Problems with Initial- and Final-State Interactions in Deep-Inelastic Scattering

Although there exists a vast literature devoted to the theory of deep-inelastic scattering, the restrictions imposed on the (electromagnetic or weak) current operator by its commutation relations with the representation operators of the Poincaré group and locality have not been considered. We argue that there is a problem with the current operator, leading to the standard parton-model results, satisfying these restrictions. At the same time, there exist models where the correct commutation relations and locality are satisfied but the initial- and final-state interactions of the struck quark with the remnants of the target cannot be neglected even in the Bjorken limit. Received June 13, 1997; revised January 19, 1998; accepted for publication January 27, 1998     

Relations between neutrino and antineutrino locality theorems as tests of Lorentz structure of the neutral weak interaction

Assuming lepton locality and Born approximation, crossing relates the locality theorems for corresponding neutrino and antineutrino scattering if only the vector and axial-vector covariants occur in the neutral weak interaction. In general, these crossing relations are violated if other covariants are present. Various crossing relations can help to pin down the parity and charge-conjugation properties of the other covariants (if present).     

J-matrix method of scattering in one dimension: The nonrelativistic theory

We formulate a theory of nonrelativistic scattering in one dimension based on the J-matrix method. The scattering potential is assumed to have a finite range such that it is well represented by its matrix elements in a finite subset of a basis that supports a tridiagonal matrix representation for the reference wave operator. Contrary to our expectation, the 1D formulation reveals a rich and highly nontrivial structure compared to the 3D formulation. Examples are given to demonstrate the utility and accuracy of the method. It is hoped that this formulation constitutes a viable alternative to the classical treatment of 1D scattering problem and that it will help unveil new and interesting applications.     

Adiabatic behavior of sine-Gordon solitons in the presence of perturbations

The behavior of sine-Gordon solitons in the presence of weak perturbations is considered. The procedure is based on the exact inverse scattering solution of the unperturbed sine-Gordon equation. Accounting for perturbations such as those arising from impurities, external forces as well damping and spatially inhomogeneous frequencies the corresponding perturbed operator equation can be solved by the Green's function technique if one expands the Green's operator in terms of a set of biorthogonal eigenfunctions. Ordinary linear differential equations prescribing the time evolution of the scattering data are obtained. Instead of solving the inverse scattering problem completely the adiabatic assumption is then used anticipating the result that solitons maintain their integrity to a high degree. Explicit solutions for the one-soliton dynamics are presented.Work supported by the Deutsche Forschungsgemeinschaft through the Sonderforschungsbereich Nr. 162 Plasmaphysik Bochum/Jülich     

Optical detection of fractional particle number in an atomic Fermi-Dirac gas

We study theoretically a Fermi-Dirac atomic gas in a one-dimensional optical lattice coupled to a coherent electromagnetic field with a topologically nontrivial soliton phase profile. We argue that the resulting fractional eigenvalues of the particle number operator can be detected via light scattering. This could be a truly quantum mechanical measurement of particle number fractionalization in a dilute atomic gas.     

Projection operator approach to the thermodynamic formalism of dynamical systems

An analytical perturbative treatment of characteristic exponents describing the fluctuations of temporal coarse-grained quantities in the context of nonlinear dynamical systems is proposed. It is based on the analysis of the resolvent of the corresponding transfer operator by a projection operator method similar to those used in statistical mechanics. Two different approximation schemes are presented and tested for the case of an exactly solvable but nontrivial model system.     

Quantum transport in topological semimetals under magnetic fields

Topological semimetals are three-dimensional topological states of matter, in which the conduction and valence bands touch at a finite number of points, i.e., the Weyl nodes. Topological semimetals host paired monopoles and antimonopoles of Berry curvature at the Weyl nodes and topologically protected Fermi arcs at certain surfaces. We review our recent works on quantum transport in topological semimetals, according to the strength of the magnetic field. At weak magnetic fields, there are competitions between the positive magnetoresistivity induced by the weak anti-localization effect and negative magnetoresistivity related to the nontrivial Berry curvature. We propose a fitting formula for the magnetoconductivity of the weak anti-localization. We expect that the weak localization may be induced by inter-valley effects and interaction effect, and occur in double-Weyl semimetals. For the negative magnetoresistance induced by the nontrivial Berry curvature in topological semimetals, we show the dependence of the negative magnetoresistance on the carrier density. At strong magnetic fields, specifically, in the quantum limit, the magnetoconductivity depends on the type and range of the scattering potential of disorder. The high-field positive magnetoconductivity may not be a compelling signature of the chiral anomaly. For long-range Gaussian scattering potential and half filling, the magnetoconductivity can be linear in the quantum limit. A minimal conductivity is found at the Weyl nodes although the density of states vanishes there.     

