Showing papers in "Journal of Physics A in 2002"
TL;DR: It is shown that the proposed CA models can be very transparent and still reproduce the two main types of congested patterns as well as their dependence on the flows near an on-ramp, in qualitative agreement with the recently developed continuum version of the three-phase traffic theory.
Abstract: The cellular automata (CA) approach to traffic modelling is extended to allow for spatially homogeneous steady state solutions that cover a two-dimensional region in the flow–density plane. Hence these models fulfil a basic postulate of a three-phase traffic theory proposed by Kerner. This is achieved by a synchronization distance, within which a vehicle always tries to adjust its speed to that of the vehicle in front. In the CA models presented, the modelling of the free and safe speeds, the slow-to-start rules as well as some contributions to noise are based on the ideas of the Nagel–Schreckenberg-type modelling. It is shown that the proposed CA models can be very transparent and still reproduce the two main types of congested patterns (the general pattern and the synchronized flow pattern) as well as their dependence on the flows near an on-ramp, in qualitative agreement with the recently developed continuum version of the three-phase traffic theory (Kerner B S and Klenov S L 2002 J. Phys. A: Math. Gen. 35 L31 ). These features are qualitatively different from those in previously considered CA traffic models. The probability of the breakdown phenomenon (i.e. of the phase transition from free flow to synchronized flow) as function of the flow rate to the on-ramp and of the flow rate on the road upstream of the on-ramp is investigated. The capacity drops at the on-ramp which occur due to the formation of different congested patterns are calculated.
398 citations
TL;DR: In this article, the authors apply the theory of commutative algebra to the Burgers-Korteweg-de Vries equation and propose a new approach which they call the first-integral method to study it.
Abstract: In this paper, applying the theory of commutative algebra, we propose a new approach which we currently call the first-integral method to study the Burgers–Korteweg–de Vries equation.
293 citations
TL;DR: The inverse scattering problem on branching graphs is studied in this article, where the Schrodinger operator is defined with real potentials with finite first momentum and using special boundary conditions connecting values of the functions at the vertices.
Abstract: The inverse scattering problem on branching graphs is studied. The definition of the Schrodinger operator on such graphs is discussed. The operator is defined with real potentials with finite first momentum and using special boundary conditions connecting values of the functions at the vertices. It is shown that in general the scattering matrix does not determine the topology of the graph, the potentials on the edges and the boundary conditions uniquely.
266 citations
TL;DR: In this paper, the authors analyse the quantum walk in higher spatial dimensions and compare classical and quantum spreading as a function of time, and find that entanglement between the dimensions serves to reduce the rate of spread.
Abstract: We analyse the quantum walk in higher spatial dimensions and compare classical and quantum spreading as a function of time. Tensor products of Hadamard transformations and the discrete Fourier transform arise as natural extensions of the 'quantum coin toss' in the one-dimensional walk simulation, and other illustrative transformations are also investigated. We find that entanglement between the dimensions serves to reduce the rate of spread of the quantum walk. The classical limit is obtained by introducing a random phase variable.
255 citations
TL;DR: It is demonstrated that the p-adic analysis is a natural basis for the construction of a wide variety of models of ultrametric diffusion constrained by hierarchical energy landscapes and can be applied to both the relaxation in complex systems and the rate processes coupled to rearrangement of the complex surrounding.
Abstract: We demonstrate that the p-adic analysis is a natural basis for the construction of a wide variety of models of ultrametric diffusion constrained by hierarchical energy landscapes. A general analytical description in terms of the p-adic analysis is given for a class of models. Two exactly solvable examples, i.e. the ultrametric diffusion constrained by the linear energy landscape and the ultrametric diffusion with a reaction sink, are considered. We show that such models can be applied to both the relaxation in complex systems and the rate processes coupled to rearrangement of the complex surrounding.
243 citations
TL;DR: In this article, the authors considered the relation between the Weyl-Wigner-Stratonovich map and the s-ordered quasi-distribution of quantum observables.
