Spectral gap (physics)

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  1. The spectral gap is important to understanding a material’s quantum phase behavior.[1]
  2. Recently, mathematicians Toby Cubitt, David Perez-Garcia and Michael Wolf proved a very interesting result on spectral gaps: that determining the spectral gap of a material is undecidable.[1]
  3. This proof shows that the decidability of the spectral gap depends on the amount of the material being considered.[1]
  4. For most materials, the amount won’t affect the spectral gap.[1]
  5. Upper and lower estimates for the spectral gap --- the difference between the two lowest eigenvalues - for these standard conditions are derived.[2]
  6. The algorithm involves estimating the best combination of these candidate CVs, as quantified by a maximum path entropy estimate of the spectral gap for dynamics viewed as a function of that CV.[3]
  7. The algorithm is called spectral gap optimization of order parameters (SGOOP).[3]
  8. The method is named spectral gap optimization of order parameters (SGOOP).[3]
  9. Our algorithm involves learning the best linear or nonlinear combination of given candidate CVs, as quantified by a maximum path entropy (30) estimate of the spectral gap for the dynamics of that CV.[3]
  10. Spectral Gap Error Bounds for Improving CUR Matrix Decomposition and the Nyström Method.[4]
  11. Nonetheless, I will present a construction of a family of nearest-neighbour, translationally invariant Hamiltonians on a spin chain, for which the spectral gap problem is undecidable.[5]
  12. We compare the obtained bounds on the spectral gap with some other known bounds.[6]
  13. The precise relationship between the spectral gap and the dynamical properties of the chain is more subtle than the rest of what I've said here.[7]
  14. The spectral gap—the energy difference between the lowest and next-lowest state of a quantum system—is one of the fundamental quantities that determine the system’s properties at low temperature.[8]
  15. An immediate consequence of the undecidability of the spectral gap is that there cannot exist an algorithm or a computable criterion that solves the spectral gap problem in general.[9]
  16. But at some threshold lattice size, a spectral gap of magnitude one will suddenly appear (or, vice versa, a gap will suddenly close27).[9]
  17. A related point is that we prove undecidabiltiy of the spectral gap (and other low-temperature properties) for Hamiltonians with a very particular form.[9]
  18. Whether there is a non-trivial bound on the dimension of the local Hilbert space below which the spectral gap problem becomes decidable is an intriguing open question.[9]
  19. We obtain an expression for the Laplace transform of the time-dependent probability distribution, from which the spectral gap is explicitly characterized.[10]
  20. The spectral gap gives the exponential rate of convergence to equilibrium.[10]
  21. We further give various asymptotic results for the spectral gap, in the limits of small and large abandonment effects.[10]
  22. In mathematics, the spectral gap is the difference between the moduli of the two largest eigenvalues of a matrix or operator; alternately, it is sometimes taken as the smallest non-zero eigenvalue.[11]
  23. We present a new explicit construction for expander graphs with nearly optimal spectral gap.[12]
  24. In particular, the spectral radius is not equal to minus the spectral gap.[13]
  25. We survey recent works on the connection between spectral gap and logarithmic Sobolev constants, and exponential integrability of Lipschitz functions.[14]
  26. So does the spectral gap problem become decidable in 1D?[15]

소스

  1. ↑ 1.0 1.1 1.2 1.3 Mathematicians shed new light on spectral gaps
  2. ↑ On the spectral gap for networks of beams
  3. ↑ 3.0 3.1 3.2 3.3 Spectral gap optimization of order parameters for sampling complex molecular systems
  4. ↑ Spectral Gap Error Bounds for Improving CUR Matrix Decomposition and the Nyström Method
  5. ↑ Undecidability of the spectral gap in one dimension
  6. ↑ Computable Bounds on the Spectral Gap for Unreliable Jackson Networks
  7. ↑ Intuitive explanation of the spectral gap in context of Markov Chain Monte Carlo (MCMC)
  8. ↑ Undecidability of the Spectral Gap in One Dimension
  9. ↑ 9.0 9.1 9.2 9.3 Undecidability of the spectral gap
  10. ↑ 10.0 10.1 10.2 Spectral Gap of the Erlang A Model in the Halfin-Whitt Regime
  11. ↑ Spectral gap
  12. ↑ Lifts, Discrepancy and Nearly Optimal Spectral Gap*
  13. ↑ Spectral gap of a graph
  14. ↑ SDG vol. 9 (2004) article 6
  15. ↑ Undecidability of the Spectral Gap in One Dimension

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