12 problems

In an integrable model, let the long-time asymptotic stationary state be the state reached after the system evolves for arbitrarily long times from a nonequilibrium initial conditi…

Consider a quantum many-body system initially prepared in the ground state of one Hamiltonian and subjected to a sudden change of interaction strength, or quench. Local relaxation…

Resonance conjecture. The observed increase in velocity could be a signature of resonant phenomena at larger noise strengths.

Universality conjecture for $X_{\infty}$. The limiting fluctuation-dissipation ratio $X_{\infty}$ is a universal constant, independent of the initial state and microscopic dynamics…

Exponent-relation conjecture. The relationship between the exponents is generally

No-go conjecture. One- and two-dimensional systems with short-range interactions cannot exhibit time-periodic behaviour.

FA-1f convergence conjecture. For any $q\in(0,1)$,

Consider the massless time-like regime of the XX chain and the complex correlation function $(-1)^m\langle\sigma^-_1(0)\sigma^+_{m+1}(t)\rangle$. Positivity conjecture. Both its re…

Attainability conjecture. Such an explicit time-dependent representation of local observables in terms of the tMPA should be attainable for any purely solitonic, deterministic mode…

Gibbs and generalised Gibbs ensemble thermalization conjecture. In a generic model, stationary values of local observables are described by Gibbs ensembles, whereas in an integrabl…

GGE applicability conjecture. The GGE is applicable to the 1D Bose gas (LL model), at least for local observables.

Let $p$ and $p'$ be the model parameters, let $p_c$ be the critical value, and let $\nu$ be the Bernoulli($p'$) product measure on $\mathcal T$. A local function is a function depe…