Theoretical description of chirping waves using phase-space waterbags

Abstract Despite being the overwhelming majority of events produced in hadron or heavy ion collisions, minimum bias events do not enjoy a robust first-principles theoretical description as their dynamics are dominated by low-energy quantum chromodynamics. In this paper, we present a novel expansion scheme of the cross section for minimum bias events that exploits an ergodic hypothesis for particles in the events and events in an ensemble of data. We identify power counting rules and symmetries of minimum bias from which the form of the squared matrix element can be expanded in symmetric polynomials of the phase space coordinates. This expansion is entirely defined in terms of observable quantities, in contrast to models of heavy ion collisions that rely on unmeasurable quantities like the number of nucleons participating in the collision, or tunes of parton shower parameters to describe the underlying event in proton collisions. The expansion parameter that we identify from our power counting is the number of detected particles N and as N → ∞ the variance of the squared matrix element about its mean, constant value on phase space vanishes. With this expansion, we show that the transverse momentum distribution of particles takes a universal form that only depends on a single parameter, has a fractional dispersion relation, and agrees with data in its realm of validity. We show that the constraint of positivity of the squared matrix element requires that all azimuthal correlations vanish in the N → ∞ limit at fixed center-of-mass energy, as observed in data. The approach we follow allows for a unified treatment of small and large system collective behavior, being equally applicable to describe, e.g., elliptic flow in PbPb collisions and the “ridge” in pp collisions. We also briefly comment on power counting and symmetries for minimum bias events in other collider environments and show that a possible ridge in e+e− collisions is highly suppressed as a consequence of its symmetries.

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A phase-space method for arbitrary bimolecular gas-phase reactions: Theoretical description

International Journal of Quantum Chemistry ◽

10.1002/qua.1403 ◽

2001 ◽

Vol 84 (5) ◽

pp. 479-492 ◽

Cited By ~ 3

Author(s):

A. Gross ◽

K. V. Mikkelsen ◽

W. R. Stockwell

Keyword(s):

Phase Space ◽

Gas Phase ◽

Theoretical Description ◽

Gas Phase Reactions ◽

Space Method

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Fluctuating Number of Energy Levels in Mixed-Type Lemon Billiards

Physics ◽

10.3390/physics3040055 ◽

2021 ◽

Vol 3 (4) ◽

pp. 888-902

Author(s):

Črt Lozej ◽

Dragan Lukman ◽

Marko Robnik

Keyword(s):

Phase Space ◽

Theoretical Prediction ◽

Gaussian Distribution ◽

Mixed Type ◽

Energy Levels ◽

Theoretical Description ◽

Golden Mean ◽

Relative Fraction ◽

Unit Radius

In this paper, the fluctuation properties of the number of energy levels (mode fluctuation) are studied in the mixed-type lemon billiards at high lying energies. The boundary of the lemon billiards is defined by the intersection of two circles of equal unit radius with the distance 2B between the centers, as introduced by Heller and Tomsovic. In this paper, the case of two billiards, defined by B=0.1953,0.083, is studied. It is shown that the fluctuation of the number of energy levels follows the Gaussian distribution quite accurately, even though the relative fraction of the chaotic part of the phase space is only 0.28 and 0.16, respectively. The theoretical description of spectral fluctuations in the Berry–Robnik picture is discussed. Also, the (golden mean) integrable rectangular billiard is studied and an almost Gaussian distribution is obtained, in contrast to theory expectations. However, the variance as a function of energy, E, behaves as E, in agreement with the theoretical prediction by Steiner.

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A one-dimensional self-gravitating stellar gas

Symposium - International Astronomical Union ◽

10.1017/s0074180900105261 ◽

1966 ◽

Vol 25 ◽

pp. 46-48 ◽

Cited By ~ 2

Author(s):

M. Lecar

Keyword(s):

Gravitational Field ◽

Phase Space ◽

Motion Picture ◽

Space Distribution ◽

Two Dimensional ◽

One Dimensional ◽

Phase Space Distribution ◽

Dimensional Phase Space ◽

The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

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