Publications

Order by: publication date number of citations

• Dark matter as a QCD effect in an anti de Sitter geometry: Cosmogonic implications of de Sitter, anti de Sitter and Poincaré symmetries

  Gilles Cohen-Tanoudji, Jean-Pierre Gazeau

  SciPost Phys. Proc. 14, 004 (2023) · published 23 November 2023 | Toggle abstract · pdf

  The $\Lambda$CDM standard model of cosmology involves two dark components of the universe, dark energy and dark matter. Whereas dark energy is usually associated with the (positive) cosmological constant $\Lambda$ associated with a de Sitter geometry, we propose to explain dark matter as a pure QCD effect, namely a gluonic Bose Einstein condensate with the status of a Cosmic Gluonic Background (CGB). This effect is due to the trace anomaly viewed as an effective negative cosmological constant determining an Anti de Sitter geometry and accompanying baryonic matter at the hadronization transition from the quark gluon plasma phase to the colorless hadronic phase. Our approach also allows to assume a ratio Dark/Visible equal to 11/2.

  1 citation

• Covariant canonical formulations of classical field theories

  Francois Gieres

  SciPost Phys. Lect. Notes 77 (2023) · published 5 December 2023 | Toggle abstract · pdf

  We review in simple terms the covariant approaches to the canonical formulation of classical relativistic field theories (in particular gauge field theories and general relativity) and we discuss the relationships between these approaches as well as the relation with the standard (non-covariant) Hamiltonian formulation. Particular attention is paid to conservation laws (notably related to geometric symmetries) within the different approaches. Moreover, for each of these approaches, the impact of space-time boundaries is also addressed. To make the text accessible to a wider audience, we have included an outline of Poisson and symplectic geometry for both classical mechanics and field theory.

  1 citation

• Multi-directional unitarity and maximal entanglement in spatially symmetric quantum states

  Márton Mestyán, Balázs Pozsgay, Ian M. Wanless

  SciPost Phys. 16, 010 (2024) · published 9 January 2024 | Toggle abstract · pdf

  We consider dual unitary operators and their multi-leg generalizations that have appeared at various places in the literature. These objects can be related to multi-party quantum states with special entanglement patterns: the sites are arranged in a spatially symmetric pattern and the states have maximal entanglement for all bipartitions that follow from the reflection symmetries of the given geometry. We consider those cases where the state itself is invariant with respect to the geometrical symmetry group. The simplest examples are those dual unitary operators which are also self dual and reflection invariant, but we also consider the generalizations in the hexagonal, cubic, and octahedral geometries. We provide a number of constructions and concrete examples for these objects for various local dimensions. All of our examples can be used to build quantum cellular automata in 1+1 or 2+1 dimensions, with multiple equivalent choices for the "direction of time".

  1 citation

• Integrability and complexity in quantum spin chains

  Ben Craps, Marine De Clerck, Oleg Evnin, Philip Hacker

  SciPost Phys. 16, 041 (2024) · published 7 February 2024 | Toggle abstract · pdf

  There is a widespread perception that dynamical evolution of integrable systems should be simpler in a quantifiable sense than the evolution of generic systems, though demonstrating this relation between integrability and reduced complexity in practice has remained elusive. We provide a connection of this sort by constructing a specific matrix in terms of the eigenvectors of a given quantum Hamiltonian. The null eigenvalues of this matrix are in one-to-one correspondence with conserved quantities that have simple locality properties (a hallmark of integrability). The typical magnitude of the eigenvalues, on the other hand, controls an explicit bound on Nielsen's complexity of the quantum evolution operator, defined in terms of the same locality specifications. We demonstrate how this connection works in a few concrete examples of quantum spin chains that possess diverse arrays of highly structured conservation laws mandated by integrability.

  1 citation

• Topological interpretation of color exchange invariants: hexagonal lattice on a torus

  Olivier Cépas, Peter M. Akhmetiev

  SciPost Phys. 10, 042 (2021) · published 18 February 2021 | Toggle abstract · pdf

  We explain a correspondence between some invariants in the dynamics of color exchange in a 2d coloring problem, which are polynomials of winding numbers, and linking numbers in 3d. One invariant is visualized as linking of lines on a special surface with Arf-Kervaire invariant one, and is interpreted as resulting from an obstruction to transform the surface into its chiral image with special continuous deformations. We also consider additional constraints on the dynamics and see how the surface is modified.

