Related papers: Eigenstate Thermalization Hypothesis for Wigner Ma…
The Eigenstate Thermalization Hypothesis (ETH) provides a sufficient condition for thermalization of isolated quantum systems. While the standard ETH is formulated in the absence of degeneracy, physical systems often possess symmetries that…
Eigenstate thermalization hypothesis is a detailed statement of the matrix elements of few-body operators in energy eigenbasis of a chaotic Hamiltonian. Part of the statement is that the off-diagonal elements fall exponential for large…
The eigenstate thermalisation hypothesis (ETH) is a statistical characterisation of eigen-energies, eigenstates and matrix elements of local operators in thermalising quantum systems. We develop an ETH-like ansatz of a partially…
The Eigenstate Thermalization Hypothesis (ETH) implies a form for the matrix elements of local operators between eigenstates of the Hamiltonian, expected to be valid for chaotic systems. Another signal of chaos is a positive Lyapunov…
We investigate the eigenstate thermalization hypothesis (ETH) for a translationally invariant quantum spin system on the $d$-dimensional cubic lattice under the periodic boundary conditions. It is known that the ETH holds in this model for…
We consider communication scenarios where one party sends quantum states of known dimensionality $D$, prepared with an untrusted apparatus, to another, distant party, who probes them with uncharacterized measurement devices. We prove that,…
Chaos and ergodicity are the cornerstones of statistical physics and thermodynamics. While classically even small systems like a particle in a two-dimensional cavity, can exhibit chaotic behavior and thereby relax to a microcanonical…
Thermalization in closed quantum systems can be explained either by means of the eigenstate thermalization hypothesis or the concept of canonical typicality. Both concepts are based on quantum mechanical formalism such as spectral…
Ergodic isolated quantum many-body systems satisfy the eigenstate thermalization hypothesis (ETH), i.e., the expectation values of local observables in the system's eigenstates approach the predictions of the microcanonical ensemble.…
The Eigenstate Thermalization Hypothesis (ETH) posits that the reduced density matrix for a subsystem corresponding to an excited eigenstate is "thermal." Here we expound on this hypothesis by asking: for which class of operators, local or…
We prove that the distribution of eigenvectors of generalized Wigner matrices is universal both in the bulk and at the edge. This includes a probabilistic version of local quantum unique ergodicity and asymptotic normality of the…
We consider $N\times N$ random matrices of the form $H = W + V$ where $W$ is a real symmetric Wigner matrix and $V$ a random or deterministic, real, diagonal matrix whose entries are independent of $W$. We assume subexponential decay for…
We investigate the eigenstate thermalization hypothesis (ETH) in integrable models, focusing on the spin-1/2 isotropic Heisenberg (XXX) chain. We provide numerical evidence that ETH holds for typical eigenstates (weak ETH scenario).…
In this work, we use quantum complexity theory to quantify the difficulty of distinguishing eigenstates obeying the Eigenstate Thermalization Hypothesis (ETH). After identifying simple operators with an algebra of low-energy observables and…
We investigate the eigenstate thermalization hypothesis (ETH) in d+1 dimensional conformal field theories by studying reduced density matrices in energy eigenstates. We show that if local probes of high energy primary eigenstates satisfy…
The Eigenstate Thermalization Hypothesis (ETH) has played a key role in recent advances in the high energy and condensed matter communities. It explains how an isolated quantum system in a far-from-equilibrium initial state can evolve to a…
It has previously been suggested that small subsystems of closed quantum systems thermalize under some assumptions; however, this has been rigorously shown so far only for systems with very weak interaction between subsystems. In this work,…
Since E.P.Wigner (1958) established his famous semicircle law, lots of attention has been paid by physicists, probabilists and statisticians to study the asymptotic properties of the largest eigenvalues for random matrices. Bai and Yin…
We study the matrix elements of few-body observables, focusing on the off-diagonal ones, in the eigenstates of the two-dimensional transverse field Ising model. By resolving all symmetries, we relate the onset of quantum chaos to the…
We use the eigenstate thermalization hypothesis to derive a quantum master equation for a system weakly coupled to a chaotic finite-sized bath prepared in a pure state. We show that the emergence of Markovianity is controlled by the…