Annals of Physics最新文献

The current study aims to examine uncertainty relations for measurements from generalized equiangular tight frames. Informationally overcomplete measurements are a valuable tool in quantum information processing, including tomography and state estimation. The maximal sets of mutually unbiased bases are the most common case of such measurements. The existence of $d+1$ mutually unbiased bases is proved for $d$ being a prime power. More general classes of informationally overcomplete measurements have been proposed for various purposes. Measurements of interest are typically characterized by some inner structure maintaining the required properties. It leads to restrictions imposed on generated probabilities. To apply the considered measurements, these restrictions should be converted into information-theoretic terms. It is interesting that certain restrictions hold irrespectively to overcompleteness. To describe the amount of uncertainty quantitatively, we use the Tsallis and Rényi entropies as well as probabilities of separate outcomes. The obtained results are based on estimation of the index of coincidence. The derived relations are briefly exemplified.

Higher-order scalar field models in two dimensions, including the ${\varphi }^8$ model, have been researched. It has been shown that for some special cases of the minima positions of the potential, the explicit kink solutions can be found. However, in physical applications, it is very important to know all the explicit solutions of a model for any minima position. In the present study, with the help of some deformation functions, we have shown that higher-order scalar field theories can be obtained with explicit kinks. In particular, we introduced two deformation functions that, when applied to the well known ${\varphi }^4$ and ${\varphi }^6$ models, produce modified ${\varphi }^8$ and ${\varphi }^{10}$ models, respectively, with all their explicit kink-like solutions which depend on a single parameter. Since this parameter controls the position of the minima of the potential, we have found interesting new solutions in many distinct cases. We have also studied the kink mass, the behavior of the excitation spectra and several kink-antikink collisions for these two new modified models. The collision outcome is determined by the initial configuration, specifically the sequence in which the kink-antikink and antikink-kink pairings emerge. Another interesting finding is the suppression of resonance windows, which may be explained by the presence of a set of internal modes in the model.

Particles initially at rest hit by a passing sandwich gravitational wave exhibit, in general, the velocity memory effect (VM): they fly apart with constant velocity. For specific values of the wave parameters their motion can however become pure displacement (DM) as suggested by Zel’dovich and Polnarev. For such a “miraculous” value, the particle trajectory is composed of an integer number of (approximate) standing half-waves. Our statements are illustrated numerically by a Gaussian, and analytically by the Pöschl–Teller profiles.

We make a conceptual overview of a particular approach to the initial-value problem in canonical gauge theories. We stress how the first-class phase-space constraints may be relaxed if we interpret them as fixing the values of new degrees of freedom. This idea goes back to Fock and Stueckelberg, leading to restrictions of the gauge symmetry of a theory, and it corresponds, in certain cases, to promoting constants of Nature to physical fields. Recently, different versions of this formulation have gained considerable attention in the literature, with several independent iterations, particularly in classical and quantum descriptions of gravity, cosmology, and electromagnetism. In particular, in the case of canonical quantum gravity, the Fock–Stueckelberg approach is relevant to the so-called problem of time. Our overview recalls and generalizes the work of Fock and Stueckelberg and its physical interpretation with the aim of conceptually unifying the different iterations of the idea that appear in the literature and of motivating further research.

We construct a new solution in the Einstein–Maxwell-dilaton theory describing accelerating, charged, and rotating black hole, i.e. the accelerating Kaluza–Klein black hole. Some properties the spacetime are discussed, such as the electromagnetic fields, the area-temperature product, and the holography according to Kerr/CFT correspondence. As expected, the macroscopic Bekenstein–Hawking entropy for an extremal accelerating Kaluza–Klein black hole can be recovered by using Cardy formula of a two dimensional conformal field theory. An interesting feature is found, namely the area-temperature product is just the one belongs to the vacuum Einstein seed solution.

