On the classical geometry of chaotic Green functions and Wigner functions

• URL: http://arxiv.org/abs/2507.07398v1
• Date: Thu, 10 Jul 2025 03:30:01 GMT
• Title: On the classical geometry of chaotic Green functions and Wigner functions
• Authors: Alfredo M. Ozorio de Almeida,
• Abstract summary: A Legendre transform generates a resolvent surface as the classical basis for semiclassical representations of the resolvent operator in double phase space.<n>In an initial study of the resolvent surface based on its caustics, its complex nature is revealed to be analogous to a multidimensional sponge.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Semiclassical approximations for various representations of a quantum state are constructed on a single (Lagrangian) surface in phase space, but it is not available for chaotic systems. An analogous evolution surface underlies semiclassical representations of the evolution operator, albeit in a doubled phase space. It is here shown that, corresponding to the Fourier transform on a unitary operator, represented as a Green function or spectral Wigner function, a Legendre transform generates a resolvent surface as the classical basis for semiclassical representations of the resolvent operator in double phase space, independently of the integrable or chaotic nature of the system. This surface coincides with derivatives of action functions (or generating functions) depending on the choice of appropriate coordinates and its growth departs from the energy shell following trajectories in double phase space. In an initial study of the resolvent surface based on its caustics, its complex nature is revealed to be analogous to a multidimensional sponge. Resummation of the trace of the resolvent in terms of linear combinations of periodic orbits, known as pseudo orbits or composite orbits, provides a cutoff to the semiclassical sum at the Heisenberg time. It is here shown that the corresponding actions for higher times can be approximately included within true secondary periodic orbits, in which multiple windings of short periodic orbits are joined by heteroclinic orbits into larger circuits.

Related papers

• Topological crystals and soliton lattices in a Gross-Neveu model with Hilbert-space fragmentation [41.94295877935867]
  We explore the finite-density phase diagram of the single-flavour Gross-Neveu-Wilson (GNW) model.<n>We find a sequence of inhomogeneous ground states that arise through a real-space version of the mechanism of Hilbert-space fragmentation.
  arXiv  Detail & Related papers  (2025-06-23T14:19:35Z)
• Exact Quantum Trace Formula from Complex Periodic Orbits [0.4506616924250028]
  We explore the full quantum version of the trace formula using the Lefschetz thimble method. Our key innovation lies in the simultaneous complexification of the periods of cycles, resulting in a fully quantum trace formula. This formulation connects the quantum spectrum to contributions across all complex time directions, encompassing all relevant homology classes.
  arXiv  Detail & Related papers  (2024-11-16T03:58:24Z)
• Quantum Random Walks and Quantum Oscillator in an Infinite-Dimensional Phase Space [45.9982965995401]
  We consider quantum random walks in an infinite-dimensional phase space constructed using Weyl representation of the coordinate and momentum operators. We find conditions for their strong continuity and establish properties of their generators.
  arXiv  Detail & Related papers  (2024-06-15T17:39:32Z)
• Quantum states resembling classical periodic trajectories in mesoscopic elliptic billiards [0.0]
  A quantum wave function with localization on classical periodic orbits in a mesoscopic elliptic billiard has been achieved. We analyze and discuss the rotational and librational regimes of motion in the elliptic billiard.
  arXiv  Detail & Related papers  (2023-12-01T22:11:28Z)
• Classical and semi-classical limits in phase space [0.0]
  A semimagnitude approximation is derived by using a family of wavepackets to map arbitrary wavefunctions into phase space. The resulting approximation is a linear first-order partial differential equation on phase space. This is a derivation of the Koopman-vonclassicalmann (KvN) formulation of classical mechanics.
  arXiv  Detail & Related papers  (2023-05-29T22:48:45Z)
• Measurement phase transitions in the no-click limit as quantum phase transitions of a non-hermitean vacuum [77.34726150561087]
  We study phase transitions occurring in the stationary state of the dynamics of integrable many-body non-Hermitian Hamiltonians. We observe that the entanglement phase transitions occurring in the stationary state have the same nature as that occurring in the vacuum of the non-hermitian Hamiltonian.
  arXiv  Detail & Related papers  (2023-01-18T09:26:02Z)
• Geometric phases along quantum trajectories [58.720142291102135]
  We study the distribution function of geometric phases in monitored quantum systems. For the single trajectory exhibiting no quantum jumps, a topological transition in the phase acquired after a cycle. For the same parameters, the density matrix does not show any interference.
  arXiv  Detail & Related papers  (2023-01-10T22:05:18Z)
• Energy transition density of driven chaotic systems: A compound trace formula [0.0]
  Oscillations in the probability density of quantum transitions of the eigenstates of a chaotic Hamiltonian have been shown to depend on closed compound orbits. The phase of the oscillations with the energies or evolution parameters agree with those previously obtained. The amplitude of the contribution of each closed compound orbit is more compact and independent of any feature of the Weyl-Wigner representation.
  arXiv  Detail & Related papers  (2022-10-08T18:10:12Z)
• Semiclassical energy transition of driven chaotic systems: phase coherence on scar disks [0.0]
  A trajectory segment in an energy shell combines to form a closed curve with a segment in another canonically driven energy shell. The exact representation of the transition density as an integral over spectral Wigner functions is here generalized to arbitrary unitary transformations. The actions of the compound orbits depend on the driving time, or on any other parameter of the transformation of the original eigenstates.
  arXiv  Detail & Related papers  (2022-03-20T22:49:38Z)
• Entanglement dynamics of spins using a few complex trajectories [77.34726150561087]
  We consider two spins initially prepared in a product of coherent states and study their entanglement dynamics. We adopt an approach that allowed the derivation of a semiclassical formula for the linear entropy of the reduced density operator.
  arXiv  Detail & Related papers  (2021-08-13T01:44:24Z)
• Quantum Mereology: Factorizing Hilbert Space into Subsystems with Quasi-Classical Dynamics [0.0]
  We study the question of how to decompose Hilbert space into a preferred tensor-product factorization. We present an in-principle algorithm for finding such a decomposition. This formalism could be relevant to the emergence of spacetime from quantum entanglement.
  arXiv  Detail & Related papers  (2020-05-26T18:01:34Z)
• Bulk detection of time-dependent topological transitions in quenched chiral models [48.7576911714538]
  We show that the winding number of the Hamiltonian eigenstates can be read-out by measuring the mean chiral displacement of a single-particle wavefunction. This implies that the mean chiral displacement can detect the winding number even when the underlying Hamiltonian is quenched between different topological phases.
  arXiv  Detail & Related papers  (2020-01-16T17:44:52Z)

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.