither symmetry-preserving nor symmetry-breaking stable stationary solutions exit. As a result, injection of a monochromatic symmetric wave gives rise to emission of nonsymmetric satellite waves with energies differing from the energy of the incident wave. Thus, the response exhibits nonmonochromatic behavior.
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The Feshbach projection formalism is applied to consider quantum transmission through a tight-binding wire subject to a time-periodic potential. The wire is coupled with two leads via the coupling constant v{C}. The periodicity of the potential implies an additional temporal dimension that reduces the problem to stationary transmission through an effectively two-dimensional lattice system. The non-Hermitian effective Hamiltonian is formulated. This allows us to trace the redistribution of resonance positions and resonance widths with the growth of v{C} from the weak-coupling to the strong-coupling regime.
Assuntos
Transporte de Elétrons , Modelos Químicos , Modelos Estatísticos , Pontos Quânticos , Simulação por Computador , Campos EletromagnéticosRESUMO
We consider the nodal points (NPs) u=0 and v=0 of the in-plane vectorial displacements u=(u,v) which obey the Navier-Cauchy equation. Similar to the Berry conjecture of quantum chaos, we present the in-plane eigenstates of chaotic billiards as the real part of the superposition of longitudinal and transverse plane waves with random phases. By an average over random phases we derive the mean density and correlation function of NPs. Consequently we consider the distribution of the nearest distances between NPs.
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This paper reports on a joint theoretical and experimental study of the Pauli quantum-mechanical stress tensor T_{alphabeta}(x,y) for open two-dimensional chaotic billiards. In the case of a finite current flow through the system the interior wave function is expressed as psi=u+iv . With the assumption that u and v are Gaussian random fields we derive analytic expressions for the statistical distributions for the quantum stress tensor components T_{alphabeta} . The Gaussian random field model is tested for a Sinai billiard with two opposite leads by analyzing the scattering wave functions obtained numerically from the corresponding Schrödinger equation. Two-dimensional quantum billiards may be emulated from planar microwave analogs. Hence we report on microwave measurements for an open two-dimensional cavity and how the quantum stress tensor analog is extracted from the recorded electric field. The agreement with the theoretical predictions for the distributions for T_{alphabeta}(x,y) is quite satisfactory for small net currents. However, a distinct difference between experiments and theory is observed at higher net flow, which could be explained using a Gaussian random field, where the net current was taken into account by an additional plane wave with a preferential direction and amplitude.
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We consider numerically the L-, T-, and X-shaped elastic waveguides with the Dirichlet boundary conditions for in-plane deformations (displacements) which obey the vectorial Navier-Cauchy equation. In the X-shaped waveguide we show the existence of a doubly degenerate bound state with frequency below the first symmetrical cutoff frequency, which belongs to the two-dimensional irreducible representation E of symmetry group C(4upsilon). Moreover the next bound state is below the next antisymmetric cutoff frequency. This bound state belongs to the irreducible representation A2. The T-shaped waveguide has only one bound state while the L-shaped one has no bound states.
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We consider the effective Hamiltonian of an open quantum system, its biorthogonal eigenfunctions phi(lambda), and define the value r(lambda)=(phi(lambda)|phi(lambda))/
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We consider two electric RLC resonance networks that are equivalent to quantum billiards. In a network of inductors grounded by capacitors, the eigenvalues of the quantum billiard correspond to the squared resonant frequencies. In a network of capacitors grounded by inductors, the eigenvalues of the billiard are given by the inverse of the squared resonant frequencies. In both cases, the local voltages play the role of the wave function of the quantum billiard. However, unlike for quantum billiards, there is a heat power because of the resistance of the inductors. In the equivalent chaotic billiards, we derive a distribution of the heat power which describes well the numerical statistics.
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We show that the wave function and current statistics in chaotic Robnik billiards crucially depend on the constant of the spin-orbit interaction (SOI). For small constant the current statistics is described by universal current distributions derived for slightly opened chaotic billiards [Saichev et al., J. Phys. A 35, L87 (2002)] although one of the components of the spinor eigenfunctions is not universal. For strong SOI both components of the spinor eigenstate are complex random Gaussian fields. This observation allows us to derive the distributions of spin-orbit persistent currents which well describe numerical statistics. For intermediate values of the statistics of the eigenstates and currents, both are deeply nonuniversal.
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Transport through quantum and microwave cavities is studied by analytic and numerical techniques. In particular, we consider the statistics for a finite net probability current (Poynting vector)
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We consider the statistics of currents for electron (microwave) transmission through rectangular and circular billiards. For the resonant transmission the current distribution is describing by the universal distribution [J. Phys. A 35, L87 (2002)]]. For the more typical case of nonresonant transmission the current statistics reveals features of the current channeling (corridor effect) interior of the billiard. The numerical statistics is compared with analytical distributions.
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The translational and orientation order of arg-cysteamine molecules chemiabsorbed on the Au(111) crystal surface is considered. Couplings between carbon, nitrogen, and hydrogen atoms of the n-alkanethiols are approximated by the Lennard-Jones potential. Moreover, hydrogen bonds between oxygen and nitrogen and dipole-dipole interactions of the dipole moments of different atomic groups are taken into account. It is found that molecules are arranged in a 2 x 2 lattice and have the total symmetry C6 x Z2. The critical temperature of the phase transition to the tilted state Tc1, which breaks the symmetry C6, is estimated to be extremely high. The spontaneous breakdown of the remaining symmetry Z2 leads to the twisted state of the molecules and has the critical temperature Tc2=340 K.
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We have calculated the F=1 ground state of a spinor Bose-Einstein condensate trapped harmonic potential with an applied Ioffe-Pitchard magnetic field. The vortex phase diagram is found in the plane spanned by perpendicular and longitudinal magnetic fields. The ferromagnetic condensate has two vortex phases which differ by winding number in the spinor components. The two vortices for the F(z)=-1 antiferromagnetic condensate are separated in space. Moreover, we considered an average local spin |