We set up the Wheeler–DeWitt (WDW) equation for late gravitational collapse. The fact that the gravitational collapse and the expanding/ collapsing universe can be described within the realm of the Robertson–Walker metric renders the corresponding WDW equation for collapsing matter a timeless Schrödinger equation. We explore the consequences of such an equation and find the density to be quantized in terms of the Planck density. Apart from that, the wave function as a solution of the WDW equation shows that the initial singularity is avoided. We concentrate on different factor orderings in the kinetic term of the equation and show how after splitting off an exponential ansatz, new polynomials entering the solution can be constructed. This enables us to conclude that the factor ordering changes the details of the solution and interpretation, but overall on a qualitative level the results remain the same. We also probe into the effects of a positive cosmological constant. It offers the possibility of a tunneling scenario at the cosmological horizon.

This paper aims to investigate the Landau problem in the framework of a two-dimensional dynamical noncommutative (DNC) space. We study the deformed Landau problem using time-independent perturbation theory, wherein the energy shift notably depends on the DNC parameter $\tau$. Using the accuracy of energy measurement, we put an upper bound on the parameter $\tau$. Moreover, we study magnetoconductivity by employing the Kubo formula. This approach has allowed us to test the effects of noncommutative and DNC spaces on the behavior of magnetoconductivity. We show that dynamical noncommutativity of space has no effects on the x-component of the magnetoconductivity, but has a direct effect on its y-component.

In a recent paper, we studied a modified version of the Einstein–Rosen bridge. This modified bridge is traversable and works as a one-way membrane: a particle on the first sheet falling towards the throat will reach it in finite time (in Eddington coordinates), and will continue its trajectory on the second sheet. In this paper, we show that the particle undergoes a PT-symmetry as it crosses the throat. This could lead to observable effects thanks to an additional ingredient proposed by Einstein and Rosen: congruent points on the two sheets are identified. We propose a bimetric model to realize this identification for our modified bridge

The deviation of the decay law from the exponential is a well known effect of quantum mechanics. Here we analyze the relativistic survival probabilities, $S(t,p)$, where $p$ is the momentum of the decaying particle and provide analytical expressions for $S(t,p)$ in the exponential (E) as well as the nonexponential (NE) regions at small and large times. Under minimal assumptions on the spectral density function, analytical expressions for the critical times of transition from the NE to the E at small times and the E to NE at large times are derived. The dependence of the decay law on the relativistic Lorentz factor, $\gamma =1/\sqrt{1-v^2/c^2}$, reveals several interesting features. In the short time regime of the decay law, the critical time, ${\tau }_{st}$, shows a steady increase with $\gamma$, thus implying a larger NE region for particles decaying in flight. Comparing $S(t,p)$ with the well known time dilation formula, $e^{-\Gamma t/\gamma }$, in the exponential region, an expression for the critical $\gamma$ where $S(t,p)$ deviates most from $e^{-\Gamma t/\gamma }$ is presented. This is a purely quantum correction. Under particular conditions on the resonance parameters, there also exists a critical $\gamma$ at large times which decides if the NE region shifts backward or forward in time as compared to that for a particle at rest. All the above analytical results are supported by calculations involving realistic decays of hadrons and leptons.

In this investigation, we perform an observational statistical analysis in the theory of $f(R,L_m)$ gravity. The proposed theoretical model is based on the Ricci scalar’s non-linear contribution. We use a distinct parametrization for the deceleration parameter and constrain the model parameters by using various observational data. To determine the best-fit model for the cosmological parameters, we use different observational datasets such as the Hubble Space Telescope, the Pantheon Supernova Survey, the Gold dataset, the Gamma-Ray Burst (GRB), and the Baryon Acoustic Oscillations (BAO). Furthermore, we study the late-time cosmic evolution of the Universe in detail and examine the implications of the constraint values on cosmological parameters. Additionally, we conduct a thorough comparison with the standard cosmological model $\Lambda$CDM and other standard models obtained by Odintsov et al. (2024); Odintsov et al. (2023) to examine the validity of our proposed model in the low-redshift regimes. Finally, we find that the proposed model encapsulates an intriguing transition from early deceleration at high redshift to acceleration at low redshift, a quintessence dark energy scenario, and convergence towards the well-established $\Lambda$CDM model in late-time Universe’s evolution.