Nodal theorems for the Dirac equation in d ≥ 1 dimensions

A single particle obeys the Dirac equation in spatial dimensions and is bound by an attractive central monotone potential that vanishes at infinity. In one dimension, the potential is even, and monotone for The asymptotic behavior of the wave functions near the origin and at infinity are discussed. Nodal theorems are proven for the cases and , which specify the relationship between the numbers of nodes n₁ and n₂ in the upper and lower components of the Dirac spinor. For , whereas for if and if where and This work generalizes the classic results of Rose and Newton in 1951 for the case Specific examples are presented with graphs, including Dirac spinor orbits      

Refined comparison theorems for the Dirac equation in d dimensions

A single spin‐1/2 particle obeys the Dirac equation in spatial dimension and is bound by an attractive central monotone potential which vanishes at infinity (in one dimension the potential is even). This work refines the relativistic comparison theorems which were derived by Hall 1 . The new theorems allow the graphs of the two comparison potentials and to crossover in a controlled way and still imply the spectral ordering for the eigenvalues at the bottom of each angular momentum subspace. More specifically in a simplest case we have: in dimension , if , then ; and in dimensions, if , where and , then .

     

Quantum information entropies for an asymmetric trigonometric Rosen–Morse potential

Shannon entropy for the position and momentum eigenstates of an asymmetric trigonometric Rosen–Morse potential for the ground and first excited states is evaluated. The position and momentum information entropies and are calculated numerically. Also, it is found that is obtained analytically and increases with the potential depth and width. Some interesting features of the information entropy densities and are demonstrated graphically. The Bialynicki‐Birula–Mycielski inequality is also tested and found to hold good.     

Theory of the Robin quantum wall in a linear potential. II. Thermodynamic properties

A theoretical analysis of the thermodynamic properties of the Robin wall characterized by the extrapolation length Λ in the electric field that pushes the particle to the surface is presented both in the canonical and two grand canonical representations and in the whole range of the Robin distance with the emphasis on its negative values which for the voltage‐free configuration support negative‐energy bound state. For the canonical ensemble, the heat capacity at exhibits a nonmonotonic behavior as a function of the temperature T with its pronounced maximum unrestrictedly increasing for the decreasing fields as and its location being proportional to . For the Fermi‐Dirac distribution, the specific heat per particle is a nonmonotonic function of the temperature too with the conspicuous extremum being preceded on the T axis by the plateau whose magnitude at the vanishing is defined as , with N being a number of the particles. The maximum of is the largest for and, similar to the canonical ensemble, grows to infinity as the field goes to zero. For the Bose‐Einstein ensemble, a formation of the sharp asymmetric feature on the ‐T dependence with the increase of N is shown to be more prominent at the lower voltages. This cusp‐like dependence of the heat capacity on the temperature, which for the infinite number of bosons transforms into the discontinuity of , is an indication of the phase transition to the condensate state. Some other physical characteristics such as the critical temperature and ground‐level population of the Bose‐Einstein condensate are calculated and analyzed as a function of the field and extrapolation length. Qualitative and quantitative explanation of these physical phenomena is based on the variation of the energy spectrum by the electric field.     

Theory of the Robin quantum wall in a linear potential. I. Energy spectrum,polarization and quantum‐information measures

Information‐theoretical concepts are employed for the analysis of the interplay between a transverse electric field applied to a one‐dimensional surface and Robin boundary condition (BC), which with the help of the extrapolation length Λ zeroes at the interface a linear combination of the quantum mechanical wave function and its spatial derivative, and its influence on the properties of the structure. For doing this, exact analytical solutions of the corresponding Schrödinger equation are derived and used for calculating energies, dipole moments, position and momentum quantum information entropies and their Fisher information and and Onicescu information energies and counterparts. It is shown that the weak (strong) electric field changes the Robin wall into the Dirichlet, (Neumann, ), surface. This transformation of the energy spectrum and associated waveforms in the growing field defines an evolution of the quantum‐information measures; for example, it is proved that for the Dirichlet and Neumann BCs the position (momentum) quantum information entropy varies as a positive (negative) natural logarithm of the electric intensity what results in their field‐independent sum . Analogously, at and the position and momentum Fisher informations (Onicescu energies) depend on the applied voltage as () and its inverse, respectively, leading to the field‐independent product (). Peculiarities of their transformations at the finite nonzero Λ are discussed and similarities and differences between the three quantum‐information measures in the electric field are highlighted with the special attention being paid to the configuration with the negative extrapolation length.

