Coexistence of up- and downstream traffic waves on a ring road

It is an observational fact that density waves in vehicle traffic can move in either direction: small-amplitude waves travel in the same direction as the cars (downstream) whereas high-amplitude waves or “jams” travel in the opposite direction (upstream). We construct a model of ring road traffic to demonstrate how this comes about. Our model shows the spontaneous generation of these density waves, explains their stability properties, and pinpoints the precise density level at which the wave speed changes direction.     

Finite Hamiltonian systems: Linear transformations and aberrations

Finite Hamiltonian systems contain operators of position, momentum, and energy, having a finite number N of equally-spaced eigenvalues. Such systems are under the æis of the algebra su(2), and their phase space is a sphere. Rigid motions of this phase space form the group SU(2); overall phases complete this to U(2). But since N-point states can be subject to U(N) ?U(2) transformations, the rest of the generators will provide all N ² unitary transformations of the states, which appear as nonlinear transformations—aberrations—of the system phase space. They are built through the “finite quantization” of a classical optical system.     

Bad communities with high modularity

In this paper we discuss some problematic aspects of Newman and Girvan’s modularity function Q _N . Given a graph G, the modularity of G can be written as Q _N = Q _f ? Q ₀, where Q _f is the intracluster edge fraction of G and Q ₀ is the expected intracluster edge fraction of the null model, i.e., a randomly connected graph with same expected degree distribution as G. It follows that the maximization of Q _N must accomodate two factors pulling in opposite directions:Q _f favors a small number of clusters and Q ₀ favors many balanced (i.e., with approximately equal degrees) clusters. In certain cases the Q ₀ term can cause overestimation of the true cluster number; this is the opposite of the well-known underestimation effect caused by the “resolution limit” of modularity. We illustrate the overestimation effect by constructing families of graphs with a “natural” community structure which, however, does not maximize modularity. In fact, we show there exist graphs G with a “natural clustering” V of G and another, balanced clustering U of G such that (i) the pair (G, U) has higher modularity than (G, V) and (ii) V and U are arbitrarily different.     

The analysis of reactions <Emphasis Type="Italic">πN</Emphasis> → <Emphasis Type="Italic">two mesons</Emphasis> + <Emphasis Type="Italic">N</Emphasis> within reggeon exchanges. Basic formulas for fit

We present technical aspects of the fitting procedure given in the paper by V.V. Anisovich and A.V. Sarantsev “The analysis of reactions πN → two mesons + N within reggeon exchanges. Fit and results.”     

Possibility of electrical conduction in filled bands

It is shown that a moving neutral particle interacting with electrons may cause an “electron drag” within a filled band. The calculation uses perturbation theory and periodic boundary conditions and is based on the one-electron model. WithN being the number and ¯v the average velocity of the electrons, one finds that for largeN the electronic velocity sumN¯v induced by the motion of the neutral particle is independent ofN, i.e. of the size of the system. The lowest-order contributions toN¯v that do not necessarily vanish are seen to be those of second order in the interaction potential. These second-order contributions are studied. In a simple one-dimensional model they are found to be, in fact, not necessarily zero and to be proportional to the velocity of the neutral particle. An order-of-magnitude formula forN¯v is derived for this case. The calculation suggests that mobile neutral particles may act as charge carriers, their effective charge possibly being much smaller than the elementary charge. In real systems, neutral particles which interact with electrons might be represented by phonons and excitons.     

Are wave mechanics and matrix mechanics equivalent theories?

The Eckart and Schrödinger proofs of 1926 are often described as having established the equivalence of wave mechanics and matrix mechanics as physical theories. The objective of this paper is to show that these “proofs” establish nothing of the kind. The Eckart-Schrödinger “proofs” have to do only with the formal identity of two different calculi. The question is, do the “proofs” establish the mathematical identity ofC ₁ andC ₂? Two views are possible: (1) Eckart and Schrödinger subsumed wave mechanics (C ₁) and matrix mechanics (C ₂) within a more comprehensive theory — which might be called “the operator calculus” (O). From this alone it does not follow thatC ₁ andC ₂ are formally identical. In general, the identity of two theories can never be established just by the fact that they both follow from the same premise. The other view (2) is thatO is simply a logical transformer which converts any statement ofC ₁ into a corresponding statement ofC ₂ — without adding any theoretical content of its own. That this is so could never beproved by an inductive selection of typical problems within microphysics; yet this is the actual procedure of Eckart and Schrödinger. Strictly speaking, one could consistently doubt thatC ₁ andC ₂ are ultimately identical even after sympathetically entertaining the Eckart-Schrödinger “proofs”. The really convincing argument for the equivalence asphysical theories of wave mechanics and matrix mechanics was provided by Born's statistical interpretation of theψ-function. Because here, in a frankly inductive procedure, Bornforces a physical interpretation onto bothC ₁ andC ₂ which at last makes it a matter of indifference which algorithm one chooses to express his predictions.     

