Gaussian Regimes Research Articles

Quantum Rényi entropy functionals for bosonic Gaussian systems

In this study, the quantum Rényi entropy power inequality of order p>1 and power κ is introduced as a quantum analog of the classical Rényi-p entropy power inequality. To derive this inequality, we first exploit the Wehrl-p entropy power inequality on bosonic Gaussian systems via the mixing operation of quantum convolution, which is a generalized beam-splitter operation. This observation directly provides a quantum Rényi-p entropy power inequality over a quasi-probability distribution for D-mode bosonic Gaussian regimes. The proposed inequality is expected to be useful for the nontrivial computing of quantum channel capacities, particularly universal upper bounds on bosonic Gaussian quantum channels, and a Gaussian entanglement witness in the case of Gaussian amplifier via squeezing operations.

Interplay between particle trapping and heterogeneity in anomalous diffusion

Heterogeneous media diffusion is often described using position-dependent diffusion coefficients and estimated indirectly through mean squared displacement in experiments. This approach may overlook other mechanisms and their interaction with position-dependent diffusion, potentially leading to erroneous conclusions. Here, we introduce a hybrid diffusion model that merges a position-dependent diffusion coefficient with the trapping mechanism of the comb model. We derive exact solutions for position distributions and mean squared displacements, validated through simulations of Langevin equations. Our model shows that the trapping mechanism attenuates the impact of media heterogeneity. Superdiffusion occurs when the position-dependent coefficient increases superlinearly, while subdiffusion occurs for sublinear and inverse power-law relations. This nontrivial interplay between heterogeneity and state-independent mechanisms also leads to anomalous yet Brownian, and non-Brownian yet Gaussian regimes. These findings emphasize the need for cautious interpretations of experiments and highlight the limitations of relying solely on mean squared displacements or position distributions for diffusion characterization.

A mixture autoregressive model based on Gaussian and Student’s t-distributions

Abstract We introduce a new mixture autoregressive model which combines Gaussian and Student’s t mixture components. The model has very attractive properties analogous to the Gaussian and Student’s t mixture autoregressive models, but it is more flexible as it enables to model series which consist of both conditionally homoscedastic Gaussian regimes and conditionally heteroscedastic Student’s t regimes. The usefulness of our model is demonstrated in an empirical application to the monthly U.S. interest rate spread between the 3-month Treasury bill rate and the effective federal funds rate.

Calibration and performance assessment of microgrid polarization cameras

We provide a method for calibrating microgrid polarization cameras that is simpler and easier to set up than existing methods. Applying this method to three different commercially available cameras, we compare the mean values and variances in their diattenuation and orientation properties. We derive formulas giving the accuracy with which the pixel polarization properties can be calibrated in both the Gaussian and Poisson noise regimes and demonstrate the statistical instability of the extinction ratio as a parameter. In a series of calibration measurements, we estimate the pixel-to-pixel variation of polarization properties and show how to separate the effects of temporal noise from manufacturing variation.

Maximally entangled states in discrete and Gaussian regimes

We study a relation between discrete-variable quantum states and continuous-variable (especially, restricted on Gaussian) ones. In the previous work, we have investigated an information-theoretic correspondence between the Gaussian maximally mixed states and their purifications as Gaussian maximally entangled states in Jeong and Lim (Phys Lett A 380:3607, 2016). We here compare the purified continuous-variable maximally entangled state with a two-mode squeezed vacuum state, which is a conventional entangled state in Gaussian regime, by the explicit calculation of quantum fidelities between those states and an $$N\times N$$ -dimensional maximally entangled state in the finite Hilbert space. Consequently, we naturally conclude that the purified maximally entangled state is more suitable to the Gaussian maximally entangled state than the two-mode squeezed vacuum state, in a sense that it might be useful for continuous-variable quantum information tasks in which entangled states are needed.

Correlation Functions of the Quantum Sine-Gordon Model in and out of Equilibrium.

