Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userStudy of hydrogen atom described by a generalized wave equation: what can we still learn about space dimensionality
116
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Hydrogen atom is supposed to be described by a generalization of Schrodinger equation, in which the Hamiltonian depends on an iterated Laplacian and a Coulomb-like potential $r^{-beta}$. Starting from previously obtained solutions for this equation using the $1/N$ expansion method, it is shown that new light can be shed on the problem of understanding the dimensionality of the world as proposed by Paul Ehrenfest. A surprisingly new result is obtained. Indeed, for the first time, we can understand that not only the sign of energy but also the value of the ground state energy of hydrogen atom is related to the threefold nature of space.
rate research
Read More
Learning problems form an important category of computational tasks that generalizes many of the computations researchers apply to large real-life data sets. We ask: what concept classes can be learned privately, namely, by an algorithm whose output does not depend too heavily on any one input or specific training example? More precisely, we investigate learning algorithms that satisfy differential privacy, a notion that provides strong confidentiality guarantees in contexts where aggregate information is released about a database containing sensitive information about individuals. We demonstrate that, ignoring computational constraints, it is possible to privately agnostically learn any concept class using a sample size approximately logarithmic in the cardinality of the concept class. Therefore, almost anything learnable is learnable privately: specifically, if a concept class is learnable by a (non-private) algorithm with polynomial sample complexity and output size, then it can be learned privately using a polynomial number of samples. We also present a computationally efficient private PAC learner for the class of parity functions. Local (or randomized response) algorithms are a practical class of private algorithms that have received extensive investigation. We provide a precise characterization of local private learning algorithms. We show that a concept class is learnable by a local algorithm if and only if it is learnable in the statistical query (SQ) model. Finally, we present a separation between the power of interactive and noninteractive local learning algorithms.
Ultra-relativistic electromagnetic plasmas can be used for improving our understanding of the quark-gluon plasma. In the weakly coupled regime both plasmas can be described by transport theoretical and quantum field theoretical methods leading to similar results for the plasma properties (dielectric tensor, dispersion relations, plasma frequency, Debye screening, transport coefficients, damping and particle production rates). In particular, future experiments with ultra-relativistic electron-positron plasmas in ultra-strong laser fields might open the possibility to test these predictions, e.g. the existence of a new fermionic plasma wave (plasmino). In the strongly coupled regime electromagnetic plasmas such as complex plasmas can be used as models or at least analogies for the quark-gluon plasma possibly produced in relativistic heavy-ion experiments. For example, pair correlation functions can be used to investigate the equation of state and cross section enhancement for parton scattering can be explained.
Precision studies at electron-positron colliders with center-of-mass energies in the charm-tau region and below have strongly contributed to our understanding of light-meson interactions at low energies. We focus on the processes involving two or three light mesons with invariant masses below nucleon-antinucleon threshold. A prominent role is given to the interactions of the nine lightest pseudoscalar mesons (pions, kaons, $eta$, and $eta$) and the two narrow neutral isoscalar vector mesons $omega$ and $phi$. Experimental methods used to produce the mesons are reviewed as well as theory tools to extract properties of the meson-meson interactions. Examples of recent results from the DA$Phi$NE, BEPCII, and VEPP-2000 colliders are presented. In the outlook we briefly discuss prospects for further studies at future super-charm-tau factories.
Machine learning is increasingly recognized as a promising technology in the biological, biomedical, and behavioral sciences. There can be no argument that this technique is incredibly successful in image recognition with immediate applications in diagnostics including electrophysiology, radiology, or pathology, where we have access to massive amounts of annotated data. However, machine learning often performs poorly in prognosis, especially when dealing with sparse data. This is a field where classical physics-based simulation seems to remain irreplaceable. In this review, we identify areas in the biomedical sciences where machine learning and multiscale modeling can mutually benefit from one another: Machine learning can integrate physics-based knowledge in the form of governing equations, boundary conditions, or constraints to manage ill-posted problems and robustly handle sparse and noisy data; multiscale modeling can integrate machine learning to create surrogate models, identify system dynamics and parameters, analyze sensitivities, and quantify uncertainty to bridge the scales and understand the emergence of function. With a view towards applications in the life sciences, we discuss the state of the art of combining machine learning and multiscale modeling, identify applications and opportunities, raise open questions, and address potential challenges and limitations. We anticipate that it will stimulate discussion within the community of computational mechanics and reach out to other disciplines including mathematics, statistics, computer science, artificial intelligence, biomedicine, systems biology, and precision medicine to join forces towards creating robust and efficient models for biological systems.
It is well known that the Klein-Gordon equation in curved spacetime is conformally noninvariant, both with and without a mass term. We show that such a noninvariance provides nontrivial physical insights at different levels, first within the fully relativistic regime, then at the nonrelativistic regime leading to the Schrodinger equation, and then within the de Broglie-Bohm causal interpretation of quantum mechanics. The conformal noninvariance of the Klein-Gordon equation coupled to a vector potential is confronted with the conformal invariance of Maxwells equations in the presence of a charged current. The conformal invariance of the non-minimally coupled Klein-Gordon equation to gravity is then examined in light of the conformal invariance of Maxwells equations. Finally, the consequence of the noninvariance of the equation on the Aharonov-Bohm effect in curved spacetime is discussed. The issues that arise at each of these different levels are thoroughly analyzed.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
