Related papers: Maximal scarring for eigenfunctions of quantum gra…
The recent discovery of quantum many-body scar states has revealed the possibility of having states with low entanglement that violate the eigenstate thermalization hypothesis in nonintegrable systems. Such states with low entanglement…
We demonstrate how the inverse scattering problem of a quantum star graph can be solved by means of diagonalization of Hermitian unitary matrix when the vertex coupling is of the scale invariant (or F\"ul\H{o}p-Tsutsui) form. This enables…
Graph states are multi-particle entangled states that correspond to mathematical graphs, where the vertices of the graph take the role of quantum spin systems and edges represent Ising interactions. They are many-body spin states of…
The existence of a maximally entangled pure state is a cornerstone result of entanglement theory that has paramount consequences in quantum information theory. A natural generalization of this property is to consider whether a notion of…
We study quantum systems on a discrete bounded lattice (lattice billiards). The statistical properties of their spectra show universal features related to the regular or chaotic character of their classical continuum counterparts. However,…
We study the eigenstate properties of a nonintegrable spin chain that was recently realized experimentally in a Rydberg-atom quantum simulator. In the experiment, long-lived coherent many-body oscillations were observed only when the system…
Unstable periodic orbits act as organizing structures for classical chaotic systems and underpin quantum scarring. Long known in single-particle systems, genuine quantum scars based on unstable periodic orbits have been recently extended to…
Quantum many-body scars (QMBS) constitute a new quantum dynamical regime in which rare "scarred" eigenstates mediate weak ergodicity breaking. One open question is to understand the most general setting in which these states arise. In this…
We consider the canonical ensemble of $N$-vertex Erd\H{o}s-R\'enyi (ER) random topological graphs with quenched vertex degree, and with fugacity $\mu$ for each closed triple of bonds. We claim complete defragmentation of large-$N$ graphs…
Quantum many-body scars (QMBS) -- rare eigenstates that evade thermalization -- are typically characterized by their low entanglement entropies compared to surrounding thermal eigenstates. However, due to finite-size effects in systems…
Quantum many-body scar states are highly excited eigenstates of many-body systems that exhibit atypical entanglement and correlation properties relative to typical eigenstates at the same energy density. Scar states also give rise to…
We generally expect quantum systems to thermalize and satisfy the eigenstate thermalization hypothesis (ETH), which states that finite energy density eigenstates are thermal. However, some systems, such as many-body localized systems and…
In this paper, we deal with the conjecture of 'Quantum Unique Ergodicity'. Z. Rudnick and P. Sarnak showed that there is no 'strong scarring' on closed geodesics for arithmetic congruence surfaces derived from a quaternion division algebra.…
Quantum many-body scars enable persistent non-ergodic dynamics in otherwise thermalizing systems, yet their stabilization typically relies on fine-tuned initial states or engineered Hamiltonian perturbations. Here we show that lattice…
Boundary conditions in quantum graph vertices are generally given in terms of a unitary matrix $U$. Observing that if $U$ has at most two eigenvalues, then the scattering matrix $\mathcal{S}(k)$ of the vertex is a linear combination of the…
It is shown, by means of a simple specific example, that for integrable systems it is possible to build up approximate eigenfunctions, called {\it asymptotic eigenfunctions}, which are concentrated as much as one wants to a classical…
Magic, or nonstabilizerness, characterizes the deviation of a quantum state from the set of stabilizer states and plays a fundamental role from quantum state complexity to universal fault-tolerant quantum computing. However, analytical or…
We consider quantum walks on a finite graphs to which infinite tails are attached. We explore how the propagating and bound states depend on the structure of the finite graph. The S-matrix for such graphs is defined. Its unitarity is proved…
We study the quantum entanglement caused by unitary operators that have classical limits that can range from the near integrable to the completely chaotic. Entanglement in the eigenstates and time-evolving arbitrary states is studied…
Quantum scars refer to eigenstates with enhanced probability density along unstable classical periodic orbits (POs). First predicted 40 years ago, scars are special eigenstates that counterintuitively defy ergodicity in quantum systems…