From granules to bulk superconductors using Richardson-Gaudin equations

We provide a compact expression of the ground-state energy of N-Cooper pairs valid from small to large sample volumes, as checked by numerically solving Richardson-Gaudin equations which give the exact eigenstates of BCS superconductors. This expression contains a contribution linear in the potential amplitude, dominant for small samples, and an exponential contribution dominant when the number of states available for pairing gets larger than a material-dependent threshold independent from sample size. These “available states” are the states feeling the BCS potential, reduced by the Pauli exclusion principle through a “moth-eaten effect” which comes from the composite boson nature of Cooper pairs. This work also presents an elegant derivation of the N-Cooper pair energy obtained recently, which makes use of the roots of the degree-N Hermite polynomial.     

Low-temperature contribution to the resonant tunneling conductance of a disordered N–I–N junction

A formula for the contribution ΔG ^res(T) to the resonant tunneling conductance of the N–I–N junction (where N is a normal metal and I is an insulator) with a weak (low impurity concentrations) structural disorder in the I layer from the low-temperature “smearing” electron Fermi surfaces in its N shores is obtained. It is shown that the temperature dependence ΔG ^res(T) in such a “dirty” junction qualitatively differs from the corresponding dependence ΔG ₀(T) in a “pure” (without resonant impurities in the I layer) junction: ΔG ^res(T) < 0, d(ΔG ^res)/dT < 0; ΔG ₀(T) > 0, d(ΔG ₀)/dT > 0, which can serve as an experimental test of the presence of impurity tunneling resonances in the disordered I layer.     

Separation of variables in anisotropic models and non-skew-symmetric elliptic <Emphasis Type="Italic">r</Emphasis>-matrix

We solve a problem of separation of variables for the classical integrable hamiltonian systems possessing Lax matrices satisfying linear Poisson brackets with the non-skew-symmetric, non-dynamical elliptic \(so(3)\otimes so(3)\)-valued classical r-matrix. Using the corresponding Lax matrices, we present a general form of the “separating functions” B(u) and A(u) that generate the coordinates and the momenta of separation for the associated models. We consider several examples and perform the separation of variables for the classical anisotropic Euler’s top, Steklov–Lyapunov model of the motion of anisotropic rigid body in the liquid, two-spin generalized Gaudin model and “spin” generalization of Steklov–Lyapunov model.     

A model of classical thermodynamics based on the partition theory of integers,Earth gravitation,and semiclassical asymptotics. I

In the paper, a new construction of the theory of partitions of integers is proposed. The author defines entropy as the natural logarithm of the number of partitions of a number M into natural summands with repetitions allowed p(M) and repetitions forbidden q(M). The passage from ln p(M) to lnq(M) through the mesoscopic values M → 0 is studied. The topological transition from the mesoscopic lower levels of the Bohr–Kalckar construction to the macroscopic levels corresponding to the critical number of neutrons according to the consequence of Einstein’s inequality M ≤ c N _c , where c is determined for the particles of the given atomic nucleus. The role of quantum mechanics in establishing the new world outlook in physics is analyzed. It is pointed out that the main equations of thermodynamics in the volume “Statistical Physics” of the Landau–Lifshits treatise are obtained without appealing to the so-called “three main principles of thermodynamics”. It is also pointed out that Niels Bohr’s liquid model of the nucleus does not involve any interaction of particles in the form of attraction and is based on the presence of a common potential trough for all elements of the nucleus. The author constructs a new approach to thermodynamics, using quantum mechanics and the Earth’s gravitational attraction as a common potential trough.     

