Wigner function for discrete phase space: Exorcising ghost images

We study a generic and paradigmatic two-degrees-of-freedom system consisting of two coupled perturbed cat maps with different types of dynamics. The Wigner separability entropy (WSE)-equivalent to the operator space entanglement entropy-and the classical separability entropy (CSE) are used as measures of complexity. For the case where both degrees of freedom are hyperbolic, the maps are classically ergodic and the WSE and the CSE behave similarly, growing to higher values than in the doubly elliptic case. However, when one map is elliptic and the other hyperbolic, the WSE reaches the same asymptotic value than that of the doubly hyperbolic case but at a much slower rate. The CSE only follows the WSE for a few map steps, revealing that classical dynamical features are not enough to explain complexity growth.

show abstract

“…2 e) and f)) . We notice that we have removed the effects of the torus periodicity on the Wigner distributions in all figures [19].…”

Section: Resultsmentioning

confidence: 99%

Quantum and classical complexity in coupled maps

2017

View full text Add to dashboard Cite

show abstract

“…In order to get rid of redundancies and "ghost images" derived essentially from the cylindrical topology of our phase space, we use a method that has been developed by Argüelles and Dittrich [29] consisting of Fourier transforming the Weyl-Wigner symbol to its symplectic analogue, known as the "chord symbol". Then, after performing a cut off for the longer chords and antifourier transforming, the new Weyl-Wigner symbol with the desired properties is obtained.…”

Section: The Phase Space Picturementioning

confidence: 99%

Classical to quantum correspondence in dissipative directed transport

2015

View full text Add to dashboard Cite

We compare the quantum and classical properties of the (Quantum) Isoperiodic Stable Structures -(Q)ISSs -which organize the parameter space of a paradigmatic dissipative ratchet model, i.e. the dissipative modified kicked rotator. We study the spectral behavior of the corresponding classical Perron-Frobenius operators with thermal noise and the quantum superoperators without it for small eff values. We find a remarkable similarity between the classical and quantum spectra. This finding significantly extends previous results -obtained for the mean currents and asymptotic distributions only -and on the other hand unveils a classical to quantum correspondence mechanism where the classical noise is qualitatively different from the quantum one. This is crucial not only for simple attractors but also for chaotic ones, where just analyzing the asymptotic distribution reveals insufficient. Moreover, we provide with a detailed characterization of relevant eigenvectors by means of the corresponding Weyl-Wigner distributions, in order to better identify similarities and differences. Finally, this model being generic, it allows us to conjecture that this classical to quantum correspondence mechanism is a universal feature of dissipative systems.

show abstract

“…In the field of signal analysis, where Wigner functions have also been widely employed, the discrete time Wigner distribution shows similar features, which are related to aliasing [33], and various alternative definitions have been proposed to construct alias-free distributions, and to allow a reconstruction of the continuum time signal from a discrete sample. In the context of finite-dimensional quantum systems, a proposal for a ghost-free Wigner function was put forward in [34]. In all such cases, the negative values of the Wigner function respond to the very structure of the discretized phase space and not to the features of the state or the signal.…”

Section: Non-classicality Of States: Negativity Of the Wigner Functionmentioning

confidence: 99%

Wigner function for a particle in an infinite lattice

2012

View full text Add to dashboard Cite

We study the Wigner function for a quantum system with a discrete, infinite-dimensional Hilbert space, such as a spinless particle moving on a onedimensional infinite lattice. We discuss the peculiarities of this scenario and of the associated phase-space construction, propose a meaningful definition of the Wigner function in this case and characterize the set of pure states for which it is non-negative. We propose a measure of non-classicality for states in this system, which is consistent with the continuum limit. The prescriptions introduced here are illustrated by applying them to localized and Gaussian states and to their superpositions.

show abstract

Wigner function for discrete phase space: Exorcising ghost images

Cited by 19 publications

References 11 publications

Quantum and classical complexity in coupled maps

Quantum and classical complexity in coupled maps

Classical to quantum correspondence in dissipative directed transport

Wigner function for a particle in an infinite lattice

Contact Info

Product

Resources

About