Publications

Order by: publication date number of citations

• Interpolating between the gauge and Schrödinger pictures of quantum dynamics

  Sayak Guha Roy, Kevin Slagle

  SciPost Phys. Core 6, 081 (2023) · published 24 November 2023 | Toggle abstract · pdf

  Although spatial locality is explicit in the Heisenberg picture of quantum dynamics, spatial locality is not explicit in the Schrödinger picture equations of motion. The gauge picture is a modification of Schrödinger's picture such that locality is explicit in the equations of motion. In order to achieve this explicit locality, the gauge picture utilizes (1) a distinct wavefunction associated with each patch of space, and (2) time-dependent unitary connections to relate the Hilbert spaces associated with nearby patches. In this work, we show that by adding an additional spatially-local term to the gauge picture equations of motion, we can effectively interpolate between the gauge and Schrödinger pictures, such that when this additional term has a large coefficient, all of the gauge picture wavefunctions approach the Schrödginer picture wavefunction (and the connections approach the identity).

• Group theoretical derivation of consistent particle theories

  Giuseppe Nisticò

  SciPost Phys. Proc. 14, 040 (2023) · published 24 November 2023 | Toggle abstract · pdf

  Current quantum theories of an elementary free particle assume unitary space inversion and anti-unitary time reversal operators. In so doing robust classes of possible theories are discarded. The present work shows that consistent theories can be derived through a strictly deductive development from the principle of relativistic invariance and position covariance, also with anti-unitary space inversion and unitary time reversal operators. In doing so the class of possible consistent theories is extended for positive but also zero mass particles. In particular, consistent theories for a Klein-Gordon particle are derived and the non-localizability theorem for a non zero helicity massless particle is extended.

• Wigner function analysis of finite matter-radiation systems

  Eduardo Nahmad-Achar, Ramón López-Peña, Sergio Cordero, Octavio Castaños Garza

  SciPost Phys. Proc. 14, 039 (2023) · published 24 November 2023 | Toggle abstract · pdf

  We show that the behaviour in phase space of the Wigner function associated to the electromagnetic modes carries the information of both, the entanglement properties between matter and field, and the regions in parameter space where quantum phase transitions take place. A finer classification for the continuous phase transitions is obtained through the computation of the surface of minimum fidelity.

• Mixed permutation symmetry quantum phase transitions of critical three-level atom models

  Alberto Mayorgas, J. Guerrero, Manuel Calixto

  SciPost Phys. Proc. 14, 036 (2023) · published 24 November 2023 | Toggle abstract · pdf

  We define the concept of Mixed Symmetry Quantum Phase Transition (MSQPT), considering each permutation symmetry sector $\mu$ of an identical particles system, as singularities in the properties of the lowest-energy state into each $\mu$ when shifting a Hamiltonian control parameter $\lambda$. A three-level Lipkin-Meshkov-Glick (LMG) model is chosen to typify our construction. Firstly, we analyze the finite number $N$ of particles case, proving the presence of MSQPT precursors. Then, in the thermodynamic limit $N\to∞$, we calculate the lowest-energy density inside each sector $\mu$, augmenting the control parameter space by $\mu$, and showing a phase diagram with four different quantum phases.

• Linking ladder operators for the Rosen-Morse and Pöschl-Teller systems

  Simon Garneau-Desroches, Véronique Hussin

  SciPost Phys. Proc. 14, 026 (2023) · published 24 November 2023 | Toggle abstract · pdf

  An analysis of the realizations of the ladder operators for the Rosen-Morse and Pöschl-Teller quantum systems is carried out. The failure of the algebraic method of construction in the general Rosen-Morse case is exposed and explained. We present the reduction of a recently obtained set of $(2n ± 1)$-th-order Rosen-Morse ladder operators to the usual first-order realization for the Pöschl-Teller case known in the literature.

• On old relations of Lie theory, classical geometry and gauge theory

  Rolf Dahm

  SciPost Phys. Proc. 14, 025 (2023) · published 24 November 2023 | Toggle abstract · pdf

  Having been led by hadron interactions and low-energy photoproduction to SU(4) and non-compact SU*(4) symmetry, the general background turned out to be projective geometry (PG) of $P^3$, or when considering line and Complex geometry to include gauge theory, aspects of $P^5$. Point calculus and its dual completion by planes introduced quaternary (quadratic) "invariants" $x_{\mu}x^{\mu}=0$ and $p_{\mu}p^{\mu}=0$, and put focus on the intermediary form $(xu)$ and its treatment. Here, the major result is the identification of the symmetric 20 of SU(4) comprising nucleon and Delta states as related to the quaternary cubic forms discussed by Hilbert in his work on full invariant systems. So PG determines geometrically the scene by representations (reps) and invariant theory without having to force affine restrictions and additional (spinorial or gauge) rep theory.

