Multi-channel collective dissipation via the symmetric irreducible representation of SU(4)

• URL: http://arxiv.org/abs/2607.07701v1
• Date: Wed, 08 Jul 2026 17:57:07 GMT
• Title: Multi-channel collective dissipation via the symmetric irreducible representation of SU(4)
• Abstract summary: We specialize Agarwal's multi-level collective spontaneous-emission formalism to the four-level case.<n>We formulate it in the fully symmetric SU(4) representation of $N$ identical atoms.<n>The SU(4)hedral flow and the seven configuration-dependent transients together provide a unified geometric picture of collective dissipation.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We specialize Agarwal's multi-level collective spontaneous-emission formalism to the four-level case by formulating it in the fully symmetric \SU(4) representation of $N$ identical atoms. In the irreducible representation $(N,0,0)$, the occupation-number basis forms a tetrahedral weight lattice on which the six embedded $\mathfrak{su}(2)$ transition subalgebras act as ladder operators. From these algebraic factors we obtain a compact Pauli-type population-rate equation and a closed-form expression for the total emitted intensity that apply to any combination of open dipole channels. The formalism is then specialized to the seven dipole-allowed four-level topologies -- tripod, inverted tripod, Y, inverted Y, double-$Λ$, closed cascade, and diamond -- and the resulting rate equations are solved numerically for atom numbers up to $N=50$. In every case the emitted intensity develops a delayed cooperative burst whose peak height obeys a power law $I_{\mathrm{peak}}=aN^{p}$ with topology-dependent parameters $(a,p)$; the fitted exponents lie in the range $1.81\lesssim p\lesssim 1.92$, indicating a superlinear. The \SU(4) tetrahedral flow and the seven configuration-dependent transients together provide a unified geometric picture of multi-channel collective dissipation in four-level atomic ensembles.

