37191194
Instantons and the spectrum of Bloch electrons in a magnetic field.
A semiclassical path-integral treatment of the spectrum of a charged particle moving in a two- dimensional periodic potential in the presence of a transverse magnetic field is presented. Complex instanton solutions to the Euclidean equations of motion are identified, and it is shown that the dilute-instanton-gas sum reproduces features of the spectrum studied by previous authors. Compar- ison of the path-integral results to a perturbative calculation of the splitting of the lowest Landau level is used to relate the self-similar nature of the spectrum to a type of duality in the parameter a, the number of flux quanta per unit cell. As a byproduct of the instanton calculation the generating functional for a sum over lattice paths of given length and algebraic area modulo a fundamental area determined by the magnetic field is evaluated. The quantum-mechanical system of an electron moving in a two-dimensional periodic potential in a magnetic field transverse to the plane of motion has attracted a great deal of interest. It provided an early example of a physical system whose properties depend crucially on the rationality or irrationality of a physical parameter, in this case the ratio of the flux through a unit cell of the lattice to the flux quantum, a=BR/@o with + =Oh /ce and 2 the area of a unit cell. When this ratio is irrational it also provides a simple model of an incommensurate system with the competing periodicities being the lattice periodi- city and a periodicity determined by a lattice whose unit cell encloses one flux quantum. Recently it has attracted renewed interest because of its connections to the quan- tized Hall effect' and to the mean-field theory of the Hub- bard model. Our own interest in this model was trig- gered by similarities between instantons in this model and instantons in gauge theory in 2+1 dimensions with a Chem-Simons term. In both cases the Euclidean func- tional integral becomes complex and one must search for complex saddle points. In addition, the T violating term in each case modifies the behavior of the solutions at large distances, making perturbation theory suspect. This problem has been studied using a variety of tech- niques in different physical regimes. Although instanton techniques have been used to study simpler problems in- volving tunneling in the presence of a magnetic field, ' to our knowledge they have not been applied to this general class of problems involving a magnetic field and a period- ic potential. We will try to show that path-integral tech- niques can be successfully applied to this problem and that they shed some new light on the intricate recursive structure of the spectrum. In the process of working out the instanton sum in this theory we have had to evaluate a sum over lattice paths of the form All 2D lattice paths w&th fixed endpoints
8898134
Localized tachyons and RG flows
We study condensation of closed string tachyons living on defects, such as orbifold fixed planes and Neveu-Schwarz fivebranes. We argue that the high energy density of localized states decreases in the process of condensation of such tachyons. In some cases this means that $c_{eff}$ decreases along the flow; in others, $c_{eff}$ remains constant and the decreasing quantity is a closed string analog, $g_{cl}$, of the ``boundary entropy'' of D-branes. We discuss the non-supersymmetric orbifolds $C/Z_n$ and $C^2/Z_n$. In the first case tachyon condensation decreases $n$ and in some cases connects type II and type 0 vacua. In the second case non-singular orbifolds are related by tachyon condensation to both singular and non-singular ones. We verify that $g_{cl}$ decreases in flows between non-singular orbifolds. The main tools in the analysis are the structure of the chiral ring of the perturbed theory, the geometry of the resolved orbifold singularities, and the throat description of singular conformal field theories.
12124707
Current directions in string theory and abstract supersymmetry
I discuss some current thoughts on how low-energy measurements and consistency constrain theories at high energies with emphasis on string theory. I also discuss some recent work on the dynamics of supersymmetric gauge theories.
117239200
Conformal Field Theory and String Compactification
120980643
Open strings on orbifolds
Abstract We consider propagation of type I SO(32) superstrings on orbifolds. It is shown that anomaly cancellation requires the existence of “twisted” open strings and we determine the Chan-Paton factors for these strings in a simple example.
42736184
Nonrenormalization of the superstring tension.
It is argued that the superstring tension is not renormalized in perturbation theory for vacua which preserve N= 1 spacetime supersymmetry. Some implications of this result for macroscopic superstrings are discussed, as well as some analogies between macroscopic superstrings and solitons in supersymmetric theories.
1166257
Peripheral reactions induced by a 2.1-GeV/nucleon 12C beam on a C target using a simple combinatorial model.
Recently acquired data on peripheral reactions induced by a /sup 12/C beam at 2.1 GeV/nucleon on a C target have been used to create a distribution of exclusive yields (''mass patterns'') in which the charge of detected fragments is ignored and the data supplemented by (presumed) missing nucleons. A simple multinomial expression using probabilities obtained from inclusive mass yields gives a satisfactory account of the revised data.
39396881
Measurement of the electric polarizability of the neutron.
38612086
Neutron resonance parameters and thermal-neutron capture by 43Ca.
Neutron transmission measurements have been carried out on a small sample (205.9 mg) of CaCO[sub 3] with a [sup 43]Ca enrichment of 49.1%. The parameters (spins and neutron widths) of eight resonances below the neutron energy of 20 keV have been determined. This information was combined with a previously measured thermal-neutron coherent scattering length to deduce the separate scattering lengths for the two spin states present in [ital s]-wave scattering. These values were used to calculate the direct (potential + valence) capture cross sections of the primary electric-dipole gamma transitions in [sup 44]Ca using optical-model potentials with physically realistic parameters. For those states below 6.2 MeV for which the [ital l]=1 ([ital d],[ital p]) spectroscopic factors are known, the experimental cross sections are consistent with our current understanding of the direct and compound-nuclear capture processes. The processes leading to states above 6.2 MeV require further experimental and theoretical studies.
12086987
Geodesics in Kasner universes.
Recently, Kasner model universes of various dimensionalities have been explored to see if they could be used in the manner of Kaluza-Klein models to provide the additional unobservable dimensions called for in current elementary-particle models. These discussions have focused narrowly on the number of dimensions and the manner in which those dimensions in excess of the observable four of spacetime behave. This paper discusses some features of Kasner models which ultimately should be considered if these models are to provide a useful arena for studying elementary particles. In particular, geodesics are examined in detail. It is found that there may be a limit to the distance traveled by timelike particles, that spacelike geodesics are limited in their temporal extent, and that for null geodesics in expanding directions the coordinate speed approaches zero.
37326897
Momentum distribution of projectile fragments and nuclear shape.
When one or two neutrons are lost in a collision between a projectile with a diffuse neutron-rich surface and a target nucleus, the transverse momentum distribution of the fragments thus produced can be fit with a double Gaussian curve in which a narrow component is superimposed on a much broader one. It is shown that this phenomenon is also observed for fragments from the normal'' projectile [sup 12]C. A density-dependent nucleon Fermi momentum and fragment recoil with the momentum of the lost nucleon give good agreement with experiment. The two Gaussian components do not require the presence near the nuclear surface of nucleons with two widely different binding energies, as often supposed.