Complete information on the equilibrium behavior and dynamics of quantum field theory (QFT) is provided by multipoint correlation functions. However, their theoretical calculation is a challenging problem, even for exactly solvable models. This has recently become an experimentally relevant problem, due to progress in cold-atom experiments simulating QFT models and directly measuring higher order correlations. Here we compute correlation functions of the quantum sine-Gordon model, a prototype integrable model of central interest from both theoretical and experimental points of view. Building upon the so-called truncated conformal space approach, we numerically construct higher order correlations in a system of finite size in various physical states of experimental relevance, both in and out of equilibrium. We measure deviations from Gaussianity due to the presence of interaction and analyze their dependence on temperature, explaining the experimentally observed crossover between Gaussian and non-Gaussian regimes. We find that correlations of excited states are markedly different from the thermal case, which can be explained by the integrability of the system. We also study dynamics after a quench, observing the effects of the interaction on the time evolution of correlation functions, their spatial dependence, and their non-Gaussianity as measured by the kurtosis.

Spatiotemporal Analysis of Coronal Loops Using Seismology of Damped Kink Oscillations and Forward Modeling of EUV Intensity Profiles

Abstract The shape of the damping profile of kink oscillations in coronal loops has recently allowed the transverse density profile of the loop to be estimated. This requires accurate measurement of the damping profile that can distinguish the Gaussian and exponential damping regimes, otherwise there are more unknowns than observables. Forward modeling of the transverse intensity profile may also be used to estimate the width of the inhomogeneous layer of a loop, providing an independent estimate of one of these unknowns. We analyze an oscillating loop for which the seismological determination of the transverse structure is inconclusive except when supplemented by additional spatial information from the transverse intensity profile. Our temporal analysis describes the motion of a coronal loop as a kink oscillation damped by resonant absorption, and our spatial analysis is based on forward modeling the transverse EUV intensity profile of the loop under the isothermal and optically thin approximations. We use Bayesian analysis and Markov chain Monte Carlo sampling to apply our spatial and temporal models both individually and simultaneously to our data and compare the results with numerical simulations. Combining the two methods allows both the inhomogeneous layer width and density contrast to be calculated, which is not possible for the same data when each method is applied individually. We demonstrate that the assumption of an exponential damping profile leads to a significantly larger error in the inferred density contrast ratio compared with a Gaussian damping profile.

Anisotropy dependence of the fluctuation spectroscopy in the critical and gaussian regimes in superconducting NaFe1\u2212xCoxAs single crystals

We investigate thermal fluctuations in terms of diamagnetism and magnetotransport in superconducting NaFe1−xCoxAs single crystals with different doping levels. Results show that in the case of optimal doped and lightly overdoped (x = 0.03, 0.05) crystals the analysis in the critical as well as in the Gaussian fluctuation regions is consistent with the Ginzburg-Landau 3D fluctuation theory. However, in the case of strongly overdoped samples (x ≥ 0.07) the Ullah-Dorsey scaling of the fluctuation induced magnetoconductivity in the critical region confirms that thermal fluctuations exhibit a 3D anisotropic nature only in a narrow temperature region around Tc(H). This is consistent with the fact that in these samples the fluctuation effects in the Gaussian region above Tc may be described by the Lawrence-Doniach approach. Our results indicate that the anisotropy of these materials increases significantly with the doping level.

Renormalized Gaussian approach to size effects and exchange interactions: Application to localized ferromagnets and amorphous magnets

This paper gives a model field-theoretic description of thermodynamic magnetization fluctuations and exchange interactions in localized ferromagnets and amorphous magnets. A local Ginzburg-Landau type Hamiltonian is used to describe the properties observed in the transition region. The approach provides another method of tackling interacting spin systems dominated by size effects, fluctuations and correlations, which lead to a dimensional phenomenology of critical behavior. It is also found that the competition between long- and short-range interactions gives rise to the redistribution of the density of spins and causes the anisotropy of the electron spectrum. Above the upper-critical dimension, the approach behaves like mean-field theory with however, thermodynamic quantities modified by intrinsic critical fluctuations, whereas it predicts correctly the universal quantities for dimension 4 and below. At all temperatures, the model matches the magnetic observables, thus providing a unified picture for both the Gaussian and critical regimes.