Reduced Maxwell-Bloch equations with anisotropic dipole momentum

We develop the inverse scattering transform for the recently found integrable system of reduced Maxwell-Bloch equations with two components of polarization and with an anisotropic dipole momentum. The model describes few-cycle pulses of optical or other field propagations. We find that the existence of a nontrivial group of symmetry of the corresponding Lax pair leads to a particular form of the inverse scattering transform equations. We show that solutions can be expressed in terms of the solution of a matrix Riemann-Hilbert problem formulated for the complex plane with a nontrivial group of automorphisms.     

Stripping to analog resonances

Stripping to analog resonances is studied by expressing the DWBA cross section in terms of the resolvent operator appropriate to the system composed of the proton and the target. The resolvent operator is decomposed, by means of the Feshbach projection operator technique, into parts corresponding to the entrance channel, the analog state and the compound states. The approximation scheme is similar to that used in our previous treatment of proton scattering at an analog resonance. The complex proton form factor depends on the Green function satisfying the inhomogeneous Schrödinger equation corresponding to elastic scattering and on the Coulomb potential generated by the target. The method is applied to (³He, d) stripping to analogs in ^{93, 95, 97}Tc.     

Quantum Flows as Markovian Limit of Emission,Absorption and Scattering Interactions

We consider a Markovian approximation, of weak coupling type, to an open system perturbation involving emission, absorption and scattering by reservoir quanta. The result is the general form for a quantum stochastic flow driven by creation, annihilation and gauge processes. A weak matrix limit is established for the convergence of the interaction-picture unitary to a unitary, adapted quantum stochastic process and of the Heisenberg dynamics to the corresponding quantum stochastic flow: the convergence strategy is similar to the quantum functional central limits introduced by Accardi, Frigerio and Lu [1]. The principal terms in the Dyson series expansions are identified and re-summed after the limit to obtain explicit quantum stochastic differential equations with renormalized coefficients. An extension of the Pulé inequalities [2] allows uniform estimates for the Dyson series expansion for both the unitary operator and the Heisenberg evolution to be obtained.     

Quantum walks with an anisotropic coin II: scattering theory

We perform the scattering analysis of the evolution operator of quantum walks with an anisotropic coin, and we prove a weak limit theorem for their asymptotic velocity. The quantum walks that we consider include one-defect models, two-phase quantum walks, and topological phase quantum walks as special cases. Our analysis is based on an abstract framework for the scattering theory of unitary operators in a two-Hilbert spaces setting, which is of independent interest.

     

The Seiberg-Witten Map and Topology

The mapping of topologically nontrivial gauge transformations in noncommutative gauge theory to corresponding commutative ones is investigated via the operator form of the Seiberg-Witten map. The role of the gauge transformation part of the map is analyzed. Chern-Simons actions are examined and the correspondence to their commutative counterparts is clarified.     

Stability of quantum states of finite macroscopic systems against classical noises,perturbations from environments,and local measurements

We study the stability of quantum states of macroscopic systems of finite volume V. By using both the locality and huge degrees of freedom, we show the following: (i) If square fluctuation of every additive operator is O(V) or less for a pure state, then it is not fragile for any weak classical noises or weak perturbations from environments. (ii) If square fluctuation of some additive operator is O(V2) for a pure state, then it is fragile for some of these. (iii) If a state, pure or mixed, has the "cluster property," then it is stable against local measurements, and vice versa. Among many applications, we discuss the mechanism of symmetry-breaking in finite systems.     

Tuning magnetotransport through a magnetic kink crystal in a chiral helimagnet

We consider magnetotransport properties in a conducting chiral helimagnet, where the magnetic kink crystal (MKC) is formed under weak magnetic field applied perpendicular to the helical axis. The MKC behaves as a magnetic superlattice potential and results in Bragg scattering of conduction electrons. Tuning of the weak magnetic field enables us to control the size of the superlattice Brillouin zone and gives rise to a series of divergent resistivity anomalies originating from resonant Bragg scatterings. We discuss as well a nontrivial magnetic structure in the resonant states realized in the subsystem of the itinerant electrons.     

