共查询到20条相似文献,搜索用时 31 毫秒
1.
We study the stability and the solvability of a family of problems with Dirichlet boundary conditions, where , u, are allowed to vary as well. Applications for boundary value problems involving the p-Laplacian operator are highlighted. 相似文献
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A geometrical formulation of estimation theory for finite-dimensional -algebras is presented. This formulation allows to deal with the classical and quantum case in a single, unifying mathematical framework. The derivation of the Cramer–Rao and Helstrom bounds for parametric statistical models with discrete and finite outcome spaces is presented. 相似文献
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A new type of quantum correction to the structure of classical black holes is investigated. This concerns the physics of event horizons induced by the occurrence of stochastic quantum gravitational fields. The theoretical framework is provided by the theory of manifestly covariant quantum gravity and the related prediction of an exclusively quantum-produced stochastic cosmological constant. The specific example case of the Schwarzschild–deSitter geometry is looked at, analyzing the consequent stochastic modifications of the Einstein field equations. It is proved that, in such a setting, the black hole event horizon no longer identifies a classical (i.e., deterministic) two-dimensional surface. On the contrary, it acquires a quantum stochastic character, giving rise to a frame-dependent transition region of radial width between internal and external subdomains. It is found that: (a) the radial size of the stochastic region depends parametrically on the central mass M of the black hole, scaling as ; (b) for supermassive black holes is typically orders of magnitude larger than the Planck length . Instead, for typical stellar-mass black holes, may drop well below . The outcome provides new insight into the quantum properties of black holes, with implications for the physics of quantum tunneling phenomena expected to arise across stochastic event horizons. 相似文献
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Zhi Lin 《Annalen der Physik》2021,533(1)
The phase boundaries of periodically driven spin–orbit coupled BECs with effective two‐body interactions are analytically calculated by using variational method. The phase diagrams of periodically driven and systems present distinguished features from undriven systems, respectively. For the BECs, the critical density (density at quantum tricritical point) will be dramatically reduced in some parameter regions, and the prospect of observing this intriguing quantum tricritical point is greatly enlarged. Moreover, a series of quantum tricritical points emerge quasi‐periodically when increasing the Raman coupling strength with fixed density. In the BECs, two hyperfine states of atoms can be miscible within the suitable regions of driving parameter space. As a result, systems will stay in the stripe phase with small Raman frequency at typical density, which expands the region of stripe phase in the phase diagram. In addition, an absence of quantum tricritical point in such system is observed, which is very unlike systems. 相似文献
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Mariano Matilla-García Isidro Morales Jose Miguel Rodríguez Manuel Ruiz Marín 《Entropy (Basel, Switzerland)》2021,23(2)
The modeling and prediction of chaotic time series require proper reconstruction of the state space from the available data in order to successfully estimate invariant properties of the embedded attractor. Thus, one must choose appropriate time delay and embedding dimension p for phase space reconstruction. The value of can be estimated from the Mutual Information, but this method is rather cumbersome computationally. Additionally, some researchers have recommended that should be chosen to be dependent on the embedding dimension p by means of an appropriate value for the time delay , which is the optimal time delay for independence of the time series. The C-C method, based on Correlation Integral, is a method simpler than Mutual Information and has been proposed to select optimally and . In this paper, we suggest a simple method for estimating and based on symbolic analysis and symbolic entropy. As in the C-C method, is estimated as the first local optimal time delay and as the time delay for independence of the time series. The method is applied to several chaotic time series that are the base of comparison for several techniques. The numerical simulations for these systems verify that the proposed symbolic-based method is useful for practitioners and, according to the studied models, has a better performance than the C-C method for the choice of the time delay and embedding dimension. In addition, the method is applied to EEG data in order to study and compare some dynamic characteristics of brain activity under epileptic episodes 相似文献
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We present computer simulation and theoretical results for a system of N Quantum Hard Spheres (QHS) particles of diameter and mass m at temperature T, confined between parallel hard walls separated by a distance , within the range . Semiclassical Monte Carlo computer simulations were performed adapted to a confined space, considering effects in terms of the density of particles , where V is the accessible volume, the inverse length and the de Broglie’s thermal wavelength , where k and h are the Boltzmann’s and Planck’s constants, respectively. For the case of extreme and maximum confinement, and , respectively, analytical results can be given based on an extension for quantum systems of the Helmholtz free energies for the corresponding classical systems. 相似文献
