Remark on the energy spectrum of a decaying system

V.M. Yeleonskii, P. S. Zyryanov

Daochen Wang

Quantum algorithms for estimating the ground state energy of a quantum system often operate by preparing a classically accessible quantum state and then applying quantum phase estimation. Whether this approach yields quantum advantage hinges on the state's energy spectrum, that is, the sequence of the state's overlaps with the energy eigenstates of the system Hamiltonian. We show that the energy spectrum of any entanglement-compressed quantum state must have large support if most energy eigenstates are highly entangled, an assumption supported by the eigenstate thermalization hypothesis. Furthermore, we show that if the compressed quantum state minimizes expected energy, then its energy spectrum decays with the inverse-squared energy eigenvalues under a convex relaxation of the compression constraint. This explains the main empirical finding of Silvester et al. [Phys. Rev. Lett. 134, 126503 (2025).PRLTAO0031-900710.1103/PhysRevLett.134.126503] that the energy spectra of matrix product states do not decay exponentially.

C. H. Woo

There are large discrepancies between the various estimates in the literature for the time interval below which the decay of a resonance may be significantly inhibited by monitoring. The disagreements arose because of our lack of knowledge of the detailed energy spectrum of the composite system undergoing decay. We emphasize here that for a large class of metastable systems the problem can be reduced to essentially kinematical considerations independent of the details of the spectrum, and point out that certain monitoring procedure can prevent even a free wave packet from spreading. If the proton is unstable, its decay will not be significantly suppressed unless the monitoring interval is shorter than 10−23 s.

Gy. I. Szász

Victor V. Slavin

Abstract The low‐energy spectrum of one‐dimensional lattice electron system with long‐range inter‐electron repulsion is studied at arbitrary electron concentration, ρ. It is established that the value of the gap in this spectrum is an oscillating function of inverse electron concentration. This value tends to zero at ρ = 1/q (q = 1, 2 …), reaching the maximum at ρ = 2/(2q + 1). It is shown that the low‐energy spectrum of the system under consideration may be described in terms of one‐dimensional structures which are analogues of domains in one‐dimensional spin systems. The question about these “domains” decay is considered. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Dmitrii Kouznetsov