Semiclassical Formulae For Wigner Distributions

• URL: http://arxiv.org/abs/2201.04892v2
• Date: Thu, 21 Apr 2022 07:55:47 GMT
• Title: Semiclassical Formulae For Wigner Distributions
• Authors: Sonja Barkhofen and Philipp Sch\"utte and Tobias Weich
• Abstract summary: We give an overview over some aspects of the modern mathematical theory of Ruelle resonances for chaotic, i.e. uniformly hyperbolic, dynamical systems. First we recall recent developments in the mathematical theory of resonances, in particular how invariant Ruelle distributions arise as residues of weighted zeta functions. We derive a correspondence between weighted and semiclassical zeta functions in the setting of negatively curved surfaces.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper we give an overview over some aspects of the modern mathematical theory of Ruelle resonances for chaotic, i.e. uniformly hyperbolic, dynamical systems and their implications in physics. First we recall recent developments in the mathematical theory of resonances, in particular how invariant Ruelle distributions arise as residues of weighted zeta functions. Then we derive a correspondence between weighted and semiclassical zeta functions in the setting of negatively curved surfaces. Combining this with results of Hilgert, Guillarmou and Weich yields a high frequency interpretation of invariant Ruelle distributions as quantum mechanical matrix coefficients in constant negative curvature. We finish by presenting numerical calculations of phase space distributions in the more physical setting of 3-disk scattering systems.

Related papers

• Curvature of Gaussian quantum states [0.0]
  The space of quantum states can be endowed with a metric structure using the second order derivatives of the relative entropy, giving rise to the so-called Kubo-Mori-Bogoliubov inner product.
  arXiv  Detail & Related papers  (2024-04-15T09:14:10Z)
• On reconstruction of states from evolution induced by quantum dynamical semigroups perturbed by covariant measures [50.24983453990065]
  We show the ability to restore states of quantum systems from evolution induced by quantum dynamical semigroups perturbed by covariant measures. Our procedure describes reconstruction of quantum states transmitted via quantum channels and as a particular example can be applied to reconstruction of photonic states transmitted via optical fibers.
  arXiv  Detail & Related papers  (2023-12-02T09:56:00Z)
• Causal Modeling with Stationary Diffusions [89.94899196106223]
  We learn differential equations whose stationary densities model a system's behavior under interventions. We show that they generalize to unseen interventions on their variables, often better than classical approaches. Our inference method is based on a new theoretical result that expresses a stationarity condition on the diffusion's generator in a reproducing kernel Hilbert space.
  arXiv  Detail & Related papers  (2023-10-26T14:01:17Z)
• Thermal equilibrium in Gaussian dynamical semigroups [77.34726150561087]
  We characterize all Gaussian dynamical semigroups in continuous variables quantum systems of n-bosonic modes which have a thermal Gibbs state as a stationary solution. We also show that Alicki's quantum detailed-balance condition, based on a Gelfand-Naimark-Segal inner product, allows the determination of the temperature dependence of the diffusion and dissipation matrices.
  arXiv  Detail & Related papers  (2022-07-11T19:32:17Z)
• Anomalous ballistic scaling in the tensionless or inviscid Kardar-Parisi-Zhang equation [0.0]
  We show that the zero surface tension or zero viscosity case eludes analytical solutions. Using numerical simulations, we elucidate a well-defined universality class for this case. The latter may be relevant to recent quantum spin chain experiments which measure KPZ and ballistic relaxation under different conditions.
  arXiv  Detail & Related papers  (2022-05-18T09:29:09Z)
• Decimation technique for open quantum systems: a case study with driven-dissipative bosonic chains [62.997667081978825]
  Unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics. We introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function. We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity.
  arXiv  Detail & Related papers  (2022-02-15T19:00:09Z)
• 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 kinetics of anomalous and nonlinear Hall effects in topological semimetals [0.0]
  We present a systematic derivation of the semiclassical Boltzmann equation for band structures with the finite Berry curvature. In particular, this formulation is suitable for the study of nonlinear Hall effect and photogalvanic phenomena.
  arXiv  Detail & Related papers  (2021-02-10T19:00:02Z)
• Quantum particle across Grushin singularity [77.34726150561087]
  We study the phenomenon of transmission across the singularity that separates the two half-cylinders. All the local realisations of the free (Laplace-Beltrami) quantum Hamiltonian are examined as non-equivalent protocols of transmission/reflection. This allows to comprehend the distinguished status of the so-called bridging' transmission protocol previously identified in the literature.
  arXiv  Detail & Related papers  (2020-11-27T12:53:23Z)
• Microscopic quantum generalization of classical Li\'{e}nard oscillators [3.2768228723567527]
  We have explored the microscopic quantum generalization of classical Li'enard systems. It has been shown that detailed balance in the form of fluctuation-dissipation relation preserves the dynamical stability of the attractors even in case of vacuum excitation.
  arXiv  Detail & Related papers  (2020-09-15T14:53:47Z)
• Quantum Brownian Motion for Magnets [0.0]
  We derive a general spin operator equation of motion that describes three-dimensional precession and damping. The results provide a powerful framework to explore general three-dimensional dissipation in quantum thermodynamics.
  arXiv  Detail & Related papers  (2020-09-01T17:44:50Z)

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.