Statistical properties of random environment of 1<Emphasis Type="Italic">D</Emphasis> quantum <Emphasis Type="Italic">N</Emphasis>-particles system in external field

The investigation of 1D quantum N-particle system (PS) with relaxation in the random environment under the influence of external field is conducted within the framework of the stochastic differential equation of the Langevin—Schrödinger (L—Sch) type. Using L—Sch equation, the 2D second-order nonstationary partial differential equation is found, which describes the quantum distribution in the environment, depending on the energy of nonperturbed 1D quantum N-PS and on the external field parameters. It is shown that the average value of the interaction potential between 1D disordered quantum N-PS and the external field, has the ultraviolet divergence. This problem is solved by the renormalization of the equation for the function of quantum distribution. It is shown that it has a sense of dimensional renormalization which is characteristic for the quantum field theory. Critical properties of the environment are investigated in detail. The possibility of the first-order phase transition in the environment distribution depending on amplitude of an external field is been shown.     

The Elusive p-air cross section

For the \(\bar pp\) and pp systems, we have used all of the extensive data of the Particle Data Group [K. Hagiwara et al. (Particle Data Group), Phys. Rev. D 66, 010001 (2002)]. We then subject these data to a screening process, the “Sieve” algorithm [M. M. Block, physics/0506010], in order to eliminate “ outliers” that can skew a χ² fit. With the “Sieve” algorithm, a robust fit using a Lorentzian distribution is first made to all of the data to sieve out abnormally high Δχ _i ² , the individual i^th point’s contribution to the total χ². The χ² fits are then made to the sieved data. We demonstrate that we cleanly discriminate between asymptotic ln s and ln² s behavior of total hadronic cross sections when we require that these amplitudes also describe, on average, low energy data dominated by resonances. We simultaneously fit real analytic amplitudes to the “sieved” high energy measurements of \(\bar pp\) and pp total cross sections and ρ-values for \(\sqrt s \) ≥ GeV, while requiring that their asymptotic fits smoothly join the the σ _pp and σ_pp total cross sections at \(\sqrt s \) = 4.0 GeV—again both in magnitude and slope. Our results strongly favor a high energy ln² s fit, basically excluding a ln s fit. Finally, we make a screened Glauber fit for the p-air cross section, using as input our precisely-determined pp cross sections at cosmic ray energies.     

Aggregation Behavior of Monomeric Surfactants and a Gemini Cationic Surfactant by NMR and Computer Simulation Data

Aggregation of decyltrimethylammonium bromide and cetyltrimethylammonium bromide (CTAB) in D₂O has been studied. Spin–lattice relaxation time and self-diffusion coefficient of surfactant molecules were measured at concentrations below and above surfactant critical micelle concentration. The aggregation properties of conventional surfactant, CTAB, examined by nuclear magnetic resonance (NMR) and molecular dynamic (MD) simulation, were compared with the properties of double-tail analog, N,N,N′,N′-tetramethyl-N,N′dihexadecyl-1,4-butan di-ammonium di-bromide (BCTA). Both NMR and computer simulation methods suggest that micellization is a stepwise process and the pre-micellar aggregates take place in a solution at concentration below critical micelle concentration. According to MD simulation Gemini surfactant, BCTA, forms worm-like micelles, whereas CTAB, which may be considered as its “monomer”, forms only elongated micelles.     

Maximizing Complementary Quantities by Projective Measurements

In this work, we study the so-called quantitative complementarity quantities. We focus in the following physical situation: two qubits (q _A and q _B ) are initially in a maximally entangled state. One of them (q _B ) interacts with a N-qubit system (R). After the interaction, projective measurements are performed on each of the qubits of R, in a basis that is chosen after independent optimization procedures: maximization of the visibility, the concurrence, and the predictability. For a specific maximization procedure, we study in detail how each of the complementary quantities behave, conditioned on the intensity of the coupling between q _B and the N qubits. We show that, if the coupling is sufficiently “strong,” independent of the maximization procedure, the concurrence tends to decay quickly. Interestingly enough, the behavior of the concurrence in this model is similar to the entanglement dynamics of a two qubit system subjected to a thermal reservoir, despite that we consider finite N. However, the visibility shows a different behavior: its maximization is more efficient for stronger coupling constants. Moreover, we investigate how the distinguishability, or the information stored in different parts of the system, is distributed for different couplings.     

