Formulation of Leggett–Garg Inequalities in Terms of q-Entropies

As is well known, the macroscopic realism and the noninvasive measurability together lead to Leggett–Garg inequalities violated by quantum mechanics. We consider tests of the Leggett–Garg type with use of the q-entropies.For all q≥1, quantum mechanics predicts violations of an entire family of q-entropic inequalities of the Leggett–Garg type. Violations are exemplified with a quantum spin-s system. In general, entropic Leggett–Garg inequalities give only necessary conditions that some probabilistic model is compatible with the macrorealism in the broader sense. The presented q-entropic inequalities allow to widen a class of situations, in which an incompatibility with the macrorealism can be tested. In the considered example, both the strength and range of violations are somehow improved by varying q.We also examine q-entropic inequalities of the Leggett–Garg type in the case of detection inefficiencies, when the no-click event may occur in each observation. With the use of the q-entropic inequalities, the required amount of efficiency may be reduced.     

Correlative Collapses and Revivals in Two Trapped Ions

An analytic solution is presented for two trapped ions resonantly interacting with laser beams to the first red side-band of the centre-of-mass mode,in the Lamb-Dicke regime and under the rotating wave approximation.This shows the existence of correlative quantum collapses and revivals for the occupation of two atoms.     

Three-flavoured neutrino oscillations and the Leggett–Garg inequality

Three-flavoured neutrino oscillations are investigated in the light of the Leggett–Garg inequality (LGI). The results obtained are: (a) The maximum violation of the LGI is 2.17036 for neutrino path length \(L_{1}=140.15 \) km and \(\Delta L=1255.7 \) km. (b) The presence of the mixing angle \(\theta _{13}\) enhances the maximum violation of LGI by \(4.6\%\). (c) The currently known mass hierarchy parameter \(\alpha = 0.0305\) increases the maximum violation of LGI by \(3.7\%\). (d) The presence of a CP-violating phase parameter enhances the maximum violation of LGI by \(0.24\%\), thus providing an alternative indicator of CP violation in three-flavoured neutrino oscillations. The outline of an experimental proposal is suggested whereby the findings of this investigation may be verified.     

On the Aharonov–Bohm Hamiltonian

Using the theory of self-adjoint extensions, we construct all the possible Hamiltonians describing the nonrelativistic Aharonov–Bohm effect. In general, the resulting Hamiltonians are not rotationally invariant so that the angular momentum is not a constant of motion. Using an explicit formula for the resolvent, we describe the spectrum and compute the generalized eigenfunctions and the scattering amplitude.     

Ion dynamics in methylcellulose–LiBOB solid polymer electrolytes

A polymer electrolyte system comprising methylcellulose (MC) as the host polymer and lithium bis(oxalato) borate (LiBOB) as the lithium ion source has been prepared via the solution cast technique. The electrolyte with the highest conductivity of 2.79 μS cm^?1 has a composition of 75 wt% MC–25 wt% LiBOB. The mobile ion concentration (n) in this sample was estimated to be 5.70?×?10²⁰ cm^?3. A good correlation between ionic conductivity, dielectric constant, and free ion concentration has been observed. The ratio of mobile ion number density (n) at a particular temperature to the concentration n ₀ of free ions at T?=?∞ (n/n ₀) and the power law exponents (s) exhibit opposite trends when varied with salt concentration.     

Temperature effects of Hamiltonian dark solitons on the stability of holographic solitons in a separate holographic–Hamiltonian soliton pair

We investigate theoretically the temperature effects on the evolution and stability of a separate holographic–Hamiltonian dark–dark or bright–dark soliton pair formed in an unbiased serial photorefractive crystal circuit. Our numerical results show that, for a stable dark–dark or bright–dark soliton pair originally formed in a crystal circuit at given temperatures, when the crystal in which formed a Hamiltonian dark soliton changes, the holographic dark or bright soliton supported by the other crystal tends to evolve into another stable soliton or experiences larger cycles of compression or breaks up into beam filaments or exhibit a common decaying process. The holographic dark soliton is more sensitive to the temperature change than the holographic bright one.     

