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Spontaneous symmetry breaking in a bridge model fed by junctions

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 Added by Martin Evans
 Publication date 2008
  fields Physics
and research's language is English




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We introduce a class of 1D models mimicking a single-lane bridge with two junctions and two particle species driven in opposite directions. The model exhibits spontaneous symmetry breaking (SSB) for a range of injection/extraction rates. In this phase the steady state currents of the two species are not equal. Moreover there is a co-existence region in which the symmetry broken phase co-exists with a symmetric phase. Along a path in which the extraction rate is varied, keeping the injection rate fixed and large, hysteresis takes place. The mean field phase diagram is calculated and supporting Monte-Carlo simulations are presented. One of the transition lines exhibits a kink, a feature which cannot exist in transition lines of equilibrium phase transitions.



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First we consider a unidirectional flux omega_bar of vehicles each of which is characterized by its `natural velocity v drawn from a distribution P(v). The traffic flow is modeled as a collection of straight `world lines in the time-space plane, with overtaking events represented by a fixed queuing time tau imposed on the overtaking vehicle. This geometrical model exhibits platoon formation and allows, among many other things, for the calculation of the effective average velocity w=phi(v) of a vehicle of natural velocity v. Secondly, we extend the model to two opposite lanes, A and B. We argue that the queuing time tau in one lane is determined by the traffic density in the opposite lane. On the basis of reasonable additional assumptions we establish a set of equations that couple the two lanes and can be solved numerically. It appears that above a critical value omega_bar_c of the control parameter omega_bar the symmetry between the lanes is spontaneously broken: there is a slow lane where long platoons form behind the slowest vehicles, and a fast lane where overtaking is easy due to the wide spacing between the platoons in the opposite direction. A variant of the model is studied in which the spatial vehicle density rho_bar rather than the flux omega_bar is the control parameter. Unequal fluxes omega_bar_A and omega_bar_B in the two lanes are also considered. The symmetry breaking phenomenon exhibited by this model, even though no doubt hard to observe in pure form in real-life traffic, nevertheless indicates a tendency of such traffic.
82 - J. Smits , H.T.C. Stoof , 2021
Spontaneous symmetry breaking (SSB) is a key concept in physics that for decades has played a crucial role in the description of many physical phenomena in a large number of different areas, like particle physics, cosmology, and condensed-matter physics. SSB is thus an ubiquitous concept connecting several, both high and low energy, areas of physics and many textbooks describe its basic features in great detail. However, to study the dynamics of symmetry breaking in the laboratory is extremely difficult. In condensed-matter physics, for example, tiny external disturbances cause a preference for the breaking of the symmetry in a particular configuration and typically those disturbances cannot be avoided in experiments. Notwithstanding these complications, here we describe an experiment, in which we directly observe the spontaneous breaking of the temporal phase of a driven system with respect to the drive into two distinct values differing by $pi$.
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