Wilsonian RG and redundant operators in nonrelativistic effective field theory

In a Wilsonian renormalization group (RG) analysis, redundant operators, which may be eliminated by using field redefinitions, emerge naturally. It is therefore important to include them. We consider a nonrelativistic effective theory (the so-called “pionless” nuclear effective field theory) as a concrete example and show that the off-shell amplitudes cannot be renormalized if the redundant operators are not included. The relation between the theories with and without such redundant operators is established in the low-energy expansion. We perform a Wilsonian RG analysis for the off-shell scattering amplitude in the theory with the redundant operator.     

A look at the generalized Darboux transformations for the quasinormal spectra in Schwarzschild black hole perturbation theory: Just how general should it be?

In this article we take a close look at three types of transformations usable in the Schwarzschild black hole perturbation theory: a standard (DT), a binary (BDT) and a generalized (GDT) Darboux transformations. In particular, we discuss the absolutely crucial property of isospectrality of the aforementioned transformations which guarantees that the quasinormal mode (QNM) spectra of potentials, related via the transformation, completely coincide. We demonstrate that, while the first two types of the Darboux transformations (DT and BDT) are indeed isospectral, the situation is wildly different for the GDT: it violates the isospectrality requirement and is therefore only valid for the solutions with just one fixed frequency. Furthermore, it is shown that although in this case the GDT does provide a relationship between two arbitrary potentials (a short-ranged and a long-ranged potentials relationship being just a trivial example), this relationship ends up being completely formal. Finally, we consider frequency-dependent potentials. A new generalization of the Darboux transformation is constructed for them and it is proven (on a concrete example) that such transformations are also not isospectral. In short, we demonstrate how a little, almost incorporeal flaw may become a major problem for an otherwise perfectly admirable goal of mathematical generalization.     

Statistical mechanics of colliding beams

The observed performance of electron-positron colliding-beam storage rings is poorly understood theoretically. The problem of a storage ring's behavior is a particular instance of statistical mechanics in an external environment that varies periodically with time, in the limit of weak—and not necessarily isotropic—friction and (additive) noise. As a practical starting point for a general theory of such problems, the following ansatz is suggested: Phase space submanifolds (tori) with fixed canonical actions are manifolds of approximately equal probability density. Such an approach is especially well suited to analysis of the long-time effects of nonlinear resonance on storage ring behavior. Formal consequences of this ansatz and some associated conceptual difficulties are discussed. These issues are considered from the standpoint of “two-time” analysis. An example of a concrete application, closely related to Kramers' analysis of noise-induced barrier crossing, is provided. This paper is meant to be self-contained, so that it can be understood by readers outside the storage-ring community.     

Spurious states in boson mapping

The possible occurrence of spurious states in boson mapping is discussed. By a concrete example it was found that the appearance of such states is a result of the choice of interactions.     

An example of quasiperiodic motion on T4

According to a theorem of Ruelle and Takens, the occurrence of quasiperiodic motion on T⁴ should be unlikely. Here with the help of numerical calculations, we give a concrete example for which such motion is shown to exist and survive under small perturbations.     

Pseudo-schwarzschild spherical accretion as a classical black hole analogue

We demonstrate that a spherical accretion onto astrophysical black holes, under the influence of Newtonian or various post-Newtonian pseudo-Schwarzschild gravitational potentials, may constitute a concrete example of classical analogue gravity naturally found in the Universe. We analytically calculate the corresponding analogue Hawking temperature as a function of the minimum number of physical parameters governing the accretion flow. We study both the polytropic and the isothermal accretion. We show that unlike in a general relativistic spherical accretion, analogue white hole solutions can never be obtained in such post-Newtonian systems. We also show that an isothermal spherical accretion is a remarkably simple example in which the only one information–the temperature of the fluid, is sufficient to completely describe an analogue gravity system. For both types of accretion, the analogue Hawking temperature may become higher than the usual Hawking temperature. However, the analogue Hawking temperature for accreting astrophysical black holes is considerably lower compared with the temperature of the accreting fluid.     

Concrete Hilbert spaces for quantum systems with infinitely many degrees of freedom

We demonstrate a method to describe quantum systems with infinitely many degrees of freedom in concrete Hilbert spaces, using the electromagnetic radiation field as a well-known example of such a system. Since our method is not only applicable to the case of countably many but even to the case of uncountably many degrees of freedom, there is no need for a finite quantization volume in radiation theory.     

