Browsing by Keywords "Phase space methods"
Now showing items 1-13 of 13
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Canonical-covariant Wigner function in polar form
(OSA - The Optical Society, 2000)The two-dimensional Wigner function was investigated in polar canonical coordinates. The covariance properties under the action of affine canonical transformations were derived. The polar canonical phase-space representations ... -
Degrees of freedom of optical systems and signals with applications to sampling and system simulation
(Optical Society of America, 2013)We study the degrees of freedom of optical systems and signals based on space-frequency (phase space) analysis. At the heart of this study is the relationship of the linear canonical transform domains to the space-frequency ... -
Equivalence of linear canonical transform domains to fractional Fourier domains and the bicanonical width product: a generalization of the space-bandwidth product
(Optical Society of America, 2010-07-30)Linear canonical transforms (LCTs) form a three-parameter family of integral transforms with wide application in optics. We show that LCT domains correspond to scaled fractional Fourier domains and thus to scaled oblique ... -
The fractional fourier transform
(IEEE, 2001)A brief introduction to the fractional Fourier transform and its properties is given. Its relation to phase-space representations (time- or space-frequency representations) and the concept of fractional Fourier domains are ... -
The Fractional Fourier transform and harmonic oscillation
(Springer, 2002)The ath-order fractional Fourier transform is a generalization of the ordinary Fourier transform such that the zeroth-order fractional Fourier transform operation is equal to the identity operation and the first-order ... -
Linear canonical transforms, degrees of freedom, and sampling in optical signals and systems
(IEEE, 2014)We study the degrees of freedom of optical systems and signals based on space-frequency (phase-space) analysis. At the heart of this study is the relationship of the linear canonical transform domains to the space-frequency ... -
Non-local, non-commutative picture in quantum mechanics and distinguished continuous canonical maps
(IOP Science, 2002)It is shown that continuous classical nonlinear canonical (Poisson) maps have a distinguished role in quantum mechanics. They act unitarily on the quantum phase space and generate h-independent quantum nonlinear canonical ... -
Non-orthogonal domains in phase space of quantum optics and their relation to fractional Fourier transforms
(Elsevier BV * North-Holland, 1995-10-15)It is customary to define a phase space such that position and momentum are mutually orthogonal coordinates. Associated with these coordinates, or domains, are the position and momentum operators. Representations of the ... -
Phase-space window and degrees of freedom of optical systems with multiple apertures
(Optical Society of America., 2013)We show how to explicitly determine the space-frequency window (phase-space window) for optical systems consisting of an arbitrary sequence of lenses and apertures separated by arbitrary lengths of free space. If the ... -
Quantum canonical transformations in star-product formalism
(IOP, 2013)We study construction of the star-product version of three basic quantum canonical transformations which are known as the generators of the full canonical algebra. By considering the fact that star-product of c-number ... -
Quantum Dynamics of Long-Range Interacting Systems Using the Positive-P and Gauge-P Representations
(American Physical Society, 2017)We provide the necessary framework for carrying out stochastic positive-P and gauge-P simulations of bosonic systems with long-range interactions. In these approaches, the quantum evolution is sampled by trajectories in ... -
Stride-to-stride energy regulation for robust self-stability of a torque-actuated dissipative spring-mass hopper
(A I P Publishing LLC, 2010)In this paper, we analyze the self-stability properties of planar running with a dissipative spring-mass model driven by torque actuation at the hip. We first show that a two-dimensional, approximate analytic return map ... -
Wigner-related phase spaces for signal processing and their optical implementation
(Optical Society of America, 2000)Phase spaces are different ways to represent signals. Owing to their properties, they are often used for signal compression and recognition with high discrimination abilities. We present several recently introduced ...
