Classical integrability in the presence of a cosmological constant: analytic and machine learning results

• URL: http://arxiv.org/abs/2404.18247v3
• Date: Sat, 21 Dec 2024 21:17:15 GMT
• Title: Classical integrability in the presence of a cosmological constant: analytic and machine learning results
• Authors: Gabriel Lopes Cardoso, Damián Mayorga Peña, Suresh Nampuri,
• Abstract summary: We study the integrability of two-dimensional theories describing the coupling of Maxwell fields and neutral scalar fields to gravity. For a certain solution subspace, we demonstrate partial integrability by showing that a subset of the equations of motion in two dimensions are the compatibility conditions for a linear system. We employ various machine learning techniques to systematise our search for numerical Lax pair matrices for these models.
• Score: 0.0
• License:
• Abstract: We study the integrability of two-dimensional theories that are obtained by a dimensional reduction of certain four-dimensional gravitational theories describing the coupling of Maxwell fields and neutral scalar fields to gravity in the presence of a potential for the neutral scalar fields. For a certain solution subspace, we demonstrate partial integrability by showing that a subset of the equations of motion in two dimensions are the compatibility conditions for a linear system. Subsequently, we study the integrability of these two-dimensional models from a complementary one-dimensional point of view, framed in terms of Liouville integrability. In this endeavour, we employ various machine learning techniques to systematise our search for numerical Lax pair matrices for these models, as well as conserved currents expressed as functions of phase space variables.

Related papers

• Quantum Scattering of Spinless Particles in Riemannian Manifolds [0.0]
  Quantum mechanics is sensitive to the geometry of the underlying space. We present a framework for quantum scattering of a non-relativistic particle confined to a two-dimensional space.
  arXiv  Detail & Related papers  (2024-02-16T10:50:50Z)
• Solvable Two-dimensional Dirac Equation with Matrix Potential: Graphene in External Electromagnetic Field [0.0]
  We find analytically the solutions for a wide class of combinations of matrix and scalar external potentials. The main tool for this progress was provided by supersymmetrical (SUSY) intertwining relations.
  arXiv  Detail & Related papers  (2024-01-21T15:39:49Z)
• Variational manifolds for ground states and scarred dynamics of blockade-constrained spin models on two and three dimensional lattices [0.0]
  We introduce a variational manifold of simple tensor network states for the study of a family of constrained models that describe spin-1/2 systems. Our method can be interpreted as a generalization of mean-field theory to constrained spin models.
  arXiv  Detail & Related papers  (2023-11-15T13:52:21Z)
• Variational Equations-of-States for Interacting Quantum Hamiltonians [0.0]
  We present variational equations of state (VES) for pure states of an interacting quantum Hamiltonian. VES can be expressed in terms of the variation of the density operators or static correlation functions. We present three nontrivial applications of the VES.
  arXiv  Detail & Related papers  (2023-07-03T07:51:15Z)
• Third quantization of open quantum systems: new dissipative symmetries and connections to phase-space and Keldysh field theory formulations [77.34726150561087]
  We reformulate the technique of third quantization in a way that explicitly connects all three methods. We first show that our formulation reveals a fundamental dissipative symmetry present in all quadratic bosonic or fermionic Lindbladians. For bosons, we then show that the Wigner function and the characteristic function can be thought of as ''wavefunctions'' of the density matrix.
  arXiv  Detail & Related papers  (2023-02-27T18:56:40Z)
• Quantum correlations, entanglement spectrum and coherence of two-particle reduced density matrix in the Extended Hubbard Model [62.997667081978825]
  We study the ground state properties of the one-dimensional extended Hubbard model at half-filling. In particular, in the superconducting region, we obtain that the entanglement spectrum signals a transition between a dominant singlet (SS) to triplet (TS) pairing ordering in the system.
  arXiv  Detail & Related papers  (2021-10-29T21:02:24Z)
• Geometric phase in a dissipative Jaynes-Cummings model: theoretical explanation for resonance robustness [68.8204255655161]
  We compute the geometric phases acquired in both unitary and dissipative Jaynes-Cummings models. In the dissipative model, the non-unitary effects arise from the outflow of photons through the cavity walls. We show the geometric phase is robust, exhibiting a vanishing correction under a non-unitary evolution.
  arXiv  Detail & Related papers  (2021-10-27T15:27:54Z)
• Exact solutions of interacting dissipative systems via weak symmetries [77.34726150561087]
  We analytically diagonalize the Liouvillian of a class Markovian dissipative systems with arbitrary strong interactions or nonlinearity. This enables an exact description of the full dynamics and dissipative spectrum. Our method is applicable to a variety of other systems, and could provide a powerful new tool for the study of complex driven-dissipative quantum systems.
  arXiv  Detail & Related papers  (2021-09-27T17:45:42Z)
• Entanglement Entropy of Non-Hermitian Free Fermions [59.54862183456067]
  We study the entanglement properties of non-Hermitian free fermionic models with translation symmetry. Our results show that the entanglement entropy has a logarithmic correction to the area law in both one-dimensional and two-dimensional systems.
  arXiv  Detail & Related papers  (2021-05-20T14:46:09Z)
• Self-consistent microscopic derivation of Markovian master equations for open quadratic quantum systems [0.0]
  We provide a rigorous construction of Markovian master equations for a wide class of quantum systems. We show that, for non-degenerate systems under a full secular approximation, the effective Lindblad operators are the normal modes of the system. We also address the particle and energy current flowing through the system in a minimal two-bath scheme and find that they hold the structure of Landauer's formula.
  arXiv  Detail & Related papers  (2021-01-22T19:25:17Z)
• Rectification induced by geometry in two-dimensional quantum spin lattices [58.720142291102135]
  We address the role of geometrical asymmetry in the occurrence of spin rectification in two-dimensional quantum spin chains. We show that geometrical asymmetry, along with inhomogeneous magnetic fields, can induce spin current rectification even in the XX model.
  arXiv  Detail & Related papers  (2020-12-02T18:10:02Z)

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.