Historically, the majority of studies in condensed matter physics have focused on Hermitian systems – closed systems that conserve energy. However, in reality, dissipative processes or non-equilibrium dynamics are commonly present and so real-world systems are anything but Hermitian.

Recently however people have begun to study non-Hermitian systems in detail and have found a range of interesting topological properties. The term topology was originally used to refer to a branch of mathematics describing geometric objects. Here, however, it means the study of the electron band structure in solids, as well as periodic motion more generally.

Topological arguments are often used to determine universal material properties such as conductivity or magnetic susceptibility. For example, topological insulators are insulating in the bulk but have conducting surface or edge states and can be used in a range of applications, such as quantum computing.

Previous work on non-Hermitian band topology has been restricted to one system at a time, or one property at a time. There’s been no way to link between materials or scenarios and no generalisation.

A research team formed of scientists from the Freie Universität Berlin, the Perimeter Institute, and Stockholm University have now brought everything together by using symmetry arguments to build a general, comprehensive theoretical framework for these exciting new systems.

Predictions made by the authors’ analysis will lead to a better understanding of condensed matter physics and hopefully to new developments in a range of fields including optics, acoustics, and electronics.

A molecular machine is an assembly of molecular components that produces mechanical movements in response to specific stimuli, similar to everyday objects like hinges and switches.

The power of what can be accomplished with these machines in biology is huge. They are responsible for everything from muscle contraction to DNA replication.

Attaining the same precise control over molecular motion with artificial molecular machines is currently an active area of research.

Researchers from the August Chełkowski Institute of Physics have been studying one component of these machines – rotary molecular motors. As the name suggests, these machines convert chemical or electrochemical energy into mechanical work by rotating one part relative to another.

The team built their motors out of phenylene molecules within a solid crystal and studied them with a technique called broadband dielectric spectroscopy.

This measures how a material responds to a varying electrical field.  In addition to imaging rotational motion, it can detect interactions between the molecular machine and its environment.

The team found several key markers within their data that reflected the strength of these interactions and therefore how well the molecular rotors were able to rotate. Using these markers will be important in optimising the design of future molecular rotors and brings us one step closer towards artificial molecular machines.

New techniques have recently allowed the study of the behaviour of electrons in a similar way to how photons are studied in traditional optics. This emerging area of research – called quantum electron optics – focuses on manipulating and controlling electron waves to create phenomena such as interference and diffraction.

These wavelike electrons are fundamentally quantum in nature. This means that they can emit light in unique ways when shaped and modulated by lasers.

In this work, the team found that the rate of light emission by electrons does not depend on the shape of the electron wave, while the quantum state of the emitted light does.

Essentially, this means that by changing the shape of the electron wave, they can control the characteristics of the light produced. The emitted light exhibits non-classical quantum properties, differing significantly from the light we encounter daily, which follows classical physics rules.

To produce a much stronger photon signal, the researchers also took advantage of superradiance, where multiple electrons emit light in a coordinated manner, resulting in a much stronger emission than the sum of individual emissions. Another purely quantum effect.

The excitement around this research is based on its potential to advance quantum computing and communication by providing new tools for controlling the many quantum states that are required to make them work.

It could also lead to the development of new light sources with special properties, useful in a whole range of scientific and technological applications.

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.

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.

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.

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.