Probing the edge between integrability and quantum chaos in interacting few-atom systems

[EN] Interacting quantum systems in the chaotic domain are at the core of various ongoing studies of many-body physics, ranging from the scrambling of quantum information to the onset of thermalization. We propose a minimum model for chaos that can be experimentally realized with cold atoms trapped in onedimensional multi-well potentials. We explore the emergence of chaos as the number of particles is increased, starting with as few as two, and as the number of wells is increased, ranging from a double well to a multi-well Kronig-Penney-like system. In this way, we illuminate the narrow boundary between integrability and chaos in a highly tunable few-body system. We show that the competition between the particle interactions and the periodic structure of the confining potential reveals subtle indications of quantum chaos for 3 particles, while for 4 particles stronger signatures are seen. The analysis is performed for bosonic particles and could also be extended to distinguishable fermions.The authors thank M. Olshanii, T. Busch, A. Fabra and M. Boubakour for insights on integrability and conversations about chaos. TF acknowledges support from JSPS KAKENHI-21K13856 and the Okinawa Institute of Science and Technology Graduate University. We are grateful for the help and support provided by the Scientific Computing and Data Analysis section of Research Support Division at OIST. LFS was supported by the NSF grant No. DMR-1936006. M.A.G.M. acknowledges funding from the Spanish Ministry of Education and Vocational Training (MEFP) through the Beatriz Galindo program 2018 (BEAGAL18/00203) and Spanish Ministry MINECO (FIDEUA PID2019106901GBI00/10.13039/501100011033).Fogarty, T.; Garcia March, MA.; Santos, LF.; Harshman, N. (2021). Probing the edge between integrability and quantum chaos in interacting few-atom systems. Quantum. 5:1-22. https://doi.org/10.22331/q-2021-06-29-486122

Clebsch-Gordan Coefficients for the Extended Quantum-Mechanical Poincar\'e Group and Angular Correlations of Decay Products

This paper describes Clebsch-Gordan coefficients (CGCs) for unitary irreducible representations (UIRs) of the extended quantum mechanical Poincar\'e group \pt. `Extended' refers to the extension of the 10 parameter Lie group that is the Poincar\'e group by the discrete symmetries $C$, $P$, and $T$; `quantum mechanical' refers to the fact that we consider projective representations of the group. The particular set of CGCs presented here are applicable to the problem of the reduction of the direct product of two massive, unitary irreducible representations (UIRs) of \pt with positive energy to irreducible components. Of the sixteen inequivalent representations of the discrete symmetries, the two standard representations with $U_C U_P = \pm 1$ are considered. Also included in the analysis are additive internal quantum numbers specifying the superselection sector. As an example, these CGCs are applied to the decay process of the $\Upsilon(4S)$ meson.Comment: 26 pages, double spaced. Version 2: typos corrected, introduction change

On the Mass and Width of the Z-boson and Other Relativistic Quasistable Particles

The ambiguity in the definition for the mass and width of relativistic resonances is discussed, in particular for the case of the Z-boson. This ambiguity can be removed by requiring that a resonance's width $\Gamma$ (defined by a Breit-Wigner lineshape) and lifetime $\tau$ (defined by the exponential law) always and exactly fulfill the relation $\Gamma = \hbar/\tau$. To justify this one needs relativistic Gamow vectors which in turn define the resonance's mass M_R as the real part of the square root $\rm{Re}\sqrt{s_R}$ of the S-matrix pole position s_R. For the Z-boson this means that $M_R \approx M_Z - 26{MeV}$ and $\Gamma_R \approx \Gamma_Z-1.2{MeV}$ where M_Z and $\Gamma_Z$ are the values reported in the particle data tables.Comment: 23 page

Entanglement or separability: The choice of how to factorize the algebra of a density matrix

We discuss the concept of how entanglement changes with respect to different factorizations of the total algebra which describes the quantum states. Depending on the considered factorization a quantum state appears either entangled or separable. For pure states we always can switch unitarily between separability and entanglement, however, for mixed states a minimal amount of mixedness is needed. We discuss our general statements in detail for the familiar case of qubits, the GHZ states, Werner states and Gisin states, emphasizing their geometric features. As theorists we use and play with this free choice of factorization, which is naturally fixed for an experimentalist. For theorists it offers an extension of the interpretations and is adequate to generalizations, as we point out in the examples of quantum teleportation and entanglement swapping.Comment: 29 pages, 9 figures. Introduction, Conclusion and References have been extended in v

Beyond braid statistics: Constructing a lattice model for anyons with exchange statistics intrinsic to one dimension

Anyons obeying fractional exchange statistics arise naturally in two dimensions: Hardcore two-body constraints make the configuration space of particles not simply-connected. The braid group describes how topologically-inequivalent exchange paths can be associated to non-trivial geometric phases for abelian anyons. Braid-anyon exchange statistics can also be found in one dimension (1D), but this requires broken Galilean invariance to distinguish different ways for two anyons to exchange. However, recently it was shown that an alternative form of exchange statistics can occur in 1D because hard-core three-body constraints also make the configuration space not simply-connected. Instead of the braid group, the topology of exchange paths and their associated non-trivial geometric phases are described by the traid group. In this article we propose a first concrete model realizing this alternative form of anyonic exchange statistics. Starting from a bosonic lattice model that implements the desired geometric phases with number-dependent Peierls phases, we then define anyonic operators so that the kinetic energy term in the Hamiltonian becomes local and quadratic with respect to them. The ground-state of this traid-anyon-Hubbard model exhibits several indications of exchange statistics intermediate between bosons and fermions, as well as signs of emergent approximate Haldane exclusion statistics. The continuum limit results in a Galilean invariant Hamiltonian with eigenstates that correspond to previously constructed continuum wave functions for traid anyons. This provides not only an a-posteriori justification of our lattice model, but also shows that our construction serves as an intuitive approach to traid anyons, i.e. anyons intrinsic to 1D.SCOPUS: ar.jinfo:eu-repo/semantics/publishe