Theory of cyclotron resonance lineshape for electron-phonon systems in two coupling schemes

A theory of cyclotron resonance lineshape due to electron-phonon interactions is presented on the basis of the projection operator method introduced by Argyres and Sigel. In addition to the extremely weak coupling scheme dealt with earlier, the moderately weak coupling scheme is included in the theory. The lineshape functions derived in the two schemes are similar to Lodder-Fujita's formula, and are reduced to Kawabata's formula in the elastic scattering approximation.     

Liouville field theory revisited: Zero modes andS-matrix element

A new analysis of the intrinsic structure of Liouville field theory (LFT) is presented. We prove that LFT displays a zero mode if its Laplacian is defined in terms of the square of the corresponding Dirac operator. Further, by interpreting the spacetime asSO(2,1)/SO(1, 1) (analogous toSO(3, 2)/SO(3, 1)) we present, arguments which support the nontrivial approximativeS-matrix element we derived in [2]. Some connected questions are also discussed.     

Optical orientation of Mn2+ ions in GaAs in weak longitudinal magnetic fields

We report on optical orientation of Mn2+ ions in bulk GaAs subject to weak longitudinal magnetic fields (B≤100 mT). A manganese spin polarization of 25% is directly evaluated by using spin-flip Raman scattering. The dynamical Mn2+ polarization occurs due to the s-d exchange interaction with optically oriented conduction band electrons. Time-resolved photoluminescence reveals a nontrivial electron spin dynamics, where the oriented Mn2+ ions tend to stabilize the electron spins.     

On sufficient conditions of locality for hierarchies of symmetries of evolution systems

We present sufficient conditions ensuring the locality of hierarchies of symmetries generated by repeated commutation of master symmetry with a seed symmetry. These conditions are applicable to a large class of (1+1)-dimensional evolution systems. Our results can also be used for proving that the time-independent part of a suitable linear-in-time symmetry is a nontrivial master symmetry and hence the system in question has infinitely many symmetries and is integrable.     

Bell’s theory with no locality assumption

We prove versions of the Bell and the GHZ theorems that do not assume locality but only the effect after cause principle (EACP) according to which for any Lorentz observer the value of an observable cannot change because of an event that happens after the observable is measured. We show that the EACP is strictly weaker than locality. As a consequence of our results, locality cannot be considered as the common cause of the contradictions obtained in all versions of Bell’s theory. All versions of Bell’s theorem assume weak realism according to which the value of an observable is well defined whenever the measurement could be made and some measurement is made. As a consequence of our results, weak realism becomes the only hypothesis common to the contradictions obtained in all versions of Bell’s theory. Usually, one avoids these contradictions by assuming non-locality; this would not help in our case since we do not assume locality. This work indicates that it is weak realism, not locality, that needs to be negated to avoid contradictions in microscopic physics, at least if one refuses as false the de Broglie-Bohm hidden variable theory because of its essential violation of Lorentz invariance.     

Are scattering amplitudes dual to super Wilson loops?

The MHV scattering amplitudes in planar N=4 SYM are dual to bosonic light-like Wilson loops. We explore various proposals for extending this duality to generic non-MHV amplitudes. The corresponding dual object should have the same symmetries as the scattering amplitudes and be invariant to all loops under the chiral half of the N=4 superconformal symmetry. We analyze the recently introduced supersymmetric extensions of the light-like Wilson loop (formulated in Minkowski space-time) and demonstrate that they have the required symmetry properties at the classical level only, up to terms proportional to field equations of motion. At the quantum level, due to the specific light-cone singularities of the Wilson loop, the equations of motion produce a nontrivial finite contribution which breaks some of the classical symmetries. As a result, the quantum corrections violate the chiral supersymmetry already at one loop, thus invalidating the conjectured duality between Wilson loops and non-MHV scattering amplitudes. We compute the corresponding anomaly to one loop and solve the supersymmetric Ward identity to find the complete expression for the rectangular Wilson loop at leading order in the coupling constant. We also demonstrate that this result is consistent with conformal Ward identities by independently evaluating corresponding one-loop conformal anomaly.