     

A generalized G‐function for the Quantum Rabi Model

The analytical solution of the quantum Rabi model is based on a transcendental function , the zeros of which determine the eigenenergies. is generalized here to a function , which allows a much better numerical control of the high‐energy part of the spectrum by an appropriate choice of the complex parameter z. Additionally, it is shown that all zeros of correspond to eigenvalues of the Hamiltonian as well as the zeros of for imaginary z.     

THz and above THz electron or hole oscillations in DNA dimers and trimers

A non conventional source or receiver of THz and above THz electromagnetic radiation is proposed. Specifically, electron or hole oscillations in DNA dimers (two interacting DNA base‐pairs or monomers) are predicted, with frequency in the range 0.25–100 THz (period 10–4000 fs) i.e. potentially absorbing or emitting electromagnetic radiation mainly in the mid‐ and far‐infrared with wavelengths ≈ 3–1200 μm. The efficiency of charge transfer between the two monomers which make up the dimer is described with the maximum transfer percentage p  and the pure maximum transfer rate . For dimers made of identical monomers , but for dimers made of different monomers . The investigation is extended to DNA trimers (three interacting DNA base‐pairs or monomers). For trimers made of identical monomers the carrier oscillates periodically with 0.5–33 THz ( 30–2000 fs); for 0 times crosswise purines , for 1 or 2 times crosswise purines . For trimers made of different monomers the carrier movement may be non periodic. Generally, increasing the number of monomers above three, the system becomes more complex and periodicity is lost; even for the simplest tetramer the carrier movement is not periodic.     

Quantum states and vortex patterns in nanosuperconductors

The quanum levels and corresponding vortex states in nanoscale superconductors are investigated within generalized Bogolubov‐de Gennes theory. For symmetric (square‐shaped) samples thermodynamically stable vortex phases form symmetry‐consistent patterns and no transition to conventional Abrikosov‐like vortex patterns occurs till T=0K for sizes not exceeding 25 nm. For vorticity a giant vortex is stabilized at temperatures in the vicinity of , which transforms into a giant antivortex and four normal vortices with lowering the temperature. On the other hand, the vortex pattern for vorticity corresponds to an antivortex and four normal vortices in the whole temperature domain.     

Uniaxial magnetic anisotropy in epitaxial α‐Fe() films

The magnetic anisotropy of epitaxial, high‐index Fe() films is investigated. The strength of the in‐plane uniaxial magnetic anisotropy increases monotonically with the inclination angle φ between Fe(001) and Fe(). This increase is demonstrated to be caused by the cubic magnetocrystalline anisotropy and not by surface‐ or interface‐related effects.     

Nonlinear arcsin‐electrodynamics and asymptotic Reissner‐Nordström black holes

A model of nonlinear electrodynamics with the Lagrangian density is proposed. The scale invariance and the dual invariance of electromagnetic fields are broken in the model. In the limit one comes to Maxwell's electrodynamics and the scale and dual invariances are recovered. We investigate the effect of coupling electromagnetic fields with the gravitational field. The asymptotic black hole solution is found which is similar to the Reissner‐Nordström solution. We obtain corrections to Coulomb's law and to the Reissner‐Nordström solution in the model proposed. The existence of the regular asymptotic at was demonstrated. The mass of the black hole is calculated possessing the electromagnetic origin. It was shown that there are not superluminal fluctuations and principles of causality and unitarity take place.     

