Exact-WKB, complete resurgent structure, and mixed anomaly in quantum mechanics on $S^1$

• URL: http://arxiv.org/abs/2103.06586v2
• Date: Fri, 19 Mar 2021 13:52:14 GMT
• Title: Exact-WKB, complete resurgent structure, and mixed anomaly in quantum mechanics on $S^1$
• Authors: Naohisa Sueishi, Syo Kamata, Tatsuhiro Misumi, Mithat \"Unsal
• Abstract summary: We investigate the exact-WKB analysis for quantum mechanics in a periodic potential. We describe the Stokes graphs of a general potential problem as a network of Airy-type or degenerate Weber-type building blocks.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We investigate the exact-WKB analysis for quantum mechanics in a periodic potential, with $N $ minima on $S^{1}$. We describe the Stokes graphs of a general potential problem as a network of Airy-type or degenerate Weber-type building blocks, and provide a dictionary between the two. The two formulations are equivalent, but with their own pros and cons. Exact-WKB produces the quantization condition consistent with the known conjectures and mixed anomaly. The quantization condition for the case of $N$-minima on the circle factorizes over the Hilbert sub-spaces labeled by discrete theta angle (or Bloch momenta), and is consistent with 't Hooft anomaly for even $N$ and global inconsistency for odd $N$. By using Delabaere-Dillinger-Pham formula, we prove that the resurgent structure is closed in these Hilbert subspaces, built on discrete theta vacua, and by a transformation, this implies that fixed topological sectors (columns of resurgence triangle) are also closed under resurgence.

Related papers

• KPZ scaling from the Krylov space [83.88591755871734]
  Recently, a superdiffusion exhibiting the Kardar-Parisi-Zhang scaling in late-time correlators and autocorrelators has been reported. Inspired by these results, we explore the KPZ scaling in correlation functions using their realization in the Krylov operator basis.
  arXiv  Detail & Related papers  (2024-06-04T20:57:59Z)
• Exact quantization conditions and full transseries structures for ${\cal PT}$ symmetric anharmonic oscillators [0.0]
  We study exact Wentzel-Kramers-Brillouin analysis (EWKB) for a $cal PT$ symmetric quantum mechanics (QM) We derive the exact quantization conditions (QCs) for arbitrary $(K,varepsilon)$ including all perturbative/non-perturbative corrections. Similarities to Hermitian QMs and resurgence are also discussed as additional remarks.
  arXiv  Detail & Related papers  (2024-06-03T11:50:51Z)
• Geometry of degenerate quantum states, configurations of $m$-planes and invariants on complex Grassmannians [55.2480439325792]
  We show how to reduce the geometry of degenerate states to the non-abelian connection $A$. We find independent invariants associated with each triple of subspaces. Some of them generalize the Berry-Pancharatnam phase, and some do not have analogues for 1-dimensional subspaces.
  arXiv  Detail & Related papers  (2024-04-04T06:39:28Z)
• Mixed-state quantum anomaly and multipartite entanglement [8.070164241593814]
  We show a surprising connection between mixed state entanglement and 't Hooft anomaly. We generate examples of mixed states with nontrivial long-ranged multipartite entanglement. We also briefly discuss mixed anomaly involving both strong and weak symmetries.
  arXiv  Detail & Related papers  (2024-01-30T19:00:02Z)
• Unbiased constrained sampling with Self-Concordant Barrier Hamiltonian Monte Carlo [18.14591309607824]
  Barrier Hamiltonian Monte Carlo (BHMC) is a version of the HMC algorithm which aims at sampling from a Gibbs distribution $pi$ on a manifold $mathrmM$. We propose a new filter step, called "involution checking step", to address this problem. Our main results establish that these two new algorithms generate reversible Markov chains with respect to $pi$ and do not suffer from any bias in comparison to previous implementations.
  arXiv  Detail & Related papers  (2022-10-21T12:56:07Z)
• A New Look at the $C^{0}$-formulation of the Strong Cosmic Censorship Conjecture [68.8204255655161]
  We argue that for generic black hole parameters as initial conditions for Einstein equations, the metric is $C0$-extendable to a larger Lorentzian manifold. We prove it violates the "complexity=volume" conjecture for a low-temperature hyperbolic AdS$_d+1$ black hole dual to a CFT living on a ($d-1$)-dimensional hyperboloid $H_d-1$.
  arXiv  Detail & Related papers  (2022-06-17T12:14:33Z)
• The Franke-Gorini-Kossakowski-Lindblad-Sudarshan (FGKLS) Equation for Two-Dimensional Systems [62.997667081978825]
  Open quantum systems can obey the Franke-Gorini-Kossakowski-Lindblad-Sudarshan (FGKLS) equation. We exhaustively study the case of a Hilbert space dimension of $2$.
  arXiv  Detail & Related papers  (2022-04-16T07:03:54Z)
• Annihilating Entanglement Between Cones [77.34726150561087]
  We show that Lorentz cones are the only cones with a symmetric base for which a certain stronger version of the resilience property is satisfied. Our proof exploits the symmetries of the Lorentz cones and applies two constructions resembling protocols for entanglement distillation.
  arXiv  Detail & Related papers  (2021-10-22T15:02:39Z)
• Reduced Phase Space Approach to the $U(1)^3$ model for Euclidean Quantum Gravity [0.0]
  A consistent model captures significant structure of the Ashtekar-Barbero $SU(2)$ gauge theory of Euclidean gravity. A non trivial realisation of the hypersurface deformation algebra makes it an interesting testing ground for quantum gravity.
  arXiv  Detail & Related papers  (2020-10-30T16:16:14Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.