Quantum scar


In physics, and especially quantum chaos, a quantum scar is a kind of quantum state with a high likelihood of existing in unstable classical periodic orbits in classically chaotic systems. The term also refers to the wave function of such a state, which is more formally defined by having an enhancement of an eigenfunction along unstable classical periodic orbits. Since the square-norm of quantum wavefunctions yield probability densities in the Copenhagen interpretation, the two notions correspond.
Quantum scars were discovered and explained in 1984 by Eric J. Heller and are part of the large field of quantum chaos. Scars are unexpected in the sense that stationary classical distributions at the same energy are completely uniform in space with no special concentrations along periodic orbits, and quantum chaos theory of energy spectra gave no hint of their existence. Scars stand out to the eye in some eigenstates of classically chaotic systems, but are quantified by projection of the eigenstates onto certain test states, often Gaussians, having both average position and average momentum along the periodic orbit. These test states give a provably structured spectrum that reveals the necessity of scars, especially for the shorter and least unstable periodic orbits.
Scars have been found and are important in membranes, wave mechanics, optics, microwave systems, water waves, and electronic motion in microstructures.
Scars have occurred in investigations for potential applications of Rydberg states to quantum computing, specifically acting as qubits for quantum simulation. The particles of the system in an alternating ground state-Rydberg state configuration continually entangled and disentangled rather than remaining entangled and undergoing thermalization. Systems of the same atoms prepared with other initial states did thermalize as expected. The researchers dubbed the phenomenon "quantum many-body scarring".
The area of quantum many-body scars is a subject of active research.

Explanation

The causes of quantum scarring are not well understood. Investigations are ongoing.
One possible proposed explanation is that quantum scars represent integrable systems, or nearly do so, and this could prevent thermalization from ever occurring. This has drawn criticisms arguing that a non-integrable Hamiltonian underlies the theory.

Potential applications to quantum computing

are desired, as any perturbations to qubit states can cause the states to thermalize, leading loss of quantum information. Scarring of qubit states is seen as a potential way to protect qubit states from outside disturbances leading to decoherence and information loss.