Solid Electrolytes: Extremely Fast Charge Carriers in Garnet‐Type Li6La3ZrTaO12 Single Crystals

The development of all‐solid‐state electrochemical energy storage systems, such as lithium‐ion batteries with solid electrolytes, requires stable, electronically insulating compounds with exceptionally high ionic conductivities. Considering ceramic oxides, garnet‐type LiLaZrO and derivatives, see Zr‐exchanged LiLaZrTaO (LLZTO), have attracted great attention due to its high Li⁺ ionic conductivity of 10 S cm at ambient temperature. Despite numerous studies focussing on conductivities of powder samples, only few use time‐domain NMR methods to probe Li ion diffusion parameters in single crystals. Here we report on temperature‐variable NMR relaxometry measurements using both laboratory and spin‐lock techniques to probe Li jump rates covering a dynamic time window spanning several decades. Both techniques revealed a consistent picture of correlated Li ion jump diffusion in the single crystal; the data perfectly mirror a modified BPP‐type relaxation response being based on a Lorentzian‐shaped relaxation function. The rates measured could be parameterized with a single set of diffusion parameters. Results from NMR are completely in line with ion transport parameters derived from conductivity spectroscopy.     

Comparative analysis of electric field influence on the quantum wells with different boundary conditions.

Analytical solutions of the Schrödinger equation for the one‐dimensional quantum well with all possible permutations of the Dirichlet and Neumann boundary conditions (BCs) in perpendicular to the interfaces uniform electric field are used for the comparative investigation of their interaction and its influence on the properties of the system. Limiting cases of the weak and strong voltages allow an easy mathematical treatment and its clear physical explanation; in particular, for the small , the perturbation theory derives for all geometries a linear dependence of the polarization on the field with the BC‐dependent proportionality coefficient being positive (negative) for the ground (excited) states. Simple two‐level approximation elementary explains the negative polarizations as a result of the field‐induced destructive interference of the unperturbed modes and shows that in this case the admixture of only the neighboring states plays a dominant role. Different magnitudes of the polarization for different BCs in this regime are explained physically and confirmed numerically. Hellmann‐Feynman theorem reveals a fundamental relation between the polarization and the speed of the energy change with the field. It is proved that zero‐voltage position entropies are BC independent and for all states but the ground Neumann level (which has ) are equal to while the momentum entropies depend on the edge requirements and the level. Varying electric field changes position and momentum entropies in the opposite directions such that the entropic uncertainty relation is satisfied. Other physical quantities such as the BC‐dependent zero‐energy and zero‐polarization fields are also studied both numerically and analytically. Applications to different branches of physics, such as ocean fluid dynamics and atmospheric and metallic waveguide electrodynamics, are discussed.

     

Casimir effect modified surface energy of a nanocavity in homogeneous media

We determine the regularized van der Waals contribution to pressure within a spherical cavity of vapor in a homogeneous, isotropic, infinite medium. The spherical Hamaker function, , has been defined, for the first time, in contrast to the conventional Hamaker function for planar surfaces, . For the materials under consideration, the pressure inside the cavity varies as , where a is the radius of the cavity. For radii below a transition radius, the surface energy (or surface tension) becomes size dependent and could have important implications for homogeneous nucleation of nanosized bubbles in liquids, as well as cavitation of bubbles.

     

Mechanical detection of ultraslow,Debye‐like Li‐ion motions in LiAlO single crystals

Single crystalline LiAlO is known as a very poor ion conductor. Thus, in its crystalline form it unequivocally disqualifies itself from being a powerful solid electrolyte in modern energy storage systems. On the other hand, its interesting crystal structure proves beneficial to sharpen our understanding of Li ion dynamics in solids which in return might influence application‐oriented research. LiAlO allows us to apply and test techniques that are sensitive to extremely slow Li ion dynamics. This helps us clarifying their diffusion behaviour from a fundamental point of view. Here, we combined two techniques to follow Li ion translational hopping in LiAlO that can be described by the same physical formalism: dynamic mechanical relaxation and electrical relaxation, i.e., ionic conductivity measurements. Via both methods we were able to track the same transport mechanism in LiAlO. Moreover, this enabled us to directly probe extremely slow Li exchange rates at temperatures slightly above 430 K. The results were compared with recent insights from nuclear magnetic resonance spectroscopy. Altogether, an Arrhenius‐type Li diffusion process with an activation energy of ca. 1.12 eV was revealed over a large dynamic range covering 10 orders of magnitude, i.e., spanning a dynamic range from the nano‐second time scale down to the second time scale.

