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A new set of equations captures the dynamical interplay of electrons and vibrations in crystals and forms a basis for computational studies.

Although a crystal is a highly ordered structure, it is never at rest: its atoms are constantly vibrating about their equilibrium positions—even down to zero temperature. Such vibrations are called phonons, and their interaction with the electrons that hold the crystal together is partly responsible for the crystal’s optical properties, its ability to conduct heat or electricity, and even its vanishing electrical resistance if it is superconducting. Predicting, or at least understanding, such properties requires an accurate description of the interplay of electrons and phonons. This task is formidable given that the electronic problem alone—assuming that the atomic nuclei stand still—is already challenging and lacks an exact solution. Now, based on a long series of earlier milestones, Gianluca Stefanucci of the Tor Vergata University of Rome and colleagues have made an important step toward a complete theory of electrons and phonons [1].

At a low level of theory, the electron–phonon problem is easily formulated. First, one considers an arrangement of massive point charges representing electrons and atomic nuclei. Second, one lets these charges evolve under Coulomb’s law and the Schrödinger equation, possibly introducing some perturbation from time to time. The mathematical representation of the energy of such a system, consisting of kinetic and interaction terms, is the system’s Hamiltonian. However, knowing the exact theory is not enough because the corresponding equations are only formally simple. In practice, they are far too complex—not least owing to the huge number of particles involved—so that approximations are needed. Hence, at a high level, a workable theory should provide the means to make reasonable approximations yielding equations that can be solved on today’s computers.

Mind mastery refers to intentionally developing self-awareness and discipline to take control of your thought patterns, emotional responses, and behaviors. Rather than operating on autopilot or being swept away by negativity, you respond consciously in alignment with your values and goals. Benefits of mind mastery include reduced stress, achieving ambitions, fulfilled relationships, and overall life satisfaction.

Mastering your mind requires commitment, but small, consistent steps to steward your thoughts and manage your emotions will compound to impact your mental health and empower your life profoundly. Here are key techniques:

Practice observing your thoughts like clouds passing by without reacting or judging. Creating this mental space between stimulus and response allows you to gain perspective. Ask what evidence supports or contradicts anxious thoughts.

Generic single-stranded oligonucleotides used as a uniform transmission signal can reliably integrate large-scale DNA integrated circuits with minimal leakage and high fidelity for general-purpose computing.

A cosmologist explains the mind-bending hypothesis that our universe could have branched off from a black hole singularity in another universe.

Advances in artificial intelligence have prompted extensive public concern about its capacity to contribute to the spread of misinformation, bias, and cybersecurity breaches—and its potential existential threat to humanity. But, if anything, AI can aid human beings in making decisions aimed at improving social equality, safety, productivity—and mitigate some existential threats.

Scientists have developed a nuclear fuel source no larger than a seed, which NASA will test for use in future moon missions.

According to Einstein’s theory of special relativity, first published in 1905, light can be converted into matter when two light particles collide with intense force. But, try as they might, scientists have never been able to do this. No one could create the conditions needed to transform light into matter — until now.

Physicists claim to have generated matter from pure light for the first time — a spectacular display of Einstein’s most famous equation.

This is a significant breakthrough, overcoming a theoretical barrier that seemed impossible only a few decades ago.

A concept video of Sky Cruise, a giant flying machine that can carry 5,000 passengers and has all the luxuries of the world, has gone viral on the internet. The maker of the video claims that such an aircraft built in the future would have no carbon footprint, The Independent reported.

The concept of a floating world in itself is not new and has been described even in Jonathan Swift’s works from the 18th century, much before the Wright Brothers made their first flight. Fans of animated movies might have also come across the concept in 1986 Japanese movie, Castle in the Sky.

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