The cycle C9 does not admit uniform mixing

• URL: http://arxiv.org/abs/2607.28345v1
• Date: Thu, 30 Jul 2026 15:15:11 GMT
• Title: The cycle C9 does not admit uniform mixing
• Abstract summary: We study continuous-time quantum walks (CTQWs) on cycles.<n>We prove that the cycle $C_9$ does not admit uniform mixing at any time.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study continuous-time quantum walks (CTQWs) on cycles. In particular, we prove that the cycle $C_9$ does not admit uniform mixing at any time via algebraic geometry and Gröbner basis techniques to rule out all cyclic 9-roots.

Related papers

• Nonlocality-induced critical-length hierarchy from non-Hermitian competition [48.9823527611878]
  In short-range systems formed by two coupled chains, competition leads to the critical-length law $N_csimln D$.<n>Here we show that long-range hoppings fundamentally reorganizes this critical behavior, producing a hierarchy of distinct scaling laws.<n>Our results offer a platform-independent framework testable in programmable topoelectrical circuits, photonic lattices and digital quantum simulators.
  arXiv  Detail & Related papers  (2026-08-03T18:00:18Z)
• Uniform mixing and $ε$-uniform mixing on cycles [6.617487928813374]
  We study continuous-time quantum walks on cycles.<n>For every prime $p2$, we show that the cycle $C_p2$ admits $$-uniform mixing.
  arXiv  Detail & Related papers  (2026-07-05T09:56:05Z)
• Quantum Trajectory Entanglement in Seeded Boundary Time Crystals [46.94763753277221]
  entanglement spreads among different spin ensembles when a BTC attempts to seed its time-crystalline behavior onto otherwise static spin ensembles.<n>We analyse both the dynamical growth of entanglement in time and the steady-state properties of the system.<n>These findings establish dissipative seeding as a powerful mechanism for controlling quantum correlations in open many-body systems.
  arXiv  Detail & Related papers  (2026-07-01T18:00:08Z)
• Uniform Mixing in Chiral Quantum Walks [0.0]
  We show that for some unitary signing $$ the complete graph $K_n$ has probabilistic uniform mixing.<n>In contrast, it is known em no complete graph has uniform mixing except for $K$, $K_3$, and $K_4$.
  arXiv  Detail & Related papers  (2026-05-06T02:12:09Z)
• Observation of Discrete Time Quasicrystal in Rydberg Atomic Gases [41.80768913783363]
  Discrete time quasicrystals (DTQC) constitute a class of non-equilibrium matter characterized by temporal order without strict periodicity.<n>Here, we experimentally observe a DTQC in a driven-dissipative ensemble of strongly interacting Rydberg atoms.<n>We demonstrate that the system exhibits a robust subharmonic response at multiple incommensurate frequencies, signifying the emergence of a DTQC phase.
  arXiv  Detail & Related papers  (2025-09-25T14:43:18Z)
• Revealing spontaneous symmetry breaking in continuous time crystals [17.62738825431278]
  Spontaneous symmetry breaking leads to a novel state of matter named continuous time crystal (CTC) We propose and experimentally realize two types of CTCs based on distinct mechanisms: manifold topology and near-chaotic motion. Our work provides general recipes for the realization of CTCs, and paves the way for exploring CTCs in various systems.
  arXiv  Detail & Related papers  (2024-07-10T14:27:06Z)
• Non-uniform Mixing of Quantum Walks on the Symmetric Group [0.0]
  We analyze the spectra of the Szegedy walk operators using the representation theory of the symmetric group. Our techniques are general, and we believe they can be applied to derive similar analytical results for other non-commutative groups.
  arXiv  Detail & Related papers  (2023-11-06T03:17:36Z)
• Measurement phase transitions in the no-click limit as quantum phase transitions of a non-hermitean vacuum [77.34726150561087]
  We study phase transitions occurring in the stationary state of the dynamics of integrable many-body non-Hermitian Hamiltonians. We observe that the entanglement phase transitions occurring in the stationary state have the same nature as that occurring in the vacuum of the non-hermitian Hamiltonian.
  arXiv  Detail & Related papers  (2023-01-18T09:26:02Z)
• Genuine Multipartite Correlations in a Boundary Time Crystal [56.967919268256786]
  We study genuine multipartite correlations (GMC's) in a boundary time crystal (BTC) We analyze both (i) the structure (orders) of GMC's among the subsystems, as well as (ii) their build-up dynamics for an initially uncorrelated state.
  arXiv  Detail & Related papers  (2021-12-21T20:25:02Z)
• Periodicity of quantum walks defined by mixed paths and mixed cycles [0.0]
  We show periodicity of quantum walks defined by mixed paths and mixed cycles. We provide a necessary and sufficient condition for a mixed cycle to be periodic and determine their periods.
  arXiv  Detail & Related papers  (2021-04-17T02:42:30Z)
• Boundary time crystals in collective $d$-level systems [64.76138964691705]
  Boundary time crystals are non-equilibrium phases of matter occurring in quantum systems in contact to an environment. We study BTC's in collective $d$-level systems, focusing in the cases with $d=2$, $3$ and $4$.
  arXiv  Detail & Related papers  (2021-02-05T19:00:45Z)

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.