Quantum systems tend to become less “quantum-y” as they interact with their environment. So when developing a mathematical description, it’s usually simpler just to view them as being closed off from their surroundings.

But ‘open’ systems are more realistic and sometimes even more interesting. Open quantum systems can be modelled using the so-called Lindblad equation, which describes the quantum evolution with time as both energy and coherence are lost to the environment.

Scientists from Tsinghua University have expanded the Lindblad equation to track the time evolution in an open system of a quantum property that that has become the hottest topic in condensed-matter physics: topology. Topology has formed the basis of numerous exotic states of matter over the last few decades. Now researchers show that an open system can undergo a topological transition as a result of dissipation, or loss.

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Ensuring that different clocks are giving the same time is crucial to enable electronic systems to talk to each other. But what is the cost of this synchronisation at the thermodynamic level?

To answer this question, scientists from the East China Normal University in Shanghai studied two tiny resonating membranes inside an optical cavity. Such optomechanical systems can exhibit quantum properties even on a macroscopic scale, and so they’re an ideal platform for studying ultrasensitive metrology and nonequilibrium thermodynamics. Each of the membranes represented a nanomechanical clock, and the two could be synchronised by increasing their coupling strength by adding more light to the cavity. In this way, the team was able to measure the dependence of the degree of synchronisation on the overall entropy cost.

They hope that this experimental investigation will serve as a starting point to explore synchronisation in navigation-satellite and fibre-optic systems with the aim of improving clock performance.

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The Earth is not a perfect sphere. This makes very precise modelling of our planet’s gravitational field rather tricky. To simplify the maths, scientists can consider a so-called Brillouin sphere: the smallest planet-centred sphere that completely encloses the mass composing the planet. In the case of the Earth, the Brillouin sphere touches the Earth at a single point—the top of Mount Chimborazo in Ecuador. The gravitational field outside the sphere can be accurately simulated by combining a series of simple equations called a spherical harmonic expansion.

But does this still hold true for the field inside the Brillouin sphere, which by definition includes the planet’s surface? Scientists from Ohio State University and the University of Connecticut say “no”. The team presented an analytical and numerical study that demonstrates clearly how and why the spherical harmonic expansion leads to prediction errors.

However, all is not lost. Their ultra-accurate simulations of the gravity field offer guidance toward a new mathematical foundation of gravity modelling. An upgraded simulator, which accounts for density variations within planets, will allow rigorous testing of proposed alternative ways to represent the gravity field beneath the Brillouin sphere.

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Periodic changes in celestial bodies provide astronomers with a great deal of information about the universe. Sporadic alterations in a star’s brightness could be a signature of it being part of a binary system or indicate the presence of an orbiting planet. And the periodic rotation of objects in the Kuiper Belt tells us about planet formation and the development of our solar system. But these changes are rarely perfectly regular, so astronomers have developed a range of statistical methods to characterize aperiodic observations.

Now, mathematical statisticians from North Carolina State University have compared the robustness of these various methods for the first time. The team investigated the success of four different methods using the same simulated data, and were able to develop a list of recommended usage and limitations that will be essential guidance for all observation astronomers.

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