  1 citation

• Unifying description of the damping regimes of a stochastic particle in a periodic potential

  Antonio Piscitelli, Massimo Pica Ciamarra

  SciPost Phys. 3, 018 (2017) · published 4 September 2017 | Toggle abstract · pdf

  We analyze the classical problem of the stochastic dynamics of a particle confined in a periodic potential, through the so called Il'in and Khasminskii model, with a novel semi-analytical approach. Our approach gives access to the transient and the asymptotic dynamics in all damping regimes, which are difficult to investigate in the usual Brownian model. We show that the crossover from the overdamped to the underdamped regime is associated with the loss of a typical time scale and of a typical length scale, as signaled by the divergence of the probability distribution of a certain dynamical event. In the underdamped regime, normal diffusion coexists with a non Gaussian displacement probability distribution for a long transient, as recently observed in a variety of different systems. We rationalize the microscopic physical processes leading to the non-Gaussian behavior, as well as the timescale to recover the Gaussian statistics. The theoretical results are supported by numerical calculations and are compared to those obtained for the Brownian model.

  1 citation

• Integrable deformations of superintegrable quantum circuits

  Tamás Gombor, Balázs Pozsgay

  SciPost Phys. 16, 114 (2024) · published 26 April 2024 | Toggle abstract · pdf

  Superintegrable models are very special dynamical systems: they possess more conservation laws than what is necessary for integrability. This severely constrains their dynamical processes, and it often leads to their exact solvability, even in non-equilibrium situations. In this paper we consider special Hamiltonian deformations of superintegrable quantum circuits. The deformations break superintegrability, but they preserve integrability. We focus on a selection of concrete models and show that for each model there is an (at least) one parameter family of integrable deformations. Our most interesting example is the so-called Rule54 model. We show that the model is compatible with a one parameter family of Yang-Baxter integrable spin chains with six-site interaction. Therefore, the Rule54 model does not have a unique integrability structure, instead it lies at the intersection of a family of quantum integrable models.

• Crossed product algebras and generalized entropy for subregions

  Shadi Ali Ahmad, Ro Jefferson

  SciPost Phys. Core 7, 020 (2024) · published 10 April 2024 | Toggle abstract · pdf

  An early result of algebraic quantum field theory is that the algebra of any subregion in a QFT is a von Neumann factor of type III$_{1}$, in which entropy cannot be well-defined because such algebras do not admit a trace or density states. However, associated to the algebra is a modular group of automorphisms characterizing the local dynamics of degrees of freedom in the region, and the crossed product of the algebra with its modular group yields a type II$_∞$ factor, in which traces and hence von Neumann entropy can be well-defined. In this work, we generalize recent constructions of the crossed product algebra for the TFD to, in principle, arbitrary spacetime regions in arbitrary QFTs, formally paving the way to the study of entanglement entropy without UV divergences. In contrast to previous works, we emphasize that this construction is independent of gravity. In this sense, the crossed product construction represents a refinement of Haag's assignment of nets of observable algebras to spacetime regions by providing a natural construction of a type II factor. We present several concrete examples: a QFT in Rindler space, a CFT in an open ball of Minkowski space, and arbitrary boundary subregions in AdS/CFT. In the holographic setting, we provide a novel argument for why the bulk dual must be the entanglement wedge, and discuss the distinction arising from boundary modular flow between causal and entanglement wedges for excited states and disjoint regions.

• Matrix product operator representations for the local conserved quantities of the Heisenberg chain

  Kyoichi Yamada, Kohei Fukai

  SciPost Phys. Core 6, 069 (2023) · published 19 October 2023 | Toggle abstract · pdf

  We present the explicit expressions for the matrix product operator (MPO) representation for the local conserved quantities of the Heisenberg chain. The bond dimension of the MPO grows linearly with the locality of the charges. The MPO has more simple form than the local charges themselves, and their Catalan tree patterns naturally emerge from the matrix products. The MPO representation of local conserved quantities is generalized to the integrable SU(N) invariant spin chain.

• Free fermions beyond Jordan and Wigner

  Paul Fendley, Balazs Pozsgay

  SciPost Phys. 16, 102 (2024) · published 10 April 2024 | Toggle abstract · pdf

  The Jordan-Wigner transformation is frequently utilised to rewrite quantum spin chains in terms of fermionic operators. When the resulting Hamiltonian is bilinear in these fermions, i.e. the fermions are free, the exact spectrum follows from the eigenvalues of a matrix whose size grows only linearly with the volume of the system. However, several Hamiltonians that do not admit a Jordan-Wigner transformation to fermion bilinears still have the same type of free-fermion spectra. The spectra of such "free fermions in disguise" models can be found exactly by an intricate but explicit construction of the raising and lowering operators. We generalise the methods further to find a family of such spin chains. We compute the exact spectrum, and generalise an elegant graph-theory construction. We also explain how this family admits an N=2 lattice supersymmetry.