32 problems

Let $v(t)$ denote the evolution speed of a state under open quantum dynamics, and let the speed of relative purity change be bounded using the Cauchy–Schwarz inequality. Monotonici…

Let an open quantum system have a nonequilibrium steady-state density operator whose level statistics are studied. Prosen–Žnidarič's conjecture. Poissonian level statistics signals…

Let $({\mathfrak M},\tau)$ be a $W^\ast$-dynamical system on a Hilbert space ${\mathcal H}$, and let $\omega(A)=(\Omega,A\Omega)$ be a faithful $(\tau,\beta)$-KMS vector state on…

Let open quantum systems have effective connections with irregular singularities, such as those arising from non-Markovian reservoirs with sharp spectral cutoffs or from Floquet sy…

Conjecture on decorated-mixture-index sampling. In future work, sampling of the decorated mixture index will be useful in parallelized algorithms which themselves might provide cru…

Let an open quantum system, particularly one governed by a non-Hermitian Hamiltonian, be considered in a regime analogous to a non-chaotic or integrable regime. Conjecture on non-c…

Let a Markovian open quantum system be described by a non-Hermitian Hamiltonian and hence have generally complex spectral data. Grobe–Haake–Sommers conjecture. Its spectral propert…

Let $\rho$ be a state with anomalous symmetry $K\times G$, where $G$ has an onsite symmetry action, and let an FDLC denote a finite-depth local circuit. Strengthened anomaly obstru…

Let $\Delta^3$ denote the probability simplex, let $\mathsf{derv}(\lambda)$ be the set of achievable derivatives at $\lambda$, let $S_4$ be the permutation group on four elements,…

Universal tight relaxation-rate conjecture. The relaxation rates satisfy

Coupled-wire edge-theory conjecture. This theory can be an edge theory of an intrinsic ASPT with exact $\mathbb{Z}_2^f$ and average $\mathbb{Z}_2^T$ symmetry.

Weak-decoherence correspondence conjecture. The lack of correspondence should extend through the larger regime

Relaxation-rate bound. Each relaxation rate satisfies

Accuracy trade-off conjecture. In general, it is impossible to increase the accuracy of the steady state with respect to the zeroth order while maintaining the same or greater accu…

General-validity conjecture. This formula holds generally, even when the compatibility condition $e^{i(\phi+\pi/2)L}=1$ is not satisfied. The formula is established in the compatib…

Consider a quantum anharmonic chain coupled to baths, with $b1$-FPUT, KG, or $b2$-FPUT nonlinearities, and let the nonlinear coupling be treated perturbatively. A nonequilibrium st…

Consider a quantum anharmonic chain with $b1$-FPUT, $b2$-FPUT, or KG nonlinearities, treated perturbatively in weak nonlinear coupling. Let the nonequilibrium steady-state (NESS) t…

Let $L$ be the Liouvillian governing a Markovian dissipative open quantum system through the Lindblad equation … For a generic chaotic dissipative open quantum system, consider the…

Consider a bipartite open quantum system with a fast subsystem converging to a unique steady state, a slow subsystem described by a reduced model, and a geometric adiabatic elimina…

Let $\epsilon$ be the perturbation parameter, and let $(\mathcal{K}_j,\mathcal{L}_j)_{1\leq j\leq n}$ denote the corrections at orders $1$ through $n$ to the mapping from reduced m…

Consider an open quantum system described by a Lindblad-type master equation with two time scales, where the fast time scale is strongly dissipative and drives the system toward a…

Let $u>0$ and $\kappa>0$, let $r>1$ be an integer, and consider the master equation … Let $\bar\rho$ be a steady density operator supported on the span of the coherent states…

Wigner-function convergence conjecture. For every initial Wigner function $W_0=W^{\rho_0}$ with finite energy,

Let $\rho(t)$ solve the cat-Kerr master equation … where $u$, $\kappa$, and $\kappa_c$ are strictly positive, and let $\rho_\infty$ be its stated unique steady state. Frobenius con…

Let $\rho_k$ be the photon state at step $k$, evolving under the quantum map described in the source, and let $\rho_\infty$ be the fixed state obtained from the common eigen-state…