Scientists have solved a Physics problem thanks to a new method for creating curved spaces. They have shown, metaphorically, that a sheet of paper can be folded without touching it because it is not actually in flat space, but curved. Amazing.
Researchers at Purdue University in the United States have verified that curved spaces can be created without applying deformations: it is like folding a sheet of paper without touching it. That means that space can be curved, at least in the quantum mechanical scenario.
Although this is a complex discovery, we can simplify it as follows: we already know how strange the quantum world is and that one of its paradoxes, known as tunnel effect, indicates that a particle can pass through a tunnel containing an insurmountable obstacle, because it is capable of becoming a wave and passing through a wall as if it were a sound wave. Once on the other side of the tunnel, he regains his particle identity.
This effect can be made more complex if we add another variable to the tunnel effect. To do this we have to go back in time and retrieve a contribution from Charles Hermite, a 19th-century French mathematician who did important research in mathematics. He created what is known as the Hermitian matrix or grid. Describe what happens when a ball is constantly bouncing back and forth in a given space.
Playing with the ball
In this mathematical assumption, the ball bounces on either side of the net and Hermite established that, when the ball bounces both to the left and to the right, this property defines the net as Hermitian. But if the ball breaks that symmetry in its travels, and bounces more to the right than to the left (for example), the net it is playing on is considered non-Hermitian.
Physicists believe that a network, Hermitian or not, also plays with the tunnel effect typical of quantum mechanics, because just as the ball bounces from one side to the other, altering its Hermitian or non-Hermitian state, the tunnel effect can play also a similar effect: the quantum particle that has crossed the insurmountable barrier, can return to its previous position, although not always in the same way. In this assumption, we could speak of a non-Hermitian tunnel, since there is no symmetry in the movement of the quantum particle in its routes to and fro within the tunnel.
What the Purdue University team, led by Chenwei Lvit is something very relevant to physics: comes to say that when a quantum particle passes through a non-Hermitian lattice (or tunnel), it is actually moving in a curvature, not in flat space.
That means a non-Hermitian lattice doubles the space where a quantum particle resides. Stated graphically, a quantum particle in a non-Hermitian lattice/tunnel moves on a curved surface. Researchers have even been able to establish that the ratio between the amplitudes of the tunnel in one direction and those in the opposite direction determines the size of the curved surface.
This means that, under certain conditions, the space (of the tunnel or the net where the ball bounces) becomes curved and normalizes the non-Hermitian phenomena, until now considered anomalous. Once again quantum mechanics opens the eyes of astonished physicists.
The researchers explain in this regard that this discovery shows that this non-Hermitian characteristic of the tunnel effect can be used to simulate quantum systems in curved spaces, a novelty, because until now most of the quantum systems simulated in the laboratory are flat.
To think that quantum systems can now be accessed in curved spaces may mean the opening of a new frontier in the knowledge of the most intriguing nature, which arises from combining tunneling with non-Hermitian networks, quantum mechanics with topological spaces.
Is duality between non-Hermitianity and curved spaces establishes a new theoretical framework to unify Hermitian and non-Hermitian physics, the protagonists of this research explain in a statement.
They add: An example is that a hyperbolic surface could be created and then threaded by a magnetic field. This could allow scientists to explore the responses of Hall quantum states to finite curvatures, a pending question in the physics of condensed matter. On the other hand, that duality allows researchers to use curved spaces to explore non-Hermitian quantum physics.
Obviously, this is a first step, since what this research has achieved is to land on the beach of an unknown island or continent in the world of physics, so the Purdue team will continue to theoretically explore more connections between physics not hermitic and curved spaces. He also hopes to help bridge the gap between these two topics in physics (non-Hermitian quantum physics and curved spaces) and bring these two different communities together in future research.
Curving the space by non-Hermiticity. Chenwei Lv et al. Nature Communications volume 13, Article number: 2184 (2022). DOI :https://doi.org/10.1038/s41467-022-29774-8