Abstract: Invertible maps from operators of quantum observables onto functions of c-number arguments and their associative products are first assessed. Different types of maps such as the Weyl-Wigner-Stratonovich map and s-ordered} quasi-distribution are discussed. The recently introduced symplectic tomography map of observables (tomograms) related to the Heisenberg-Weyl group is shown to belong to the standard framework of the maps from quantum observables onto the c-number functions. The star product for symbols of the quantum observable for each one of the maps (including the tomographic map) and explicit relations among different star products are obtained. Deformations of the Moyal star product and alternative commutation relations are also considered.
226 citations
TL;DR: In this paper, a microscopic model for phase transitions in traffic flow is presented, where the basic assumption of the model is that hypothetical homogeneous and stationary, i.e., vehicles cover a two-dimensional region in the flow-density plane.
Abstract: A microscopic model for phase transitions in traffic flow is presented. The basic assumption of the model is that hypothetical homogeneous and stationary, i.e. `equilibrium' states of the model cover a two-dimensional region in the flow-density plane. As in empirical observations, in the model moving jams do not spontaneously occur in free flow. Instead, the first-order phase transition to synchronized flow beginning at some density in free flow is realized. The moving jams emerge only in synchronized flow. As a result, the diagrams of patterns (states) both for a homogeneous road without bottlenecks and at on-ramps are qualitatively different from those found in other approaches at present. In particular, only one type of pattern occurs at on-ramps, if the flow rates to the on-ramp and on the road are high enough: in this general pattern synchronized flow occurs upstream of the on-ramp and wide moving jams spontaneously emerge in this synchronized flow.
217 citations
TL;DR: In this article, it was shown that the exponential map is a C 1 local diffeomorphism and that if two diffeomorphic points are sufficiently close on D,t hey can be joined by a unique length-minimizing geodesic, a state of the system is transformed to another nearby state by going through a uniquely determined flow that minimizes the energy.
Abstract: According to the principle of least action, the spatially periodic motions of one-dimensional mechanical systems with no external forces are described in the Lagrangian formalism by geodesics on a manifold-configuration space, the group D of smooth orientation-preserving diffeomorphisms of the circle. The periodic inviscid Burgers equation is the geodesic equation on D with the L 2 right-invariant metric. However, the exponential map for this right-invariant metric is not a C 1 local diffeomorphism and the geometric structure is therefore deficient. On the other hand, the geodesic equation on D for the H 1 rightinvariant metric is also a re-expression of a model in mathematical physics. We show that in this case the exponential map is a C 1 local diffeomorphism and that if two diffeomorphisms are sufficiently close on D ,t heycan be joined by a unique length-minimizing geodesic—a state of the system is transformed to another nearby state by going through a uniquely determined flow that minimizes the energy. We also analyse for both metrics the breakdown of the geodesic flow.
214 citations
TL;DR: The fact that the eigenvalues of PT-symmetric Hamiltonians H can be real for some values of ap arameter and complex for others is explained by showing that the matrix elements of H,a ndhence the secular equation, are real, not only for PT but also for an entity A satisfying A 2k = 1w ith k odd.
Abstract: The fact that eigenvalues of PT-symmetric Hamiltonians H can be real for some values of ap arameter and complex for others is explained by showing that the matrix elements ofH ,a ndhence the secular equation, are real, not only for PT but also for an ya ntiunitary operator A satisfying A 2k = 1w ith k odd. The argument is illustrated by a 2 × 2m atrix Hamiltonian, and two examples of the generalization are given.
212 citations
TL;DR: In this article, the quantum Cramer-Rao-type bound for many cases was calculated using a newly proposed powerful technique, and the use of collective measurement in statistical estimation was discussed.
Abstract: This paper sheds light on non-commutativity in quantum theory as regards theoretical estimation. In it, we calculate the quantum Cramer-Rao-type bound for many cases, by use of a newly proposed powerful technique. We also discuss the use of collective measurement in statistical estimation.
197 citations
TL;DR: In this article, the authors derived the first integral integral of the shape equation for axially symmetric configurations by examining the forces which are balanced along the circles of constant latitude and the corresponding torque tensor.