     

Quantum Temporal Steering in a Dephasing Channel With Quantum Criticality

We investigate the quantum temporal steering (TS), i.e., a temporal analogue of Einstein‐Podolsky‐Rosen steering, in a dephasing channel which is modeled by a central spin half surrounded by a spin‐1/2 XY chain where quantum phase transition happens. The TS parameter and the TS weight are employed to characterize the TS dynamics. We analytically obtain the dependence of on the decoherence factor. The numerical results show an obvious suppression of and when the XY chain approaches to the critical point. In view of the significance of quantum channel, we develop a new concept, TS weight power, in order to quantify the capacity of the quantum channel in dominating TS behavior. This new quantity enables us to indicate the quantum criticality of the environment by the quantum correlation of TS in the coupled system.     

The gravitational energy‐momentum pseudo‐tensor of higher‐order theories of gravity

We derive the gravitational energy momentum tensor for a general Lagrangian of any order and in particular for a Lagrangian such as . We prove that this tensor, in general, is not covariant but only affine, then it is a pseudo‐tensor. Furthermore, the pseudo‐tensor is calculated in the weak field limit up to a first non‐vanishing term of order h² where h is the metric perturbation. The average value of the pseudo‐tensor over a suitable spacetime domain is obtained. Finally we calculate the power per unit solid angle Ω carried by a gravitational wave in a direction for a fixed wave number under a suitable gauge. These results are useful in view of searching for further modes of gravitational radiation beyond the standard two modes of General Relativity and to deal with nonlocal theories of gravity where terms involving are present. The general aim of the approach is to deal with theories of any order under the same standard of Landau pseudo‐tensor.     

Equivalence and hermiticity of Dirac Hamiltonians in the Kerr gravitational field

In the paper, for the Kerr field, we prove that Chandrasekhar's Dirac Hamiltonian and the self‐adjoint Hamiltonian with a flat scalar product of the wave functions are physically equivalent. Operators of transformation of Chandrasekhar's Hamiltonian and wave functions to the η representation with a flat scalar product are defined explicitly. If the domain of the wave functions of Dirac's equation in the Kerr field is bounded by two‐dimensional surfaces of revolution around the z axis, Chandrasekhar's Hamiltonian and the self‐adjoint Hamiltonian in the η representation are Hermitian with equality of the scalar products, .

     

Ultra‐Fast Control of Magnetic Relaxation in a Periodically Driven Hubbard Model

Motivated by cold atom and ultra‐fast pump‐probe experiments we study the melting of long‐range antiferromagnetic order of a perfect Néel state in a periodically driven repulsive Hubbard model. The dynamics is calculated for a Bethe lattice in infinite dimensions with non‐equilibrium dynamical mean‐field theory. In the absence of driving melting proceeds differently depending on the quench of the interactions to hopping ratio from the atomic limit. For decay occurs due to mobile charge‐excitations transferring energy to the spin sector, while for it is governed by the dynamics of residual quasi‐particles. Here we explore the rich effects that strong periodic driving has on this relaxation process spanning three frequency ω regimes: (i) high‐frequency , (ii) resonant with integer l, and (iii) in‐gap away from resonance. In case (i) we can quickly switch the decay from quasi‐particle to charge‐excitation mechanism through the suppression of ν₀. For (ii) the interaction can be engineered, even allowing an effective regime to be reached, giving the reverse switch from a charge‐excitation to quasi‐particle decay mechanism. For (iii) the exchange interaction can be controlled with little effect on the decay. By combining these regimes we show how periodic driving could be a potential pathway for controlling magnetism in antiferromagnetic materials. Finally, our numerical results demonstrate the accuracy and applicability of matrix product state techniques to the Hamiltonian DMFT impurity problem subjected to strong periodic driving.     

Tunable pinning effects produced by non‐uniform antidot arrays in YBCO thin films

Uniform, graded and spaced arrays of 3 μm triangular antidots in pulsed laser deposited YBa₂Cu₃O₇ (YBCO) superconducting thin films are compared by examining the improvements in the critical current density they produced. The comparison is made to establish the role of their lithographically defined (non‐)uniformity and the effectiveness to control and/or enhance the critical current density. It is found that almost all types of non‐uniform arrays, including graded ones enhance over the broad applied magnetic field and temperature range due to the modified critical state. Whereas uniform arrays of antidots either reduce or produce no effect on compared to the original (as‐deposited) thin films.