“Phase space” papers · AI for Research

Phase space

Valeriy A Ryabov · 2018

In the first chapter, the equations of motion of the particles in Hamiltonian and Lagrangian representations are considered. The difference between them is illustrated by an animation.

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phase space

Jack Ellison · Zenodo (CERN European Organization for Nuclear Research) · 2024

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phase space

E Villa, L De, La Fuente et al. · Electronics Letters · 2013

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Phase space.

Nathaniel Rodriguez (3330831), Johan Bollen (262505), Yong-Yeol Ahn (220468) · Figshare · 2016

(a-c) Phase diagrams of various combinations of the three parameters J, I, and T. Along with corresponding slices through the phase space as indicated by the dashed red lines (bottom row). (a,d) peer-influence I and susceptibility T conflict creating a regime where multiple belief systems with various coherences can coexist. We see a similar regime appear in (b, e) where peer-influence and coherentism contend for dominance. More traditional disorder-to-order transitions as in other opinion models also take place when I is small and fixed (c, f). S/N is the fractional size of the largest group. ER graphs with N = 104 nodes and average degree of 5 were used. The density was calculated from a 160 trails per point. The belief network was fully connected with M = 5.

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Phase Space

Pure and applied physics · 1971

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phase space

Jack Ellison · Zenodo (CERN European Organization for Nuclear Research) · 2024

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phase space

R Filip · 2001

Amplification and cloning of the Schrödinger-cat state (even coherent-state superposition) in the optical nondegenerate parametric amplifier are analysed. In the long-time limit, distinguishability and interference in the marginal probability distributions of the Schrödinger-cat state cannot be preserved simultaneously during amplification. The mutual ratio between distinguishability and interference can be controlled by the squeezed vacuum state injected in the idler mode. Thus only one of either quantum interference of indistinguishable states or distinguished states without interference can be obtained on the output of the amplifier. The purity of the initial state in the signal mode disappears during the amplification for both cases, even if the interference is preserved. Thus the interference in the marginal probability distribution is connected with indistinguishability in the phase space rather than with purity of the state. On the other hand, the nonclassical oscillations in the photon-number distribution vanish simultaneously, as the state is more mixed, irrespective of the existence of the interference. Keywords: Schrödinger-cat state, phase space, superposition 1.

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Phase Space

Krešimir Veselić · Lecture notes in mathematics · 2011

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Phase space and space-time

Vitaly Kuyukov · 2019

Phase space and space-time

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Phase Space Representation

Claudio Conti · Quantum science and technology · 2023

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Multicomponent Phase Space

B. Cantor · 2024

Abstract This chapter introduces the concept of multicomponent phase space and describes and discusses its size, shape and geography. This is important for developing strategies to explore multicomponent phase space and find particular materials with interesting and/or valuable structures and properties. Multicomponent phase space contains large regions of single-phase multicomponent solid solutions, multicomponent amorphous alloys and multicomponent compounds, as well as other large regions with more complex, multiphase structures, formed for instance, by eutectic solidification and/or solid-state precipitation. This chapter sets out definitions of these different kinds of materials to create a clear taxonomy with which to describe the size, shape and occurrence of the different regions of multicomponent phase space.

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Phase Space Methods

C. W. Gardiner, P. Zoller · Springer series in synergetics · 2000

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Phase Space Reconstruction.

Ray Huffaker (686132), Marco Bittelli (686133) · Figshare · 2015

Wind speed dynamics evolve along a nonlinear low-dimension attractor reconstructed from lagged copies of the denoised and detrended SSA-reconstructed series. The attractor exhibits the dominant four-cycle of six-hour blocks giving the diurnal oscillation. The inset highlights the internal structure of the attractor by plotting only the first 200 points.

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Phase Space Fractons

Anonymous, Abhishodh Prakash, S. L. Sondhi et al. · Physical Review Letters · 2026

Perhaps the simplest approach to constructing models with subdimensional particles or fractons is to require the conservation of dipole or higher multipole moments. We generalize this approach to allow for moments in phase space and classify all possible classical fracton models with phase-space multipole conservation laws. We focus on a new self-dual model that conserves both dipole and quadrupole moments in position and momentum; we analyze its dynamics and find quasiperiodic orbits in phase space that evade ergodic exploration of the full phase space.

