Symmetry and History Quantum Theory: An analogue of Wigner's Theorem

The basic ingredients of the `consistent histories' approach to quantum theory are a space \UP of `history propositions' and a space \D of `decoherence functionals'. In this article we consider such history quantum theories in the case where \UP is given by the set of projectors \P(\V) on some Hilbert space \V. We define the notion of a `physical symmetry of a history quantum theory' (PSHQT) and specify such objects exhaustively with the aid of an analogue of Wigner's theorem. In order to prove this theorem we investigate the structure of \D, define the notion of an `elementary decoherence functional' and show that each decoherence functional can be expanded as a certain combination of these functionals. We call two history quantum theories that are related by a PSHQT `physically equivalent' and show explicitly, in the case of history quantum mechanics, how this notion is compatible with one that has appeared previously.Comment: To appear in Jour.Math.Phys.; 25 pages; Latex-documen

Density fluctuations and phase separation in a traffic flow model

Within the Nagel-Schreckenberg traffic flow model we consider the transition from the free flow regime to the jammed regime. We introduce a method of analyzing the data which is based on the local density distribution. This analyzes allows us to determine the phase diagram and to examine the separation of the system into a coexisting free flow phase and a jammed phase above the transition. The investigation of the steady state structure factor yields that the decomposition in this phase coexistence regime is driven by density fluctuations, provided they exceed a critical wavelength.Comment: in 'Traffic and Granular Flow 97', edited by D.E. Wolf and M. Schreckenberg, Springer, Singapore (1998

Continuous Time and Consistent Histories

We discuss the use of histories labelled by a continuous time in the approach to consistent-histories quantum theory in which propositions about the history of the system are represented by projection operators on a Hilbert space. This extends earlier work by two of us \cite{IL95} where we showed how a continuous time parameter leads to a history algebra that is isomorphic to the canonical algebra of a quantum field theory. We describe how the appropriate representation of the history algebra may be chosen by requiring the existence of projection operators that represent propositions about time average of the energy. We also show that the history description of quantum mechanics contains an operator corresponding to velocity that is quite distinct from the momentum operator. Finally, the discussion is extended to give a preliminary account of quantum field theory in this approach to the consistent histories formalism.Comment: Typeset in RevTe

Experiments and Simulations on Day-to-Day Route Choice-Behaviour

The paper reports laboratory experiments on a day-to-day route choice game with two routes. Subjects had to choose between a main road M and a side road S. The capacity was greater for the main road. 18 subjects participated in each session. In equilibrium the number of subjects is 12 on M and 6 on S. Two treatments with 6 sessions each were run at the Laboratory of Experimental Economics at Bonn University using RatImage. Feedback was given in treatment I only about own travel time and in treatment II on travel time for M and S. Money payoffs increase with decreasing time. The main results are as follows. 1. Mean numbers on M and S are very near to the equilibrium. 2. Fluctuations persist until the end of the sessions in both treatments. 3. Fluctuations are smaller under treatment II .The effect is small but significant. 4. The total number of changes is significantly greater in treatment I. 5. Subjects’ road changes and payoffs are negatively correlated in all sessions. 6. A direct response mode reacts with more changes for bad payoffs whereas a contrary response mode shows opposite reactions. Both response modes can be observed. 7. The simulation of an extended payoff sum learning model closely fits the main results of the statistical evaluation of the data.travel behaviour research, information in intelligent transportation systems, day-to-day route choice, laboratory experiments, payoff sum model

Quantum Fields in Nonstatic background: A Histories Perspective

For a quantum field living on a non - static spacetime no instantaneous Hamiltonian is definable, for this generically necessitates a choice of inequivalent representation of the canonical commutation relations at each instant of time. This fact suggests a description in terms of time - dependent Hilbert spaces, a concept that fits naturally in a (consistent) histories framework. Our primary tool for the construction of the quantum theory in a continuous -time histories format is the recently developed formalism based on the notion of the history group . This we employ to study a model system involving a 1+1 scalar field in a cavity with moving boundaries. The instantaneous (smeared) Hamiltonian and a decoherence functional are then rigorously defined so that finite values for the time - averaged particle creation rate are obtainable through the study of energy histories. We also construct the Schwinger - Keldysh closed- time - path generating functional as a ``Fourier transform'' of the decoherence functional and evaluate the corresponding n - point functions.Comment: 27 pages, LATEX; minor changes and corrections; version to appear in JM