Fluctuation-induced conductivity in melt-textured Pr-doped YBa2Cu3O7-δ composite superconductor

ABSTRACTIn this study, the effects of thermal fluctuations on the electrical conductivity in melt-textured YBa2Cu3O7-δ, Y0.95Pr0.05Ba2Cu3O7-δ and (YBa2Cu3O7-δ)0.95–(PrBa2Cu3O7-δ)0.05 composite superconductor were considered. The composite superconductor samples were prepared through the top seeding method using melt-textured NdBa2Cu3O7-d seeds. The resistivity measurements were performed with a low-frequency, low-current AC technique in order to extract the temperature derivative and analyze the influence of the praseodymium ion on the normal superconductor transition and consequently on the fluctuation regimes. The results show that the resistive transition is a two-step process. In the normal phase, above the critical temperature, Gaussian and critical fluctuation regimes were identified, while below the critical temperature, in the regime near the approach to the zero-resistance state, the fluctuation conductivity diverges as expected in a paracoherent-coherent transition.

Crossing statistics of laser light scattered through a nanofluid.

In this paper, we investigate the crossing statistics of speckle patterns formed in the Fresnel diffraction region by a laser beam scattering through a nanofluid. We extend zero-crossing statistics to assess the dynamical properties of the nanofluid. According to the joint probability density function of laser beam fluctuation and its time derivative, the theoretical frameworks for Gaussian and non-Gaussian regimes are revisited. We count the number of crossings not only at zero level but also for all available thresholds to determine the average speed of moving particles. Using a probabilistic framework in determining crossing statistics, a priori Gaussianity is not essentially considered; therefore, even in the presence of deviation from Gaussian fluctuation, this modified approach is capable of computing relevant quantities, such as mean value of speed, more precisely. Generalized total crossing, which represents the weighted summation of crossings for all thresholds to quantify small deviation from Gaussian statistics, is introduced. This criterion can also manipulate the contribution of noises and trends to infer reliable physical quantities. The characteristic time scale for having successive crossings at a given threshold is defined. In our experimental setup, we find that increasing sample temperature leads to more consistency between Gaussian and perturbative non-Gaussian predictions. The maximum number of crossings does not necessarily occur at mean level, indicating that we should take into account other levels in addition to zero level to achieve more accurate assessments.

Coronal loop density profile estimated by forward modelling of EUV intensity

Aims. The transverse density structuring of coronal loops was recently calculated for the first time using the general damping profile for kink oscillations. This seismological method assumes a density profile with a linear transition region. We consider to what extent this density profile accounts for the observed intensity profile of the loop, and how the transverse intensity profile may be used to complement the seismological technique.Methods. We use isothermal and optically transparent approximations for which the intensity of extreme ultraviolet (EUV) emission is proportional to the square of the plasma density integrated along the line of sight. We consider four different models for the transverse density profile; the generalised Epstein profile, the step function, the linear transition region profile, and a Gaussian profile. The effect of the point spread function is included and Bayesian analysis is used for comparison of the models.Results. The two profiles with finite transitions are found to be preferable to the step function profile, which supports the interpretation of kink mode damping as being due to mode coupling. The estimate of the transition layer width using forward modelling is consistent with the seismological estimate.Conclusions. For wide loops, that is those observed with sufficiently high spatial resolution, this method can provide an independent estimate of density profile parameters for comparison with seismological estimates. In the ill-posed case of only one of the Gaussian or exponential damping regimes being observed, it may provide additional information to allow a seismological inversion to be performed. Alternatively, it may be used to obtain structuring information for loops that do not oscillate.

Active cage model of glassy dynamics.