Abstract: The stresses in a closed lipid membrane described by the Helfrich Hamiltonian, quadratic in th ee xtrinsic curvature, are identified using Noether’s theorem. Three equations describe the conservation of the stress tensor: the norma lp rojection is identified as the shape equation describing equilibrium configurations; the tangential projections are consistency conditions on the stresses which capture the fluid character of such membranes. The corresponding torque tensor is also identified. The use of the stress tensor as a basis for perturbation theory is discussed. The conservation laws are cast in terms of the forces and torques on closed curves. As an application, the first integral of the shape equation for axially symmetric configurations is derived by examining the forces which are balanced along the circles of constant latitude.
TL;DR: In this article, the authors formulate a perturbative version of the symmetry approach in the symbolic representation and generalize it in order to make it suitable for the study of nonlocal and non-evolution equations.
Abstract: The aim of our paper is to formulate a perturbative version of the symmetry approach in the symbolic representation and to generalize it in order to make it suitable for the study of nonlocal and non-evolution equations. Our formalism is the development and incorporation of the perturbative approach of Zakharov and Schulman, the symbolic method of Sanders and Wang and the standard symmetry approach of Shabat et al. We apply our theory to describe integrable generalizations of the Benjamin-Ono type equations and to isolate integrable cases of the Camassa-Holm type equations.
TL;DR: In this article, a new direct and unified algebraic method for constructing multiple travelling wave solutions of general nonlinear evolution equations is presented and implemented in a computer algebraic system, which not only gives new and more general solutions, but also provides a guideline to classify the various types of the traveling wave solutions according to the values of some parameters.
Abstract: A new direct and unified algebraic method for constructing multiple travelling wave solutions of general nonlinear evolution equations is presented and implemented in a computer algebraic system. Compared with most of the existing tanh methods, the Jacobi elliptic function method or other sophisticated methods, the proposed method not only gives new and more general solutions, but also provides a guideline to classify the various types of the travelling wave solutions according to the values of some parameters. The solutions obtained in this paper include (a) kink-shaped and bell-shaped soliton solutions, (b) rational solutions, (c) triangular periodic solutions and (d) Jacobi and Weierstrass doubly periodic wave solutions. Among them, the Jacobi elliptic periodic wave solutions exactly degenerate to the soliton solutions at a certain limit condition. The efficiency of the method can be demonstrated on a large variety of nonlinear evolution equations such as those considered in this paper, KdV–MKdV, Ito's fifth MKdV, Hirota, Nizhnik–Novikov–Veselov, Broer–Kaup, generalized coupled Hirota–Satsuma, coupled Schrodinger–KdV, (2 + 1)-dimensional dispersive long wave, (2 + 1)-dimensional Davey–Stewartson equations. In addition, as an illustrative sample, the properties of the soliton solutions and Jacobi doubly periodic solutions for the Hirota equation are shown by some figures. The links among our proposed method, the tanh method, extended tanh method and the Jacobi elliptic function method are clarified generally.
TL;DR: In this paper, the authors studied the Casimir effect for scalar fields with general curvature coupling subject to mixed boundary conditions (1 + βmnμ∂μ) = 0 at x = am on one (m = 1) and two (m= 1, 2) parallel plates at a distance a ≡ a2 − a1 from each other.
Abstract: We study the Casimir effect for scalar fields with general curvature coupling subject to mixed boundary conditions (1 + βmnμ∂μ) = 0 at x = am on one (m = 1) and two (m = 1, 2) parallel plates at a distance a ≡ a2 − a1 from each other. Making use of the generalized Abel–Plana formula previously established by one of the authors [1], the Casimir energy densities are obtained as functions of β1 and of β1, β2, a respectively. In the case of two parallel plates, a decomposition of the total Casimir energy into volumic and superficial contributions is provided. The possibility of finding a vanishing energy for particular parameter choices is shown and the existence of a minimum to the surface part is also observed. We show that there is a region in the space of parameters defining the boundary conditions in which the Casimir forces are repulsive for small distances and attractive for large distances. This yields the interesting possibility of stabilizing the distance between the plates by using the vacuum forces.
TL;DR: The basic frameworks and techniques of the Bayesian approach to image restoration are reviewed from the statistical-mechanical point of view and a few basic notions in digital image processing are explained to convince the reader that statistical mechanics has a close formal similarity to this problem.
