# A new duality solves a

## Found at: gopher.erb.pw:70/roman/phlog2022/529.txt

A new duality solves a physics mystery

In conventional wisdom, producing a curved space requires

distortions, such as bending or stretching a flat space. A team

of researchers at Purdue University have discovered a new

method to create curved spaces that also solves a mystery in

physics. Without any physical distortions of physical systems,

the team has designed a scheme using non-Hermiticity, which

exists in any systems coupled to environments, to create a

hyperbolic surface and a variety of other prototypical curved

spaces (https://bit.ly/3znz4Cu).

The team recently published their findings in Nature Communications.

Of the members of the team, most work at Purdue University's West

Lafayette campus. Chenwei Lv, graduate student, is the lead author,

and other members of the Purdue team include Prof. Qi Zhou, and

Zhengzheng Zhai, postdoctoral fellow. The co-first author, Prof.

Ren Zhang from Xi'an Jiaotong University, was a visiting scholar

at Purdue when the project was initiated.

In order to understand how this discovery works, first one must

understand the difference between Hermitian and non-Hermitian

systems in physics. Zhou explains it using an example in which

a quantum particle can "hop" between different sites on a lattice.

If the probability for a quantum particle to hop in the right

direction is the same as the probability to hop in the left

direction, then the Hamiltonian is Hermitian. If these two

probabilities are different, the Hamiltonian is non-Hermitian. This

is the reason that Chenwei and Ren Zhang have used arrows with

different sizes and thicknesses to denote the hopping probabilities

in opposite directions in their plot.

He further explains that their work provides an unprecedented

explanation of fundamental non-Hermitian quantum phenomena.

They found that a non-Hermitian Hamiltonian has curved the space

where a quantum particle resides. For instance, a quantum particle

in a lattice with nonreciprocal tunneling is in fact moving on

a curved surface. The ratio of the tunneling amplitudes along one

direction to that in the opposite direction controls how large the

surface is curved. In such curved spaces, all the strange non

Hermitian phenomena, some of which may even appear unphysical,

immediately become natural. It is the finite curvature that requires

orthonormal conditions distinct from their counterparts in flat

spaces. As such, eigenstates would not appear orthogonal if we

used the theoretical formula derived for flat spaces. It is also the

finite curvature that gives rise to the extraordinary non-Hermitian

skin effect that all eigenstates concentrate near one edge of the

system.

Now that the team has published their findings, they anticipate it

spinning off into multiple directions for further study. Physicists

studying curved spaces could implement their apparatuses to address

challenging questions in non-Hermitian physics. Also, physicists

working on non-Hermitian systems could tailor dissipations to

access non-trivial curved spaces that cannot be easily obtained by

conventional means. The Zhou research group will continue to

theoretically explore more connections between non-Hermitian

physics and curved spaces. They also hope to help bridge the gap

between these two physics subjects and bring these two different

communities together with future research.