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The ratio between the Landé g‐factors of the Rb and Rb ground‐state hyperfine levels is experimentally measured to be , consistent with previous measurements. The g‐factor ratio is determined by comparing the Larmor frequencies of overlapping ensembles of Rb and Rb atoms contained within an evacuated, antirelaxation‐coated vapor cell. The atomic spins are polarized via synchronous optical pumping and the Larmor frequencies are measured by off‐resonant probing using optical rotation of linearly polarized light. The accuracy of this measurement of exceeds that of previous measurements by a factor of ≈50 and is sensitive to effects related to quantum electrodynamics. 相似文献
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Probability is an important question in the ontological interpretation of quantum mechanics. It has been discussed in some trajectory interpretations such as Bohmian mechanics and stochastic mechanics. New questions arise when the probability domain extends to the complex space, including the generation of complex trajectory, the definition of the complex probability, and the relation of the complex probability to the quantum probability. The complex treatment proposed in this article applies the optimal quantum guidance law to derive the stochastic differential equation governing a particle’s random motion in the complex plane. The probability distribution of the particle’s position over the complex plane is formed by an ensemble of the complex quantum random trajectories, which are solved from the complex stochastic differential equation. Meanwhile, the probability distribution is verified by the solution of the complex Fokker–Planck equation. It is shown that quantum probability and classical probability can be integrated under the framework of complex probability , such that they can both be derived from by different statistical ways of collecting spatial points. 相似文献
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Juhui Wei Zhangming He Jiongqi Wang Dayi Wang Xuanying Zhou 《Entropy (Basel, Switzerland)》2021,23(3)
Weak fault signals, high coupling data, and unknown faults commonly exist in fault diagnosis systems, causing low detection and identification performance of fault diagnosis methods based on statistics or cross entropy. This paper proposes a new fault diagnosis method based on optimal bandwidth kernel density estimation (KDE) and Jensen–Shannon (JS) divergence distribution for improved fault detection performance. KDE addresses weak signal and coupling fault detection, and JS divergence addresses unknown fault detection. Firstly, the formula and algorithm of the optimal bandwidth of multidimensional KDE are presented, and the convergence of the algorithm is proved. Secondly, the difference in JS divergence between the data is obtained based on the optimal KDE and used for fault detection. Finally, the fault diagnosis experiment based on the bearing data from Case Western Reserve University Bearing Data Center is conducted. The results show that for known faults, the proposed method has and higher detection rate than statistics and the cross entropy method, respectively. For unknown faults, statistics cannot effectively detect faults, and the proposed method has approximately higher detection rate than the cross entropy method. Thus, the proposed method can effectively improve the fault detection rate. 相似文献
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C. W. J. Beenakker A. Donís Vela G. Lemut M. J. Pacholski J. Tworzydło 《Annalen der Physik》2023,535(7):2300081
Methods to discretize the Hamiltonian of a topological insulator or topological superconductor, without giving up on the topological protection of the massless excitations (respectively, Dirac fermions or Majorana fermions) are reviewed. The method of tangent fermions, pioneered by Richard Stacey, is singled out as being uniquely suited for this purpose. Tangent fermions propagate on a dimensional space-time lattice with a tangent dispersion: in dimensionless units. They avoid the fermion doubling lattice artefact that will spoil the topological protection, while preserving the fundamental symmetries of the Dirac Hamiltonian. Although the discretized Hamiltonian is nonlocal, as required by the fermion-doubling no-go theorem, it is possible to transform the wave equation into a generalized eigenproblem that is local in space and time. Applications that are discussed include Klein tunneling of Dirac fermions through a potential barrier, the absence of localization by disorder, the anomalous quantum Hall effect in a magnetic field, and the thermal metal of Majorana fermions. 相似文献
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Sanghoon Kwon 《Entropy (Basel, Switzerland)》2021,23(1)
The discrete geodesic flow on Nagao lattice quotient of the space of bi-infinite geodesics in regular trees can be viewed as the right diagonal action on the double quotient of by and . We investigate the measure-theoretic entropy of the discrete geodesic flow with respect to invariant probability measures. 相似文献