Abstract: The basic frameworks and techniques of the Bayesian approach to image restoration are reviewed from the statistical-mechanical point of view. First, a few basic notions in digital image processing are explained to convince the reader that statistical mechanics has a close formal similarity to this problem. Second, the basic formulation of the statistical estimation from the observed degraded image by using the Bayes formula is demonstrated. The relationship between Bayesian statistics and statistical mechanics is also listed. Particularly, it is explained that some correlation inequalities on the Nishimori line of the random spin model also play an important role in Bayesian image restoration. Third, the framework of Bayesian image restoration for binary images by means of the Ising model is reviewed. Some practical algorithms for binary image restoration are given by employing the mean-field and the Bethe approximations. Finally, Bayesian image restoration for a grey-level image using the Gaussian model is reviewed, and the Gaussian model is extended to a more practical probabilistic model by introducing the line state to treat the effects of edges. The line state is also extended to quantized values.
TL;DR: In this article, the thermal conductivity of the integrable spin-½ XXZ chain was investigated and the low and high-temperature limits were analyzed analytically for wide ranges of temperature and anisotropy.
Abstract: Motivated by recent investigations of transport properties of strongly correlated 1D models and thermal conductivity measurements of quasi 1D magnetic systems, we present results for the integrable spin-½ XXZ chain. The thermal conductivity κ(ω) of this model has κ(ω) = δ(ω), i.e. it is infinite for zero frequency ω. The weight of the delta peak is calculated exactly by a lattice path integral formulation. Numerical results for wide ranges of temperature and anisotropy are presented. The low- and high-temperature limits are studied analytically.
TL;DR: For real (time-reversal symmetric) quantum billiards, the mean length L of nodal line is calculated for the nth mode (n>>1), with wavenumber k, using a Gaussian random wave model adapted locally to satisfy Dirichlet or Neumann boundary conditions.
Abstract: For real (time-reversal symmetric) quantum billiards, the mean length L of nodal line is calculated for the nth mode (n>>1), with wavenumber k, using a Gaussian random wave model adapted locally to satisfy Dirichlet or Neumann boundary conditions. The leading term is of order k (i.e. √n), and the first (perimeter) correction, dominated by an unanticipated long-range boundary effect, is of order log k (i.e. log n), with the same sign (negative) for both boundary conditions. The leading-order state-to-state fluctuations δL are of order √log k. For the curvature κ of nodal lines, |κ| and √κ2 are of order k, but |κ|3 and higher moments diverge. For complex (e.g. Aharonov-Bohm) billiards, the mean number N of nodal points (phase singularities) in the mode has a leading term of order k2 (i.e. n), the perimeter correction (again a long-range effect) is of order klog k (i.e. √nlog n) (and positive, notwithstanding nodal depletion near the boundary) and the fluctuations δN are of order k√log k. Generalizations of the results for mixed (Robin) boundary conditions are stated.
TL;DR: In this article, a dual one-to-one correspondence between the candidates of the two concepts is shown. And they show that Fisher information is obtained from relative entropies as contrast functions on the state space and argue that the scalar curvature might be interpreted as an uncertainty density on a statistical manifold.
Abstract: Variance and Fisher information are ingredients of the Cramer-Rao inequality. We regard Fisher information as a Riemannian metric on a quantum statistical manifold and choose monotonicity under coarse graining as the fundamental property of variance and Fisher information. In this approach we show that there is a kind of dual one-to-one correspondence between the candidates of the two concepts. We emphasize that Fisher information is obtained from relative entropies as contrast functions on the state space and argue that the scalar curvature might be interpreted as an uncertainty density on a statistical manifold.
TL;DR: In this article, the su(1,1) algebra is used as a spectrum generating algebra and as a potential algebra to obtain exact solutions of effective mass Schrodinger equations corresponding to a number of potentials.
Abstract: We use Lie algebraic techniques to obtain exact solutions of the effective mass Schrodinger equation. In particular we use the su(1,1) algebra, both as a spectrum generating algebra and as a potential algebra, to obtain exact solutions of effective mass Schrodinger equations corresponding to a number of potentials. We also discuss the construction of isospectral Hamiltonians for which both the mass and the potential are different.