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Phase Space Representation

Herbert Gross · 2025

The concept of the phase space is a very important approach that is well known from quantum physics. In optics, the phase space is spanned by spatial and angle coordinates; alternatively the angle can be expressed as a spatial frequency. The Wigner function as a quasi-density function in the phase space of a physical beam can be used to illustrate the development of the energy density in spatial and angle coordinates of a light field. The phase space has been well known in mechanics and quantum mechanics for a long time. A typical light emitting diode (LED) is nearly constant in the spatial domain, but has a wide Lambertian angle distribution. A Gaussian beam has a corresponding energy density in the angle as well as in the spatial domain. Correspondingly the colours of the LED and the Gaussian laser beam are shaded, illustrating the varying energy density as the Wigner distribution function.

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Discrete Phase Space

Giovanni Gallavotti · Theoretical and mathematical physics · 2014

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Phase Space Distributions

B. J. Dalton, John Jeffers, Stephen M. Barnett · 2014

Abstract This chapter formally presents the representation of the quantum density operator by phase space distribution functions of phase space variables, leading to expressions for quantum correlation functions in terms of phase space integrals in which phase space variables for each mode—c-numbers for bosons, Grassmann numbers for fermions—replace mode annihilation and creation operators. The emphasis is on double-phase-space normally ordered (positive P type) normalised distribution functions, with distinct phase space variables for annihilation and creation operators; however, symmetrically ordered (Wigner type) distribution functions are also considered, along with unnormalised B distribution functions, which lead to phase space integrals for Fock state populations and coherences. Characteristic functions are first defined and then shown to be related to distribution functions via phase space integrals. The existence and symmetry properties of distribution functions—which are non-unique and non-analytic for bosons—is demonstrated using Bargmann coherent-state projectors.

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Phase space dynamics

Physics Subject Headings (PhySH) · 2018

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Phase space analysis.

Dionysios Perdikis (203283), Raoul Huys (151793), Viktor K. Jirsa (203285) · Figshare · 2015

From top to bottom: means and standard deviations of y (denoted as yµ and ys), of dy/dt ((dy/dt)µ and (dy/dt)s), of δy (δyµ and δys), of z (z µ and z s), of dz/dt ((dz/dt)µ and (dz/dt)s), of δz (δzµ and δzs), and of {ξj} (ξj µ and ξj s). Colors, shadings and line styles are similar as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002198#pcbi-1002198-g006" target="_blank">Figure 6</a>. The effect of δ-‘kicks’ on the architecture's output is as evident as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002198#pcbi-1002198-g006" target="_blank">Figure 6</a> (notice also that (dy/dt)s and (dz/dt)s are almost identical to δys and δzs, respectively, in the segments with a δ-‘kick’). The variability of {ξj} (ξjs) that signals mode transitions, now has a significant effect on standard deviations of dy/dt and dz/dt that approximate the phase flow. This effect cannot be identified unambiguously in the variability of the trajectory in the phase space (ys and zs). At the first transition, the δ-‘kick’ variability follows that of the {ξj}, and their effects are easily separable. Instead, at the second transition, the mean of the {ξj} modulates the standard deviation of δz and thereby the one of dz/dt as well (because of their overlapping in the data set). At the third transition no δ-‘kick’ is involved; however, there is still a significant increase in (dy/dt)s and (dz/dt)s due to the increase in ξj s.

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phase-space density

V. Avila-reese, A. Carrillo, O. Valenzuela et al. · 2008

It was argued in the past that bulges of galaxies cannot be formed through collisionless secular evolution because that would violate constraints on the phase-space density: the phase-space density in bulges is several times larger than in the inner parts of discs. We show that these arguments against secular evolution are not correct. Observations give estimates of the coarse-grained phase-space densities of galaxies, f ′ = ρs/σRσφσz, where ρs is stellar density and σR, σφ, σz are the radial, tangential, and vertical rms velocities of stars. Using high-resolution N-body simulations, we study the evolution of f ′ in discs of Galaxy-size models. During the secular evolution, the discs, which are embedded in live Cold Dark Matter haloes, form a bar and then a thick, dynamically hot, central mass concentration. In the course of evolution f ′ declines at all radii, not just in the central region. The decline is different in different parts of the disc. In the inner disc, f ′ (R) develops a valley with a minimum around the end of the central mass concentration. We conclude that the phase-space density in the central regions can be larger than in the inner disc without violating the Lioville’s theorem. The minimum, which gets deeper with time, seems to be due to a large phase mixing produced by the outer bar. We find that the shape and the amplitude of f ′ (R) for different simulations agree qualitatively with the observed f ′ (R) in our Galaxy. Curiously enough, the phase space-density turns out to be an argument in favor of secular formation of bulges not against it.

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