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Word embeddings based on a conditional model are commonly used in Natural Language Processing (NLP) tasks to embed the words of a dictionary in a low dimensional linear space. Their computation is based on the maximization of the likelihood of a conditional probability distribution for each word of the dictionary. These distributions form a Riemannian statistical manifold, where word embeddings can be interpreted as vectors in the tangent space of a specific reference measure on the manifold. A novel family of word embeddings, called -embeddings have been recently introduced as deriving from the geometrical deformation of the simplex of probabilities through a parameter , using notions from Information Geometry. After introducing the -embeddings, we show how the deformation of the simplex, controlled by , provides an extra handle to increase the performances of several intrinsic and extrinsic tasks in NLP. We test the -embeddings on different tasks with models of increasing complexity, showing that the advantages associated with the use of -embeddings are present also for models with a large number of parameters. Finally, we show that tuning allows for higher performances compared to the use of larger models in which additionally a transformation of the embeddings is learned during training, as experimentally verified in attention models. 相似文献
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We explore the quadratic form of the gravitational theory to derive rotating N-dimensions black hole solutions with rotation parameters. Here, R is the Ricci scalar and b is the dimensional parameter. We assumed that the N-dimensional spacetime is static and it has flat horizons with a zero curvature boundary. We investigated the physics of black holes by calculating the relations of physical quantities such as the horizon radius and mass. We also demonstrate that, in the four-dimensional case, the higher-order curvature does not contribute to the black hole, i.e., black hole does not depend on the dimensional parameter b, whereas, in the case of , it depends on parameter b, owing to the contribution of the correction term. We analyze the conserved quantities, energy, and angular-momentum, of black hole solutions by applying the relocalization method. Additionally, we calculate the thermodynamic quantities, such as temperature and entropy, and examine the stability of black hole solutions locally and show that they have thermodynamic stability. Moreover, the calculations of entropy put a constraint on the parameter b to be to obtain a positive entropy. 相似文献
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Ofir E. Alon 《Entropy (Basel, Switzerland)》2020,22(12)
A solvable model of a periodically driven trapped mixture of Bose–Einstein condensates, consisting of interacting bosons of mass driven by a force of amplitude and interacting bosons of mass driven by a force of amplitude , is presented. The model generalizes the harmonic-interaction model for mixtures to the time-dependent domain. The resulting many-particle ground Floquet wavefunction and quasienergy, as well as the time-dependent densities and reduced density matrices, are prescribed explicitly and analyzed at the many-body and mean-field levels of theory for finite systems and at the limit of an infinite number of particles. We prove that the time-dependent densities per particle are given at the limit of an infinite number of particles by their respective mean-field quantities, and that the time-dependent reduced one-particle and two-particle density matrices per particle of the driven mixture are condensed. Interestingly, the quasienergy per particle does not coincide with the mean-field value at this limit, unless the relative center-of-mass coordinate of the two Bose–Einstein condensates is not activated by the driving forces and . As an application, we investigate the imprinting of angular momentum and its fluctuations when steering a Bose–Einstein condensate by an interacting bosonic impurity and the resulting modes of rotations. Whereas the expectation values per particle of the angular-momentum operator for the many-body and mean-field solutions coincide at the limit of an infinite number of particles, the respective fluctuations can differ substantially. The results are analyzed in terms of the transformation properties of the angular-momentum operator under translations and boosts, and as a function of the interactions between the particles. Implications are briefly discussed. 相似文献
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In this paper, the cosmological model of the Universe has been presented in gravity and the parameters are constrained from the cosmological data sets. At the beginning, a well motivated form of has been employed, where α, β, and n are model parameters. The Hubble parameter is obtained in redshift with some algebraic manipulation from the considered form of . Then it is parameterized with the recent data and data using Markov chain Monte Carlo analysis. The obtained model parameter values are validated with the baryon acoustic oscillation data set. A parametrization of the cosmographic parameters shows the early deceleration and late time acceleration with the transition at . The diagnostics gives positive slope which shows that the model is in the phantom phase. Also the current age of the Universe has been obtained as, . Based on the present analysis, it indicates that the gravity may provide an alternative to dark energy for addressing the current cosmic acceleration. 相似文献
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