TL;DR: An exact uncertainty principle, formulated as the assumption that a classical ensemble is subject to random momentum fluctuations of a strength which is determined by and scales inversely with uncertainty in position, leads from the classical equations of motion to the Schrodinger equation as discussed by the authors.
Abstract: An exact uncertainty principle, formulated as the assumption that a classical ensemble is subject to random momentum fluctuations of a strength which is determined by and scales inversely with uncertainty in position, leads from the classical equations of motion to the Schrodinger equation.
TL;DR: It is shown that the single-lane dynamics can be extended to the two-lane case without changing the basic properties of the model, which are known to be in good agreement with empirical single-vehicle data.
Abstract: A two-lane extension of a recently proposed cellular automaton model for traffic flow is discussed. The analysis focuses on the reproduction of the lane usage inversion and the density dependence of the number of lane changes. It is shown that the single-lane dynamics can be extended to the two-lane case without changing the basic properties of the model, which are known to be in good agreement with empirical single-vehicle data. Therefore it is possible to reproduce various empirically observed two-lane phenomena, like the synchronization of the lanes, without fine tuning of the model parameters.
TL;DR: In this article, a necessary and sufficient condition for a sequence of quantum measurements to achieve the optimal performance in quantum hypothesis testing is derived, and a projection measurement characterized by the irreducible representation theory of the special linear group SL is proposed.
Abstract: We derive a necessary and sufficient condition for a sequence of quantum measurements to achieve the optimal performance in quantum hypothesis testing. We discuss what quantum measurement we should perform in order to attain the optimal exponent of the second error probability under the condition that the first error probability goes to 0. As an asymptotically optimal measurement, we propose a projection measurement characterized by the irreducible representation theory of the special linear group SL(). Especially, in the spin-1/2 system, it is realized by the simultaneous measurement of the total momentum and a momentum of a specified direction. As a by-product, we obtain another proof of quantum Stein's lemma. In addition, an asymptotically optimal measurement is constructed in the quantum Gaussian case, and it is physically meaningful.
TL;DR: In this paper, the authors derived a relation between the fidelity of quantum motion, characterizing the stability of quantum dynamics with respect to arbitrary static perturbation of the unitary evolution propagator, and the integrated time auto-correlation function of the generator.
Abstract: We derive a simple and general relation between the fidelity of quantum motion, characterizing the stability of quantum dynamics with respect to arbitrary static perturbation of the unitary evolution propagator, and the integrated time auto-correlation function of the generator of perturbation. Surprisingly, this relation predicts the slower decay of fidelity the faster the decay of correlations. In particular, for non-ergodic and non-mixing dynamics, where asymptotic decay of correlations is absent, a qualitatively different and faster decay of fidelity is predicted on a timescale 1/δ as opposed to mixing dynamics where the fidelity is found to decay exponentially on a timescale 1/δ2, where δ is the strength of perturbation. A detailed discussion of a semiclassical regime of small effective values of Planck constant is given where classical correlation functions can be used to predict quantum fidelity decay. Note that the correct and intuitively expected classical stability behaviour is recovered in the classical limit → 0, as the two limits δ → 0 and → 0 do not commute. In addition, we also discuss non-trivial dependence on the number of degrees of freedom. All the theoretical results are clearly demonstrated numerically on the celebrated example of a quantized kicked top.
TL;DR: In this paper, the authors give conditions under which general bipartite entangled non-orthogonal states become maximally entangled states, and then they construct a large class of entangled NOMA states with exactly one ebit of entanglement.
Abstract: We give conditions under which general bipartite entangled non-orthogonal states become maximally entangled states. Using these conditions we construct a large class of entangled non-orthogonal states with exactly one ebit of entanglement in both bipartite and multipartite systems. One remarkable property is that the amount of entanglement in this class of states is independent on the parameters involved in the states. Finally we discuss how to generate the bipartite entangled non-orthogonal states.
TL;DR: In this article, pairwise quantum entanglement in systems of fermions itinerant in a lattice from a second-quantized perspective is studied, both for energy eigenstates and for the thermal state.