Nonlinear dynamics of deformation bands in aluminum–magnesium alloy in the creep test

Various types of plastic instabilities that emerge in intermittent creep have been studied experimentally for AlMg6 aluminum–magnesium alloy. It has been shown that intermittent creep exhibits threshold dynamics. The deformation step on the creep curve of amplitude is ~1–6% and begins when the rate of the preceding continuous creep attains a certain critical value. In the course of evolution of the step, the strain rate varies in the interval that spans more than two orders of magnitude, and transitions occur between different dynamic regimes of type A and B characterized by different stress drop regularity levels in the force response. Nonlinear aspects of the deformation behavior of the alloy in the intermittent creep conditions are considered.     

Unbounded Trace Orbits of Thue–Morse Hamiltonian

It is well known that, an energy is in the spectrum of Fibonacci Hamiltonian if and only if the corresponding trace orbit is bounded. However, it is not known whether the same result holds for the Thue–Morse Hamiltonian. In this paper, we give a negative answer to this question. More precisely, we construct two subsets \(\Sigma _{II}\) and \(\Sigma _{III}\) of the spectrum of the Thue–Morse Hamiltonian, both of which are dense and uncountable, such that each energy in \(\Sigma _{II}\cup \Sigma _{III}\) corresponds to an unbounded trace orbit. Exact estimates on the norm of the transfer matrices are also obtained for these energies: for \(E\in \Sigma _{II}\cup \Sigma _{III}, \) the norms of the transfer matrices behave like

$$\begin{aligned} e^{c_1\gamma \sqrt{n}}\le \Vert T_{ n}(E)\Vert \le e^{c_2\gamma \sqrt{n}}. \end{aligned}$$

However, two types of energies are quite different in the sense that each energy in \(\Sigma _{II}\) is associated with a two-sided pseudo-localized state, while each energy in \(\Sigma _{III}\) is associated with a one-sided pseudo-localized state. The difference is also reflected by the local dimensions of the spectral measure: the local dimension is 0 for energies in \(\Sigma _{II}\) and is larger than 1 for energies in \(\Sigma _{III}.\) As a comparison, we mention another known countable dense subset \(\Sigma _I\). Each energy in \(\Sigma _I\) corresponds to an eventually constant trace map and the associated eigenvector is an extended state. In summary, the Thue–Morse Hamiltonian exhibits “mixed spectral nature”.

     

On the Maximal Excess Charge of the Chandrasekhar–Coulomb Hamiltonian in Two Dimension

We show that for the straightforward quantized relativistic Coulomb Hamiltonian of a two-dimensional atom – or the corresponding magnetic quantum dot – the maximal number of electrons does not exceed twice the nuclear charge. The result is then generalized to the presence of external magnetic fields and atomic Hamiltonians. This is based on the positivity of $$|{\bf x}| T({\bf p}) + T({\bf p} ) |{\bf x}|$$ which – in two dimensions – is false for the non-relativistic case T(p) = p ²/2, but is proven in this paper for T(p) = |p|, i.e., the ultra-relativistic kinetic energy.     

Coexistence of chaotic and non-chaotic states in the two-dimensional Gauss–Navier–Stokes dynamics

Recently, Gallavotti proposed an Equivalence Conjecture in hydrodynamics, which states that forced-damped fluids can be equally well represented by means of the Navier–Stokes equations (NS) and by means of time reversible modifications of NS called Gauss–Navier–Stokes equations (GNS). This Equivalence Conjecture received numerical support in several recent papers concerning two-dimensional fluid mechanics. The corresponding results rely on the fact that the NS and GNS systems only have one attracting set. Performing similar two-dimensional simulations, we find that there are conditions to be met by the GNS system for this to be the case. In particular, increasing the Reynolds number, while keeping fixed the number of Fourier modes, leads to the coexistence of different attractors. This makes difficult a test of the Equivalence Conjecture, but constitutes a spurious effect due to the insufficient spectral resolution. With sufficiently fine spectral resolution, the steady states are unique and the Equivalence Conjecture can be conveniently established.     

Hamiltonian Chaos in Homogeneous ADM Cosmologies?