• BRST invariant formulation of the Bell-CHSH inequality in gauge field theories

  David Dudal, Philipe De Fabritiis, Marcelo Santos Guimaraes, Giovani Peruzzo, Silvio Paolo Sorella

  SciPost Phys. 15, 201 (2023) · published 23 November 2023 | Toggle abstract · pdf

  A study of the Bell-CHSH inequality in gauge field theories is presented. By using the Kugo-Ojima analysis of the BRST charge cohomology in Fock space, the Bell-CHSH inequality is formulated in a manifestly BRST invariant way. The examples of the free four-dimensional Maxwell theory and the Abelian Higgs model are scrutinized. The inequality is probed by using BRST invariant squeezed states, allowing for large Bell-CHSH inequality violations, close to Tsirelson's bound. An illustrative comparison with the entangled state of two $1/2$ spin particles in Quantum Mechanics is provided.

  1 citation

• Symmetry-protected exceptional and nodal points in non-Hermitian systems

  Sharareh Sayyad, Marcus Stålhammar, Lukas Rødland, Flore K. Kunst

  SciPost Phys. 15, 200 (2023) · published 23 November 2023 | Toggle abstract · pdf

  One of the unique features of non-Hermitian (NH) systems is the appearance of NH degeneracies known as exceptional points (EPs). The extensively studied defective EPs occur when the Hamiltonian becomes non-diagonalizable. Aside from this degeneracy, we show that NH systems may host two further types of non-defective degeneracies, namely, non-defective EPs and ordinary (Hermitian) nodal points. The non-defective EPs manifest themselves by i) the diagonalizability of the NH Hamiltonian at these points and ii) the non-diagonalizability of the Hamiltonian along certain intersections of these points, resulting in instabilities in the Jordan decomposition when approaching the points from certain directions. We demonstrate that certain discrete symmetries, namely parity-time, parity-particle-hole, and pseudo-Hermitian symmetry, guarantee the occurrence of both defective and non-defective EPs. We extend this list of symmetries by including the NH time-reversal symmetry in two-band systems. Two-band and four-band models exemplify our findings. Through an example, we further reveal that ordinary nodal points may coexist with defective EPs in NH models when the above symmetries are relaxed.

  10 citations

• Hilbert space structure and classical limit of the low energy sector of U(N) quantum Hall ferromagnets

  Manuel Calixto, Alberto Mayorgas, Julio Guerrero

  SciPost Phys. Proc. 14, 021 (2023) · published 23 November 2023 | Toggle abstract · pdf

  Using the Lieb–Mattis ordering theorem of electronic energy levels, we identify and construct the Hilbert space of the low energy sector of U(N) quantum Hall/Heisenberg ferromagnets at filling factor M for L Landau/lattice sites. The carrier Hilbert space of irreducible representations of U(N) is described by rectangular Young tableaux of M rows and L columns, and associated with Grassmannian phase spaces U(N)/U(M)×U(N-M). Replacing U(N)-spin operators by their expectation values in a Grassmannian coherent state allows for a semi-classical treatment of the low energy U(N)-spin-wave coherent excitations (skyrmions) of U(N) quantum Hall ferromagnets in terms of Grasmannian nonlinear sigma models.

• The prediction of anyons: Its history and wider implications

  Gerald A. Goldin

  SciPost Phys. Proc. 14, 005 (2023) · published 23 November 2023 | Toggle abstract · pdf

  Prediction of "anyons," often attributed exclusively to Wilczek, came first from Leinaas and Myrheim in 1977, and independently from Goldin, Menikoff, and Sharp in 1980-81. In 2020, experimentalists successfully created anyonic excitations. This paper discusses why the possibility of quantum particles in two-dimensional space with intermediate exchange statistics eluded physicists for so long after bosons and fermions were understood. The history suggests ideas for the preparation of future researchers. I conclude by addressing failures to attribute scientific achievements accurately, both inadvertent and intentional. Such practices disproportionately hurt women and minorities in physics.