Baryogenesis in a flat direction with neither baryon nor lepton charge

We present a new mechanism of spontaneous baryogenesis. Usually such mechanisms require a derivative coupling between a scalar field and baryon current. In our model, the scalar field instead derivatively couples to a current associated with some global symmetry U(1)(Q). In this case, baryogenesis is still possible provided that an interaction exists, which violates the baryon and U(1)(Q) symmetries simultaneously. As a concrete example, we discuss baryogenesis in a flat direction with neither baryon nor lepton charge.     

Gap bifurcations in nonlinear dynamical systems

We investigate the dynamics generated by a type of equation which is common to a variety of physical systems where the undesirable effects of a number of self-consistent nonlinear forces are balanced by an externally imposed controlling harmonic force. We show that the equation presents a new sequence of bifurcations where periodic orbits are created and destroyed in such a nonsimultaneous way that may leave the appropriate phase-space occasionally empty of fundamental harmonic orbits and confined trajectories. A generic analytical model is developed and compared with a concrete physical example.     

Fundamental study on ultrasonic measurement system to detect penetration of boulders using cepstrum analysis

Generally, ultrasonic method and an elastic impact wave method are mentioned as examples representing the nondestructive test method. However, the ultrasonic method is known for the investigation of shallow depth becoming very shallow because of its small input. And the elastic impact wave method uses for example, a hammer for the discrimination of the reflection wave produced by minute cracks existing in the object, which is difficult. Theoretically, if it becomes possible to input the vibration of an ultrasonic domain into artificial structures such as a concrete and a boulder with strong amplitude, deeper investigation of depth and higher precision will be attained. The authors have developed a new ultrasonic method by using ultrasonic wave of the chirp signal, using the input of this system and using auto correlation and cepstrum as the analysis methods. In this paper, the experiment is classified into Pattern 1 and Pattern 2. In Pattern 1, the experiment of receiving the reflection wave was carried out using the concrete block with a width of 1300 mm and the down chirp signal from 50 kHz to 40 kHz. In Pattern 1, a reflection wave was clearly detected, and the length of the concrete block was calculated using auto correlation analysis, and was obtained as 1311.76 mm. In Pattern 2, the experiment of receiving the reflection wave was carried out using the same concrete block and the down chirp signal from 150 kHz to 130 kHz. In Pattern 2, the direct wave and the reflection wave were mixed, therefore it was not possible to presume the length from the obtained waveform. So cepstrum analysis method was used, and the traveling time of the reflection wave was obtained. In this result, the length of the concrete block was given as 1278.25 mm.     

Electron-nuclear dynamics in a quantum dot under nonunitary electron control

We introduce a method for solving the problem of an externally controlled electron spin in a quantum dot interacting with host nuclei via the hyperfine interaction. Our method accounts for generalized (nonunitary) evolution effected by external controls and the environment, such as coherent lasers combined with spontaneous emission. As a concrete example, we develop the microscopic theory of the dynamics of nuclear-induced frequency focusing as first measured in Science 317, 1896 (2007); we find that the nuclear relaxation rates are several orders of magnitude faster than those quoted in that work.     

The inverse scattering method in an invariant form with respect to internal symmetry algebra representations

By the example of the sine—Gordon equation, we develop a technique for obtaining soliton solutions. This procedure is not connected with a concrete matrix realization of the Lax pair operators but it directly appeals to the properties of internal symmetry spectrum of the corresponding equations.     

Remarks on Concrete Orthomodular Lattices

An orthomodular lattice (OML) is called concrete if it is isomorphic to a collection of subsets of a set with partial ordering given by set inclusion, orthocomplementation given by set complementation, and finite orthogonal joins given by disjoint unions. Interesting examples of concrete OMLs are obtained by applying Kalmbach's construction K(L) to an arbitrary bounded lattice L. This note provides several results regarding Kalmbach's construction, concrete OMLs, and the relationship between the notions. First, we provide order-theoretic and categorical characterizations of the OML K(L) in terms of the bounded lattice L. Second, we provide an identity satisfied by each OML K(L), but not valid in every concrete OML. This shows that the class of OMLs of the form K(L) do not generate the variety of all concrete OMLs. Finally, we show that every concrete OML can be embedded into a concrete OML in which every element is a join of two or fewer atoms.     