More than six hundred new families of Newtonian periodic planar collisionless three-body orbits

The famous three-body problem can be traced back to Isaac Newton in the 1680 s. In the 300 years since this "three-body problem"was first recognized, only three families of periodic solutions had been found, until 2013 when ˇSuvakov and Dmitraˇsinovi′c [Phys.Rev. Lett. 110, 114301(2013)] made a breakthrough to numerically find 13 new distinct periodic orbits, which belong to 11 new families of Newtonian planar three-body problem with equal mass and zero angular momentum. In this paper, we numerically obtain 695 families of Newtonian periodic planar collisionless orbits of three-body system with equal mass and zero angular momentum in case of initial conditions with isosceles collinear configuration, including the well-known figure-eight family found by Moore in 1993, the 11 families found by ˇSuvakov and Dmitraˇsinovi′c in 2013, and more than 600 new families that have never been reported, to the best of our knowledge. With the definition of the average period T = T=Lf, where Lf is the length of the so-called "free group element", these 695 families suggest that there should exist the quasi Kepler's third law T* ≈ 2:433 ± 0:075 for the considered case, where T*= T|E|~(3/2) is the scale-invariant average period and E is its total kinetic and potential energy,respectively. The movies of these 695 periodic orbits in the real space and the corresponding close curves on the "shape sphere"can be found via the website: http://numericaltank.sjtu.edu.cn/three-body/three-body.htm.     

Hyperfine interactions in Sc<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Y<Subscript>x</Subscript>Fe<Subscript>2</Subscript> cubic Laves alloys

Effects of hybridization of 3d bands of iron with 3d bands of scandium and 4d bands of yttrium in Sc_1?xY_xFe₂ cubic Laves alloys (0≤_x≤1) are studied by the nuclear magnetic resonance method. The concentration dependences of the lattice parameters a, saturation magnetization σ, and hyperfine fields at the ⁵⁷Fe, ⁴⁵Sc, and ⁸⁹Y nuclei—as well as the ²⁷Al impurity nuclei, whose atoms substitute iron atoms in the lattices of these alloys—are measured. The “local” and “induced” contributions to hyperfine fields at the ⁵⁷Fe nuclei are separated and the magnetic moments at iron atoms are estimated. It is found that the hybridization effect leads to the formation of magnetic moments at Sc and Y atoms (whose direction is opposite to the direction of the magnetic moment at iron atoms) and is responsible for the ferrimagnetic structure in Sc_1?xY_xFe₂ alloys.     

On the Bosonic Atoms

We investigate the ground state properties of atoms, in which substitute fermions—electrons by bosons, namely, π^?-mesons. We perform some calculations in the frame of modified Hartree–Fock (HF) equation. The modification takes into account symmetry, instead of antisymmetry of the pair identical bosons wavefunction. The modified HF approach thus enhances (doubles) the effect of self-action for the boson case. Therefore, we accordingly modify the HF equations by eliminating the self-action terms “by hand.” The contribution of meson–meson and meson–nucleon non-Coulomb interaction is inessential at least for atoms with low and intermediate nuclear charge, which is our main subject. We found that the binding energy of pion negative ions A_π^-, pion atoms A_π, and the number of extra bound pions ΔN_π increases with the nuclear charge Z. In particular, for Xe ΔN_π = 4. As an example of a simple process with a pion atom, we consider photoionization that differs essentially from that for electron atoms. Namely, it is not monotonic decreasing from the threshold but has instead a prominent maximum above threshold. We study also elastic scattering of pions by pion atoms.     

Large negative numbers in number theory,thermodynamics, information theory,and human thermodynamics

We show how the abstract analytic number theory of Maier, Postnikov, and others can be extended to include negative numbers and apply this to thermodynamics, information theory, and human thermodynamics. In particular, we introduce a certain large number N ₀ on the “zero level” with a high multiplicity number q _i ? 1 related to the physical concept of gap in the spectrum. We introduce a general notion of “hole,” similar to the Dirac hole in physics, in the theory. We also consider analogs of thermodynamical notions in human thermodynamics, in particular, in connection with the role of the individual in history.