Related papers

• Finite Weyl polynomials and the approach to Tsirelson's bound in relativistic scalar quantum field theory [0.0]
  We construct four bounded Hermitian operators, each one a finite in the unitary Weyl operators.<n>We show that the supremum over the finite-polynomial family equals $2sqrt$, although no finite member attains it.
  arXiv  Detail & Related papers  (2026-08-21T09:42:23Z)
• Complex spacing ratio statistics in the partially open asymmetric quantum baker map [36.94429692322632]
  We study the complex eigenvalue statistics of the asymmetric quantum baker map with partial projective openings.<n>We find a smooth crossover from a quasi-1D spectral regime, where eigenvalues cluster near the unit circle and the phase distribution of $z$ is peaked.<n>Both the number of open channels $M$ and the reflectivity $$ modulate this crossover, and $$ provides an additional continuous control even at fixed opening size.
  arXiv  Detail & Related papers  (2026-07-08T19:24:35Z)
• Towards a microscopic model for an electronic quantum charge liquid [0.0]
  We provide a route to constructing an electronic quantum charge liquid (QCL), a state made up of fermions at fractional filling of a lattice that does not break translation.<n>The gapped nature of this state, along with its $mathbbZ_4$ symmetry, leads us to propose that it is an example of the elusive bosonic QCL displaying the minimal $mathbbZ_4$ topological order.
  arXiv  Detail & Related papers  (2026-04-28T18:00:00Z)
• On the Coupled Cluster Doubles Truncation Variety of Four Electrons [0.0]
  We study the first genuinely nonlinear doubles regime of four electrons in the doubles approximation (CCD)<n>Using representation-theoretic arguments, we uncover a Pfaffian structure governing the quadratic relations that define the truncation variety for any $n$, and show that an exact tensor product factorization holds in a distinguished limit of disconnected doubles.
  arXiv  Detail & Related papers  (2026-02-18T16:28:24Z)
• Transmutation based Quantum Simulation for Non-unitary Dynamics [35.35971148847751]
  We present a quantum algorithm for simulating dissipative diffusion dynamics generated by positive semidefinite operators of the form $A=Ldagger L$.<n>Our main tool is the Kannai transform, which represents the diffusion semigroup $e-TA$ as a Gaussian-weighted superposition of unitary wave propagators.
  arXiv  Detail & Related papers  (2026-01-07T05:47:22Z)
• Quantum two-dimensional superintegrable systems in flat space: exact-solvability, hidden algebra, polynomial algebra of integrals [41.99844472131922]
  It includes the Smorodinsky-Winternitz potentials I-II (the Holt potential), the Fokas-Lagerstrom model, the 3-body Calogero and Wolfes (equivalently, $G$ rational, or $I_6$) models.<n>It is shown that all of them are exactly-solvable, thus, confirming the Montreal conjecture.<n>Each model is characterized by infinitely-many finite-dimensional invariant subspaces, which form the infinite flag.
  arXiv  Detail & Related papers  (2025-12-30T07:39:35Z)
• Algebraic Obstructions and the Collapse of Elementary Structure in the Kronecker Problem [0.0]
  No explicit closed-form formulas have been obtained for genuinely three-row cases in the 87 years since Murnaghan's foundational work.<n>We derive five explicit formulas for staircase-hook coefficients, and verify Saxl's conjecture for 132 three-row partitions.<n>We develop integer forcing, a proof technique exploiting the tension between continuous obstructions and discrete integrality.
  arXiv  Detail & Related papers  (2025-11-28T03:21:01Z)
• Learning single-index models via harmonic decomposition [21.065469907392643]
  We study the problem of learning single-index models, where the label $y in mathbbR$ depends on the input $boldsymbolx in mathbbRd$ only through an unknown one-dimensional projection.<n>We introduce two families of estimators -- based on tensor unfolding and online SGD -- that respectively achieve either optimal sample complexity or optimal runtime.
  arXiv  Detail & Related papers  (2025-06-11T15:59:53Z)
• Scheme of quantum communications based on Witting polytope [55.2480439325792]
  Presented paper describes how to use this configuration for a quantum key distribution protocol based on contextuality using some illustrative examples with 40 "quantum cards"<n>In a more general case, two arbitrary quantum systems with four basis states (ququarts) can be used instead.
  arXiv  Detail & Related papers  (2025-03-24T08:26:48Z)
• Bridging conformal field theory and parton approaches to SU(n)_k chiral spin liquids [21.876059213677966]
  We employ the $mathrmSU(n)_k$ Wess-Zumino-Witten (WZW) model in conformal field theory to construct lattice wave functions in both one and two dimensions.<n>The spins on all lattice sites are chosen to transform under the $mathrmSU(n)$ irreducible representation with a single row and $k$ boxes in the Young tableau.
  arXiv  Detail & Related papers  (2025-01-16T14:42:00Z)
• Geometric bound on structure factor [44.99833362998488]
  We show that a quadratic form of quantum geometric tensor in $k$-space sets a bound on the $q4$ term in the static structure factor $S(q)$ at small $vecq$.<n> Bands that saturate this bound satisfy a condition similar to Laplace's equation, leading us to refer to them as $textitharmonic bands$.
  arXiv  Detail & Related papers  (2024-12-03T18:30:36Z)
• 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)
• Role of mixed permutation symmetry sectors in the thermodynamic limit of critical three-level Lipkin-Meshkov-Glick atom models [0.0]
  Mixed Symmetry Quantum Phase Transition (MSQPT) Four distinct quantum phases in the $lambda$-$mu$ plane coexist at a quadruple point. The restoration of this discrete symmetry leads to the formation of four-component Schr"odinger cat states.
  arXiv  Detail & Related papers  (2021-02-15T20:15:55Z)
• Anisotropy-mediated reentrant localization [62.997667081978825]
  We consider a 2d dipolar system, $d=2$, with the generalized dipole-dipole interaction $sim r-a$, and the power $a$ controlled experimentally in trapped-ion or Rydberg-atom systems. We show that the spatially homogeneous tilt $beta$ of the dipoles giving rise to the anisotropic dipole exchange leads to the non-trivial reentrant localization beyond the locator expansion.
  arXiv  Detail & Related papers  (2020-01-31T19:00:01Z)

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.