变焦凸轮曲线的优化设计

本文以２．５￣（×）小变焦照相物镜为例。推导了变焦凸轮曲线斜率之间的关系式，以及如何选取变焦凸曲线压力角的值域。并介绍了具体的设计步骤、方法。     

Groundstatable fermionic wavefunctions and their associated many-body Hamiltonians

In the vast majority of many-body problems, it is the kinetic energy part of the Hamiltonian that is best known microscopically, and it is the detailed form of the interactions between the particles, the potential energy term, that is harder to determine from first principles. An example is the case of high temperature superconductors: while a tight-binding model captures the kinetic term, it is not clear that there is superconductivity with only an onsite repulsion and, thus, that the problem is accurately described by the Hubbard model alone. Here we pose the question of whether, once the kinetic energy is fixed, a candidate ground state is groundstatable or not. The easiness to answer this question is strongly related to the presence or the absence of a sign problem in the system. When groundstatability is satisfied, it is simple to obtain the potential energy that will lead to such a ground state. As a concrete case study, we apply these ideas to different fermionic wavefunctions with superconductive or spin-density wave correlations and we also study the influence of Jastrow factors. The kinetic energy considered is a simple nearest neighbor hopping term.     

Radiation shielding of concrete containing zeolite

The linear attenuation coefficient (μ, cm^?1) for concrete containing zeolite as an aggregate in different concentrations (0%, 10%, 30% and 50%) has been measured and the results are compared with calculation. The linear attenuation coefficient, measured with four concrete blocks, decreased with increasing zeolite concentration. It is concluded that the addition of zeolite as an aggregate in concrete is not an alternative option to be used for the purposes of radiation shielding.     

Abstract Polymer Models with General Pair Interactions

A convergence criterion of cluster expansion is presented in the case of an abstract polymer system with general pair interactions (i.e. not necessarily hard core or repulsive). As a concrete example, the low temperature disordered phase of the BEG model with infinite range interactions, decaying polynomially as 1/r ^d+λ with λ>0, is studied.     

Current filamentation in bistable semiconductor systems with two global constraints

The recent advent of integral circuits combining bistable semiconductor structures with a spatially distributed driving gate has opened up new possibilities for development of self-organizing active media with controllable properties which are of potential interest for neural computer technology. In the present paper the theoretical study of instabilities and current filamentation in such systems is advanced. The consideration is based on a generalized model which treats a gate driven bistable system as an extended active medium with two global constraints related to the main and gate circuits, respectively. It is shown that the presence of a spatially distributed controlling subsystem — a driving gate — leads to a new effect of transversal nonlocal coupling between system elements which acts dramatically upon the system behaviour. The results obtained in a general form regardless of the concrete semiconductor structure design are illustrated by the example of a gate-driven pnpn-structure.     

Deformations of Quantum Field Theories on Spacetimes with Killing Vector Fields

The recent construction and analysis of deformations of quantum field theories by warped convolutions is extended to a class of curved spacetimes. These spacetimes carry a family of wedge-like regions which share the essential causal properties of the Poincaré transforms of the Rindler wedge in Minkowski space. In the setting of deformed quantum field theories, they play the role of typical localization regions of quantum fields and observables. As a concrete example of such a procedure, the deformation of the free Dirac field is studied.     

Prediction of noise changes due to traffic speed control

The effects of vehicle speed variation on road traffic noise are analyzed. The steady speed motion is replaced by deceleration, cruise, and acceleration. Because of a relatively loud acceleration noise, such a speed variation results not only in the noise decrease zones, but in the noise increase zones as well. The location of these zones depends slightly upon the ground covering (grass, concrete, etc.). Conversely, their boundaries change dramatically with the parameters describing noise emission during deceleration, cruise, and acceleration. For example, the Japanese and Polish models of noise emission have been applied. The critical length L(*) of the cruise segment of the road is introduced: for L>L(*) the sound energy decline (due to speed reduction) compensates the sound energy growth (due to acceleration). The results obtained could be useful for road administrators.