A simple Monte Carlo model for crowd dynamics

In this paper we introduce a simple Monte Carlo method for simulating the dynamics of a crowd. Within our model a collection of hard-disk agents is subjected to a series of two-stage steps, implying (i) the displacement of one specific agent followed by (ii) a rearrangement of the rest of the group through a Monte Carlo dynamics. The rules for the combined steps are determined by the specific setting of the granular flow, so that our scheme should be easily adapted to describe crowd dynamics issues of many sorts, from stampedes in panic scenarios to organized flow around obstacles or through bottlenecks. We validate our scheme by computing the serving times statistics of a group of agents crowding to be served around a desk. In the case of a size homogeneous crowd, we recover intuitive results prompted by physical sense. However, as a further illustration of our theoretical framework, we show that heterogeneous systems display a less obvious behavior, as smaller agents feature shorter serving times. Finally, we analyze our results in the light of known properties of non-equilibrium hard-disk fluids and discuss general implications of our model.Comment: to be published in Physical Review

On- and Off-ramps Generating 1/f Noise in Traffic Flow

A simple model of a motorway junction consisting of two connected periodic roads is presented; each of them is connected to the other by on- and off-ramps. This constitutes a detailed structure for the region of on- and off-ramps, which is a new aspect of this paper and a useful step towards a more realistic modelling of the vehicular dynamics near the ramps. The traffic flow through the ramps has an effect on the capacity of the main roads. This effect is identified by the formation of the so-called ”plateau” in the fundamental diagram. The value increase of one of the probabilities pin and pout decreases the value of the indicated plateau. Here pin is the probability to enter the main road through the on-ramp and pout denotes the probability to exit the main road through the off-ramp. The first important feature in the simulated system is the symmetry between the connected main roads. This symmetry does not depend on the variation of the difference between the probabilities pin and pout. The other most outstanding feature is the existence of correlations between the connected main roads, which can be traced back to the lane change of vehicles in the ramp regions. These correlations are characterized by the occurrence of 1/fα fluctuations in the global traffic flow of a chosen main road of the simulated system.A simple model of a motorway junction consisting of two connected periodic roads is presented; each of them is connected to the other by on- and off-ramps. This constitutes a detailed structure for the region of on- and off-ramps, which is a new aspect of this paper and a useful step towards a more realistic modelling of the vehicular dynamics near the ramps. The traffic flow through the ramps has an effect on the capacity of the main roads. This effect is identified by the formation of the so-called ”plateau” in the fundamental diagram. The value increase of one of the probabilities pin and pout decreases the value of the indicated plateau. Here pin is the probability to enter the main road through the on-ramp and pout denotes the probability to exit the main road through the off-ramp. The first important feature in the simulated system is the symmetry between the connected main roads. This symmetry does not depend on the variation of the difference between the probabilities pin and pout. The other most outstanding feature is the existence of correlations between the connected main roads, which can be traced back to the lane change of vehicles in the ramp regions. These correlations are characterized by the occurrence of 1/fα fluctuations in the global traffic flow of a chosen main road of the simulated system

Deterministic approach to microscopic three-phase traffic theory

Two different deterministic microscopic traffic flow models, which are in the context of the Kerner's there-phase traffic theory, are introduced. In an acceleration time delay model (ATD-model), different time delays in driver acceleration associated with driver behaviour in various local driving situations are explicitly incorporated into the model. Vehicle acceleration depends on local traffic situation, i.e., whether a driver is within the free flow, or synchronized flow, or else wide moving jam traffic phase. In a speed adaptation model (SA-model), vehicle speed adaptation occurs in synchronized flow depending on driving conditions. It is found that the ATD- and SA-models show spatiotemporal congested traffic patterns that are adequate with empirical results. In the ATD- and SA-models, the onset of congestion in free flow at a freeway bottleneck is associated with a first-order phase transition from free flow to synchronized flow; moving jams emerge spontaneously in synchronized flow only. Differences between the ATD- and SA-models are studied. A comparison of the ATD- and SA-models with stochastic models in the context of three phase traffic theory is made. A critical discussion of earlier traffic flow theories and models based on the fundamental diagram approach is presented.Comment: 40 pages, 14 figure