Development of the Federal Law of Gambling

The Commission on the Review of the National Policy Toward Gambling, believing that the States should have the primary responsibility for determining what forms of gambling may legally take place within their borders, recently suggested that the federal government should prevent interference by one State with the gambling policies of another, and should act to protect identifiable national interests. Although this broad recommendation reinforces the role the federal government has traditionally played in regulating gambling, the Commission also proposed specific amendments to the cur- rent federal gambling laws. Should Congress act upon the Commission\u27s report or otherwise attempt a comprehensive review of federal gambling policy–such legislation, S. 1437, has already passed the Senate–its members ought to bring to their task a firm grasp of what the federal gambling law is, how that law developed, and what policies underlie it. This Article seeks to shed light on each of these questions

Measuring the Impact of the COVID-19 Lockdown on Crime in a Medium-Sized City in China

Objectives: The study examines the variation in the daily incidence of eight acquisitive crimes: automobile theft, electromobile theft, motorcycle theft, bicycle theft, theft from automobiles, pickpocketing, residential burglary, and cyber-fraud before the lockdown and the duration of the lockdown for a medium-sized city in China. Methods: Regression discontinuity in time (RDiT) models are used to test the effect of the lockdown measures on crime by examining the daily variation of raw counts and rate. Results: It is indicated that in contrast to numerous violent crime categories such as domestic violence where findings have repeatedly found increases during the COVID-19 pandemic, acquisitive crimes in this city were reduced during the lockdown period for all categories, while “cyber-fraud” was found more resilient in the sense that its decrease was not as salient as for most other crime types, possibly due to people’s use of the internet during the lockdown period. Conclusions: The findings provide further support to opportunity theories of crime that are contingent upon the need for a motivated offender to identify a suitable target in physical space

Scalar and vector Keldysh models in the time domain

The exactly solvable Keldysh model of disordered electron system in a random scattering field with extremely long correlation length is converted to the time-dependent model with extremely long relaxation. The dynamical problem is solved for the ensemble of two-level systems (TLS) with fluctuating well depths having the discrete Z_2 symmetry. It is shown also that the symmetric TLS with fluctuating barrier transparency may be described in terms of the planar Keldysh model with dime-dependent random planar rotations in xy plane having continuous SO(2) symmetry. The case of simultaneous fluctuations of the well depth and barrier transparency is subject to non-abelian algebra. Application of this model to description of dynamic fluctuations in quantum dots and optical lattices is discussed.Comment: 6 pages, 5 eps figures. Extended version of the paper to be published in JETP Lett 89 (2009

Finite Size Corrections for the Pairing Hamiltonian

We study the effects of superconducting pairing in small metallic grains. We show that in the limit of large Thouless conductance one can explicitly determine the low energy spectrum of the problem as an expansion in the inverse number of electrons on the grain. The expansion is based on the formal exact solution of the Richardson model. We use this expansion to calculate finite size corrections to the ground state energy, Matveev-Larkin parameter, and excitation energies.Comment: 22 pages, 1 figur

Ground state spin and Coulomb blockade peak motion in chaotic quantum dots

We investigate experimentally and theoretically the behavior of Coulomb blockade (CB) peaks in a magnetic field that couples principally to the ground-state spin (rather than the orbital moment) of a chaotic quantum dot. In the first part, we discuss numerically observed features in the magnetic field dependence of CB peak and spacings that unambiguously identify changes in spin S of each ground state for successive numbers of electrons on the dot, N. We next evaluate the probability that the ground state of the dot has a particular spin S, as a function of the exchange strength, J, and external magnetic field, B. In the second part, we describe recent experiments on gate-defined GaAs quantum dots in which Coulomb peak motion and spacing are measured as a function of in-plane magnetic field, allowing changes in spin between N and N+1 electron ground states to be inferred.Comment: To appear in Proceedings of the Nobel Symposium 2000 (Physica Scripta

Quantum dots with two electrons: Singlet-triplet transitions

The magnetic character of the ground-state of two electrons on a double quantum dot, connected in series to left and right single-channel leads, is considered. By solving exactly for the spectrum of the two interacting electrons, it is found that the coupling to the continuum of propagating states on the leads, in conjunction with the electron-electron interactions, may result in a delocalization of the bound state of the two electrons. This, in turn, reduces significantly the range of the Coulomb interaction parameters over which singlet-triplet transitions can be realized. It is also found that the coupling to the leads favors the singlet ground-state.Comment: 8 pages, submitted to Phys. Rev.

A nearly closed ballistic billiard with random boundary transmission

A variety of mesoscopic systems can be represented as a billiard with a random coupling to the exterior at the boundary. Examples include quantum dots with multiple leads, quantum corrals with different kinds of atoms forming the boundary, and optical cavities with random surface refractive index. The specific example we study is a circular (integrable) billiard with no internal impurities weakly coupled to the exterior by a large number of leads with one channel open in each lead. We construct a supersymmetric nonlinear $\sigma$-model by averaging over the random coupling strengths between bound states and channels. The resulting theory can be used to evaluate the statistical properties of any physically measurable quantity in a billiard. As an illustration, we present results for the local density of states.Comment: 5 pages, 1 figur

Role of a parallel magnetic field in two dimensional disordered clusters containing a few correlated electrons

An ensemble of 2d disordered clusters with a few electrons is studied as a function of the Coulomb energy to kinetic energy ratio r_s. Between the Fermi system (small r_s) and the Wigner molecule (large r_s), an interaction induced delocalization of the ground state takes place which is suppressed when the spins are aligned by a parallel magnetic field. Our results confirm the existence of an intermediate regime where the Wigner antiferromagnetism defavors the Stoner ferromagnetism and where the enhancement of the Lande g factor observed in dilute electron systems is reproduced.Comment: 4 pages, 3 figure

Nonequilibrium theory of Coulomb blockade in open quantum dots

We develop a non-equilibrium theory to describe weak Coulomb blockade effects in open quantum dots. Working within the bosonized description of electrons in the point contacts, we expose deficiencies in earlier applications of this method, and address them using a 1/N expansion in the inverse number of channels. At leading order this yields the self-consistent potential for the charging interaction. Coulomb blockade effects arise as quantum corrections to transport at the next order. Our approach unifies the phase functional and bosonization approaches to the problem, as well as providing a simple picture for the conductance corrections in terms of renormalization of the dot's elastic scattering matrix, which is obtained also by elementary perturbation theory. For the case of ideal contacts, a symmetry argument immediately allows us to conclude that interactions give no signature in the averaged conductance. Non-equilibrium applications to the pumped current in a quantum pump are worked out in detail.Comment: Published versio