We build up a phenomenological picture in terms of the effective dynamics of a tracer confined in a cage experiencing random hops to capture some characteristics of glassy systems. This minimal description exhibits scale invariance properties for the small-displacement distribution that echo experimental observations. We predict the existence of exponential tails as a crossover between two Gaussian regimes. Moreover, we demonstrate that the onset of glassy behavior is controlled only by two dimensionless numbers: the number of hops occurring during the relaxation of the particle within a local cage and the ratio of the hopping length to the cage size.

Coronal loop seismology using damping of standing kink oscillations by mode coupling

Context. Kink oscillations of solar coronal loops are frequently observed to be strongly damped. The damping can be explained by mode coupling on the condition that loops have a finite inhomogeneous layer between the higher density core and lower density background. The damping rate depends on the loop density contrast ratio and inhomogeneous layer width. Aims. The theoretical description for mode coupling of kink waves has been extended to include the initial Gaussian damping regime in addition to the exponential asymptotic state. Observation of these damping regimes would provide information about the structuring of the coronal loop and so provide a seismological tool. Methods. We consider three examples of standing kink oscillations observed by the Atmospheric Imaging Assembly (AIA) of the Solar Dynamics Observatory (SDO) for which the general damping profile (Gaussian and exponential regimes) can be fitted. Determining the Gaussian and exponential damping times allows us to perform seismological inversions for the loop density contrast ratio and the inhomogeneous layer width normalised to the loop radius. The layer width and loop minor radius are found separately by comparing the observed loop intensity profile with forward modelling based on our seismological results. Results. The seismological method which allows the density contrast ratio and inhomogeneous layer width to be simultaneously determined from the kink mode damping profile has been applied to observational data for the first time. This allows the internal and external Alfven speeds to be calculated, and estimates for the magnetic field strength can be dramatically improved using the given plasma density. Conclusions. The kink mode damping rate can be used as a powerful diagnostic tool to determine the coronal loop density profile. This information can be used for further calculations such as the magnetic field strength or phase mixing rate.

Contextually in a Peres—Mermin square using arbitrary operators

The contextuality of quantum mechanics can be shown by the violation of inequalities based on measurements of well chosen observables. These inequalities have been designed separately for both discrete and continuous variables. Here we unify both strategies by introducing general conditions to demonstrate the contextuality of quantum mechanics from measurements of observables of arbitrary dimensions. Among the consequences of our results is the impossibility of having a maximal violation of contextuality in the Peres-Mermin scenario with discrete observables of odd dimensions. In addition, we show how to construct a large class of observables with a continuous spectrum enabling the realization of contextuality tests both in the Gaussian and non-Gaussian regimes.

Magneto-conductivity fluctuation in YBCO prepared by sintering of ball-milled precursor powder

We compare the electrical magneto-conductivity fluctuation between YBa2Cu3Oy (Y-123) and YBa2Cu3Oy embedded by an Y-deficient Y-123 nano-phase, generated by planetary ball-milling. Both samples were synthesized by solid state reaction with two stages of sintering at 950 °C and separated by energetic milling (milled sample) and hand grinding (unmilled sample). SEM analysis of the milled samples shows the appearance of spherical shaped nano-entities of Y-deficient Y-123 embedded in the Y-123 matrix. The magneto-conductivity data are analysed in terms of the temperature derivative of the resistivity and the logarithmic temperature derivative of the conductivity. The results show the occurrence of two-stage transitions: intragranular and intergranular, as well as a pairing transition splitting in the milled sample related to the presence of the Y-deficient nanoparticles. In the normal state, we identify a contribution of the Gaussian regimes for both samples. In the presence of a high magnetic field, the critical exponent near Tco of the milled material is higher than the one of the unmilled, indicating that the nanoparticles strengthen the effects of the order-parameter phase of individual grains of the Y-123 strongly disordered. This result fits well into a description based on a dirty limit of the general vortex-glass theory. In the paracoherent state, a crossover occurs and a small temperature range appears where the fluctuation conductivity may be governed by others mechanisms related to vortices dynamics. This temperature range is smaller in the milled sample.

