Interference Energy Spectrum of the Infinite Square Well

Certain superposition states of the 1-D infinite square well have transient zeros at locations other than the nodes of the eigenstates that comprise them. It is shown that if an infinite potential barrier is suddenly raised at some or all of these zeros, the well can be split into multiple adjacent infinite square wells without affecting the wavefunction. This effects a change of the energy eigenbasis of the state to a basis that does not commute with the original, and a subsequent measurement of the energy now reveals a completely different spectrum, which we call the {interference energy spectrum} of the state. This name is appropriate because the same splitting procedure applied at the stationary nodes of any eigenstate does not change the measurable energy of the state. Of particular interest, this procedure can result in measurable energies that are greater than the energy of the highest mode in the original superposition, raising questions about the conservation of energy akin to those that have been raised in the study of superoscillations. An analytic derivation is given for the interference spectrum of a given wavefunction $\Psi(x,t)$ with $N$ known zeros located at points $s_i = (x_i, t_i)$. Numerical simulations were used to verify that a barrier can be rapidly raised at a zero of the wavefunction without significantly affecting it. The interpretation of this result with respect to the conservation of energy and the energy-time uncertainty relation is discussed, and the idea of alternate energy eigenbases is fleshed out. The question of whether or not a preferred discrete energy spectrum is an inherent feature of a particle's quantum state is examined.Comment: 26 Pages, 5 Figure

Above-well, Stark, and potential-barrier resonances of an open square well in a static external electric field

Besides the well known Stark resonances, which are localized in the potential well and tunnel through the potential barrier created by the dc-field, "strange" long and short-lived resonances are analytically obtained. These resonances are not localized inside the potential well. We show that the narrow ones are localized above the potential well. These narrow resonances give rise to a {\it peak structure} in a 1D scattering experiment. We also show that the broad overlapping resonances are associated with the static electric field potential barrier. These "strange" overlapping resonances do not give rise to a {\it peak structure} in a 1D scattering experiment. We propose a 2D experimental set-up where in principle these short-lived states should be observed as {\it peaks}. Broad overlapping resonances, associated only with the static electric field potential barrier, could also have observable effects in a $N>1$ array of quantum wells in the presence of a truncated static electric field. This last problem is associated with the resonance tunnelling phenomena which are used in the construction of resonance-tunnelling diodes and transistors.Comment: submitted to Phys. Rev. A, April 08 200

Superconducting Quantum Interference in Fractal Percolation Films. Problem of 1/f Noise

An oscillatory magnetic field dependence of the DC voltage is observed when a low-frequency current flows through superconducting Sn-Ge thin-film composites near the percolation threshold. The paper also studies the experimental realisations of temporal voltage fluctuations in these films. Both the structure of the voltage oscillations against the magnetic field and the time series of the electric "noise" possess a fractal pattern. With the help of the fractal analysis procedure, the fluctuations observed have been shown to be neither a noise with a large number of degrees of freedom, nor the realisations of a well defined dynamic system. On the contrary the model of voltage oscillations induced by the weak fluctuations of a magnetic field of arbitrary nature gives the most appropriate description of the phenomenon observed. The imaging function of such a transformation possesses a fractal nature, thus leading to power-law spectra of voltage fluctuations even for the simplest types of magnetic fluctuations including the monochromatic ones. Thus, the paper suggests a new universal mechanism of a "1/f noise" origin. It consists in a passive transformation of any natural fluctuations with a fractal-type transformation function.Comment: 17 pages, 13 eps-figures, Latex; title page and figures include

Unconventional Flatband Line States in Photonic Lieb Lattices

Flatband systems typically host "compact localized states"(CLS) due to destructive interference and macroscopic degeneracy of Bloch wave functions associated with a dispersionless energy band. Using a photonic Lieb lattice(LL), we show that conventional localized flatband states are inherently incomplete, with the missing modes manifested as extended line states which form non-contractible loops winding around the entire lattice. Experimentally, we develop a continuous-wave laser writing technique to establish a finite-sized photonic LL with specially-tailored boundaries, thereby directly observe the unusually extended flatband line states.Such unconventional line states cannot be expressed as a linear combination of the previously observed CLS but rather arise from the nontrivial real-space topology.The robustness of the line states to imperfect excitation conditions is discussed, and their potential applications are illustrated

Wightman function and Casimir densities for Robin plates in the Fulling-Rindler vacuum

Wightman function, the vacuum expectation values of the field square and the energy-momentum tensor are investigated for a massive scalar field with an arbitrary curvature coupling parameter in the region between two infinite parallel plates moving by uniform proper acceleration. We assume that the field is prepared in the Fulling-Rindler vacuum state and satisfies Robin boundary conditions on the plates. The mode-summation method is used with a combination of a variant of the generalized Abel-Plana formula. This allows to extract manifestly the contributions to the expectation values due to a single boundary and to present the second plate-induced parts in terms of exponentially convergent integrals. Various limiting cases are investigated. The vacuum forces acting on the boundaries are presented as a sum of the self-action and 'interaction' terms. The first one contains well known surface divergences and needs a further renormalization. The 'interaction' forces between the plates are investigated as functions of the proper accelerations and coefficients in the boundary conditions. We show that there is a region in the space of these parameters in which the 'interaction' forces are repulsive for small distances and attractive for large distances.Comment: 20 pages, 2 figures, discussion added, accepted for publication in Int. J. Mod. Phys.

Matter-wave interferometry in periodic and quasi-periodic arrays

We calculate within a Bose-Hubbard tight-binding model the matter-wave flow driven by a constant force through a Bose-Einstein condensate of Rb 87 atoms in various types of quasi-onedimensional arrays of potential wells. Interference patterns are obtained when beam splitting is induced by creating energy minigaps either through period doubling or through quasi-periodicity governed by the Fibonacci series. The generation of such condensate modulations by means of optical-laser structures is also discussed.Comment: 11 pages, 6 figures. To appear in Opt. Com

Majorana states in prismatic core-shell nanowires

We consider core-shell nanowires with conductive shell and insulating core, and with polygonal cross section. We investigate the implications of this geometry on Majorana states expected in the presence of proximity-induced superconductivity and an external magnetic field. A typical prismatic nanowire has a hexagonal profile, but square and triangular shapes can also be obtained. The low-energy states are localized at the corners of the cross section, i.e. along the prism edges, and are separated by a gap from higher energy states localized on the sides. The corner localization depends on the details of the shell geometry, i.e. thickness, diameter, and sharpness of the corners. We study systematically the low-energy spectrum of prismatic shells using numerical methods and derive the topological phase diagram as a function of magnetic field and chemical potential for triangular, square, and hexagonal geometries. A strong corner localization enhances the stability of Majorana modes to various perturbations, including the orbital effect of the magnetic field, whereas a weaker localization favorizes orbital effects and reduces the critical magnetic field. The prismatic geometry allows the Majorana zero-energy modes to be accompanied by low-energy states, which we call pseudo Majorana, and which converge to real Majoranas in the limit of small shell thickness. We include the Rashba spin-orbit coupling in a phenomenological manner, assuming a radial electric field across the shell.Comment: 14 pages, 16 figures, accepted for publication in Phys. Rev.