Abstract: We study pairwise quantum entanglement in systems of fermions itinerant in a lattice from a second-quantized perspective. Entanglement in the grand-canonical ensemble is studied, both for energy eigenstates and for the thermal state. Relations between entanglement and superconducting correlations are discussed in a BCS-like model and for η-pair superconductivity.
TL;DR: In this article, a generalized Euler angle parametrization for SU(N) was given, and the Haar measure and its relation to Marinov's volume formula were derived.
Abstract: In a previous paper [1] an Euler angle parametrization for SU(4) was given. Here we present the derivation of a generalized Euler angle parametrization for SU(N). The formula for the calculation of the Haar measure for SU(N) as well as its relation to Marinov's volume formula for SU(N) [2, 3] will also be derived. As an example of this parametrization's usefulness, the density matrix parametrization and invariant volume element for a qubit/qutrit, three qubit and two three-state systems, also known as two qutrit systems [4], will also be given.
TL;DR: In this paper, it was shown that the set of states with infinite entropy of entanglement is trace-norm dense in state space, implying that in any neighbourhood of every product state lies an arbitrarily strongly entangled state.
Abstract: We investigate entanglement measures in the infinite-dimensional regime. First, we discuss the peculiarities that may occur if the Hilbert space of a bi-partite system is infinite dimensional, most notably the fact that the set of states with infinite entropy of entanglement is trace-norm dense in state space, implying that in any neighbourhood of every product state lies an arbitrarily strongly entangled state. The starting point for a clarification of this counterintuitive property is the observation that if one imposes the natural and physically reasonable constraint that the mean energy is bounded from above, then the entropy of entanglement becomes a trace-norm continuous functional. The considerations will then be extended to the asymptotic limit, and we will prove some asymptotic continuity properties. We proceed by investigating the entanglement of formation and the relative entropy of entanglement in the infinite-dimensional setting. Finally, we show that the set of entangled states is still trace-norm dense in state space, even under the constraint of a finite mean energy.
TL;DR: In this article, the authors derive a recursion relation that allows one to compute the spectrum of the matrix of incidence for finite trees that determines completely the low concentration limit of sparse random matrices.
Abstract: We revisit the derivation of the density of states of sparse random matrices. We derive a recursion relation that allows one to compute the spectrum of the matrix of incidence for finite trees that determines completely the low concentration limit. Using the iterative scheme introduced by Biroli and Monasson (1999 J. Phys. A: Math. Gen. 32 L255) we find an approximate expression for the density of states expected to hold exactly in the opposite limit of large but finite concentration. The combination of the two methods yields a very simple geometric interpretation of the tails of the spectrum. We test the analytic results with numerical simulations and we suggest an indirect numerical method to explore the tails of the spectrum.
TL;DR: It is argued that fluctuations in the number of nodes of degree k become Gaussian for fixed degree as the size of the network diverges and the fluctuations between different realizations are characterized in terms of higher moments of the degree distribution.
Abstract: We study the role of finiteness and fluctuations about average quantities for basic structural properties of growing networks. We first determine the exact degree distribution of finite networks by generating function approaches. The resulting distributions exhibit an unusual finite-size scaling behaviour and they are also sensitive to the initial conditions. We argue that fluctuations in the number of nodes of degree k become Gaussian for fixed degree as the size of the network diverges. We also characterize the fluctuations between different realizations of the network in terms of higher moments of the degree distribution.
TL;DR: In this paper, the space of states of -symmetric quantum mechanics is examined and self-consistent expressions for the probability amplitude and the average value of operator are suggested, satisfying the equation of continuity and vanishing for the bound state.
Abstract: The space of states of -symmetric quantum mechanics is examined. The requirement that eigenstates with different eigenvalues must be orthogonal leads to the conclusion that eigenfunctions belong to a space with an indefinite metric. Self-consistent expressions for the probability amplitude and the average value of operator are suggested. Further specification of the space of state vectors yields a superselection rule, redefining the notion of the superposition principle. An expression for the probability current density, satisfying the equation of continuity and vanishing for the bound state, is proposed.