Crystallographic analysis and conductivity fluctuations of the Y2Ba5Cu8O17 superconductor

Synthesis of the Y 2 Ba 5 Cu 8 O 17 superconducting material by the standard solid state reaction is reported. DC resistivity measurements reveal a bulk Tc = 104.95 K which was determined by the criterion of the maximum in the numerical temperature derivative of electrical resistivity. Structure characterization was performed by means of the X-ray diffraction (XRD) technique. A Rietveld refinement of XRD patterns shows that the material crystallizes in an orthorhombic structure, space group Pmm2 with cell parameters a = 3.8712(0) Å, b = 3.8481(4) Å and c = 27.1601(4) Å. In order to study the pairing mechanism close to Tc, conductivity fluctuation analysis was performed by the method of logarithmic temperature derivative of the conductivity excess. Close and above Tc, the conductivity fluctuation analysis reveal the occurrence of two fluctuation regimes characterized by the critical exponents λ 3D = 0.52 and λ 1D = 1.51, corresponding to 3D and 1D Gaussian regimes, respectively. The correlations of the critical exponents with the dimensionality of the fluctuation system for each Gaussian regime were performed by using the Aslamazov–Larkin theory.

Portmanteau inequalities on the Poisson space: mixed regimes and multidimensional clustering

Using Malliavin operators together with an interpolation technique inspired by Arratia, Goldstein and Gordon (1989), we prove a new inequality on the Poisson space, allowing one to measure the distance between the laws of a general random vector, and of a target random element composed of Gaussian and Poisson random variables. Several consequences are deduced from this result, in particular: (1) new abstract criteria for multidimensional stable convergence on the Poisson space, (2) a class of mixed limit theorems, involving both Poisson and Gaussian limits, (3) criteria for the asymptotic independence of U-statistics following Gaussian and Poisson asymptotic regimes. Our results generalize and unify several previous findings in the field. We provide an application to joint sub-graph counting in random geometric graphs.

Asset Pricing with Second-Order Esscher Transforms

The purpose of the paper is to introduce, in the class of discrete time no-arbitrage asset pricing models, a wider bridge between the historical and the risk-neutral state vector dynamics and to preserve, at the same time, its tractability and flexibility. This goal is achieved by introducing the notion of Exponential-Quadratic stochastic discount factor (SDF) or, equivalently, the notion of Second-Order Esscher Transform. Then, focusing on security market models, this approach is developed in three important multivariate stochastic frameworks: the conditionally Gaussian framework, the conditionally Mixed-Normal and the conditionally Gaussian Switching Regimes framework. In the conditionally multivariate Gaussian case, our approach determines a risk-neutral mean as a function of (the short rate and of) the risk-neutral variance-covariance matrix which is different from the historical one. The conditionally mixed-normal Gaussian case provides a first generalization of the Gaussian setting, in which the risk-neutral variance-covariance matrices and mixing weights of all components (in the finite mixture) can be different from the historical ones. The Gaussian switching regime case introduces further flexibility given the serial dependence of regimes and the introduction of the regime indicator function in the exponential-quadratic SDF. We also develop switching regime models which include (in the factor's conditional mean and conditional variance) additive impacts of the present and past regimes and we stress their interpretation in terms of general discrete-time jump-diffusion'' models in which the risk included in the first and second moment of jumps is priced. Even if we focus on security market models, we do not make any particular assumption about the state vector and therefore this approach could be used not only in option pricing models, but also for instance in interest rate and credit risk models.

Theory of temperature fluctuation statistics in superconductor-normal metal tunnel structures

We describe the statistics of temperature fluctuations in a SINIS structure, where a normal metal island (N) is coupled by tunnel junctions (I) to two superconducting leads (S). We specify conditions under which this structure exhibits manifestly non-Gaussian fluctuations of temperature. We consider both the Gaussian and non-Gaussian regimes of these fluctuations, and the current fluctuations that are caused by the fluctuating temperature. We also describe a measurement setup that could be used to observe the temperature fluctuations.