Chaos in dynamical systems has best been understood in terms of Hamiltonian systems. A primary method of diagnosis of chaos in these systems is the Lyapunov exponent. According to general relativity, space-time is itself a dynamical system. When the evolution of a model universe is expressed in the ADM form it can be described as a Hamiltonian system. Among the various model cosmologies, the Mixmaster or Bianchi IX cosmology has been extensively studied as a candidate to exhibit chaos. However, the Lyapunov exponents in this system have shown contradictory properties, including a seeming dependence on the coordinates used to describe space-time. Such dependencies, if true, would be surprising as the time coordinate of space-time is unrelated to the parameterization of phase space. Further, this sort of dependence would relegate chaos to a bad coordinate choice rather than a dynamic property of the system. The problem with the Lyapunov exponent lies in the ambiguities remaining in the ADM action integral. The current interpretation involves an arbitrary Lagrange multiplier—thought to be necessary for the coordinate invariance of space-time. An arbitrary multiplier turns out to be unnecessary for coordinate invariance, and in addition destroys the symplectic structure of phase space. In reality, the geometry selects the parameterization of phase space, and any change in the parameter results in a changed Hamiltonian system. It must be emphasized that the fixing of the phase space parameter does NOT impose a coordinate choice on space-time. The parameter is selected by the symplectic structure of phase space and full coordinate invariance of space-time is left intact. Once the demands of both geometries, space-time and phase space, have been satisfied, the Lyapunov exponent becomes independent of the coordinate imposed on space-time. Additionally, the correction of the phase space structure leads to a Hamiltonian that is more general, in that it describes a gravitational system with a cosmological constant, than is currently the case.     

Ionic liquid confined in silica nanopores: molecular dynamics in the isobaric–isothermal ensemble

Molecular dynamics simulations in the isobaric–isothermal ensemble are used to investigate the structure and dynamics of an ionic liquid confined at ambient temperature and pressure in hydroxylated amorphous silica nanopores. The use of the isobaric–isothermal ensemble allows estimating the effect of confinement and surface chemistry on the density of the confined ionic liquid. The structure of the confined ionic liquid is investigated using density profiles and structural order parameters while its dynamics is assessed by determining the mobility and ionic conductivity of the confined phase. Despite the important screening of the electrostatic interactions (owing to the small Debye length in ionic liquids), the local structure of the confined ionic liquid is found to be mostly driven by electrostatic interactions. We show that both the structure and dynamics of the confined ionic liquid can be described as the sum of a surface contribution arising from the ions in contact with the surface and a bulk-like contribution arising from the ions located in the pore centre; as a result, most properties of the confined ionic liquid are a simple function of the surface-to-volume ratio of the host porous material. In contrast, the ionic conductivity of the confined ionic liquid, which is a collective dynamical property, is found to be similar to the bulk. This study sheds light on the complex behaviour of hybrid materials made up of ionic liquid confined in inorganic porous materials.     

Optical properties and ultrafast electron dynamics in gold–silver alloy and core–shell nanoparticles

Silver and gold are the two most popular metals used for many nanoparticle applications, such as surface enhanced Raman scattering or surface enhanced fluorescence, in which the local field enhancement associated with the excitation of the localized surface-plasmon–polariton resonance (SPR) is exploited. Therefore, tunability of the SPR over a wide energy range is required. For this purpose we have investigated core–shell nanoparticles composed of gold and silver with different shell thicknesses as well as the impact of alloying on these nanoparticles due to a tempering process. The nanoparticles were prepared by subsequent deposition of Au and Ag atoms or vice versa on quartz substrates followed by diffusion and nucleation. Their linear extinction spectra were measured as a function of shell thickness and annealing temperature. It turned out that different gold shell thicknesses on silver cores allow a tuning of the SPR position from 2.79 to 2.05 eV, but interestingly without a significant change on the extinction amplitude. Heating of core–shell nanoparticles up to only 540 K leads to the formation of alloy nanoparticles, accompanied by a back shift of the SPR to 2.60 eV. Calculations performed in quasi-static approximation describe the experimental results quite well and prove the structural assignments of the samples. In additional experiments, we applied the well-established persistent spectral hole burning technique to the alloy nanoparticles in order to determine the ultrafast dephasing time T ₂. We obtained a dephasing time of T ₂=(8.1±1.6) fs, in good agreement with the dephasing time of T _2,∞=8.9 fs, which is already included in the dielectric function of the bulk.     

Solitonic eigenstates of the chaotic Bose–Hubbard Hamiltonian

We study the evolving energy spectrum of interacting ultra-cold atoms in an optical lattice as a function of an external parameter, the tilt of the lattice. In a regime where the quantum mechanical model, the Bose–Hubbard Hamiltonian, shows predominantly chaotic behavior, we identify regular structures in the parametric level evolution and characterize the eigenstates associated with these structures. The mechanism generating these structures is found to be different from Stark localization or energetic isolation and is induced by an interplay of driving and interaction.