Leonid Lerner

University of Wisconsin - Milwaukee | UWM · Department of Chemistry and Biochemistry

The evolution of a system subject to measurement is restricted to Zeno subspaces of the measurement Hamiltonian in the limit of strong measurements k in a phenomenon known as the quantum Zeno effect (QZE). As the limit constrains QZE to the lowest orders of perturbation in 1/k, we derive general expressions for the maximum probability leakage from...

Measurement lies at the heart of quantum theory, and introductory textbooks in quantum mechanics cover the measurement problem in topics such as the Schrödinger's cat thought experiment, the EPR problem, and the quantum Zeno effect (QZE). In this article we present a new treatment of the QZE suitable for undergraduate students, for the case of a pa...

We present a simplified analysis suitable for a beginners' course in quantum mechanics of a recently presented model of positional decoherence in a gas of scatterers. As such, no reference is made to the density matrix formalism, many body theory, or even operator algebra. We only make use of the properties of quantum states and the position and mo...

We present for the first time analytic solutions for the nonlinear dynamics of a Wien bridge oscillator stabilised by three common methods: an incandescent lamp, signal diodes, and the field effect transistor. The results can be used to optimise oscillator design, and agree well with measurements. The effect of operational amplifier marginal nonlin...

Simple apparatus is developed, providing undergraduate students with a solid understanding of Fourier Transform Infrared (FTIR) spectroscopy in a hands on experiment. Apart from its application to measuring the mid-IR spectra of organic molecules, the experiment introduces several techniques with wide applicability in physics, including interferome...

The reaction of nitric oxide with oxy-myoglobin (oxyMb) to form ferric myoglobin (metMb) and nitrate, and the metMb-catalyzed isomerization of peroxynitrite to nitrate, have long been assumed to proceed via the same iron-bound peroxynitrite intermediate (metMb(OONO)). More recent research showed that the metMb-catalyzed isomerization of peroxynitri...

The integral form of Ampere's law applied to an infinitely long solenoid gives a good first approximation to the magnetic field of finite air-cored solenoids with length L to width w ratios (aspect ratios) significantly greater than 1. It is less well known that this approximation requires much larger aspect ratios to be applicable to solenoids who...

Galois theory is developed using elementary polynomial and group algebra. The method follows closely the original prescription of Galois, and has the benefit of making the theory accessible to a wide audience. The theory is illustrated by a solution in radicals of lower degree polynomials, and the standard result of the insolubility in radicals of...

The structure of a colored intermediate commonly formed in the oxidation of p-aminophenol at low pH is established by analysis of H NMR and UV/vis spectra, kinetics, and molecular modeling, following a new method for synthesizing the dye in high concentrations. The chromogen is shown to consist of two compounds with absorption maxima at 540-560 and...

We use many-body quantum theory to calculate the decay rate of a quantum state in a junction barrier undergoing Coulombic interaction with a tunneling current flowing through the junction. The tunneling current effectively measures the junction state occupation, and we find the measurement generaly acts to increase the decay rate in the limit of sm...

We calculate the rate for stimulated transitions with photon emission between two trapped bosonic gases in thermal equilibrium, for both the box and harmonic oscillator traps in the weak interaction limit. It is shown that stimulation has a peak at a temperature characteristic of the kinetic energy of final state bosons. The problem of nuclear γ- a...

The Weisskopf–Wigner solution of a two-level decay is extended to a simple three-level model. We calculate the influence of daughter state decay on the decay rate of the initial state. We show that this effect is dependent on the exact form of the spectral density functions, precluding a general quantum Zeno effect.

A derivation of the Dirac and Weyl equations is presented which does not assume a first-order time derivative but instead is based on the relativistic transformation of spinors in ordinary quantum mechanics. The Dirac and Weyl 4-currents, the transformation properties of the Dirac and Weyl spinors, and the Lorentz covariance of the resulting equati...

The problem of the deflection of light in a medium with varying refractive index is applied to the motion of light in a weak Schwarzschild gravitational field. In contrast to the standard deviation, the present method is physically transparent, providing a clear reason for the factor-of-2 deviation of the general relativistic result from that of th...

A simple method is presented for deriving the Schwarzschild metric in the weak-field limit of the field equations of general relativity. The solution is derived in spherical coordinates natural to the problem, but to which standard weak-field theory does not apply. It is shown that the partial differential equations encountered in the exact analysi...

We present what is to our knowledge the first general theory for describing interacting well-separated gray spatial solitons, propagating in an arbitrary self-defocusing nonlinearity. It reveals why two dark solitons will in general repel, becoming less dark as they propagate. The results are illustrated with analytic expressions for the Kerr and t...

It is demonstrated that bent dielectric waveguides can convert incident radiation into guided-mode power. A beam-propagation method simulation of the effect in a slab single-moded weakly guiding waveguide is shown to be in accordance with a theoretical formulation of the process. I establish a simple analytical approximation for power captured by a...

Presented is a formula for calculating transition losses for arbitrary deviations from a straight line path of an otherwise uniform single-moded waveguide. The formula is not restricted to any particular index profile and utilizes only two parameters of the fundamental mode field. Using it several methods for minimizing transition losses in bent wa...

We solve the coupled mode equations for the even and odd modes of an asymmetric tapered coupler by means of an accurate analytical approximation. Using this we calculate the taper-induced power transfer as a function of asymmetry for constant taper angle and core width in slab geometry. We show that further simplications can be made when the power...

The author presents an optimum interconnection path for integrated optics circuits in the form of a simple parameter equation, which is not restricted to any particular core shape due to the planar nature of bend radiation. Insertion loss is reduced by 20-30% over the conventional circular geometry. A BPM simulation verifies the results.

We analyse single core excitation in a single-mode twin-core weakly guiding tapered coupler with a slight systematic asymmetry and show that although initially only one coupler supermode is excited a second supermode is subsequently excited over a certain range of core separations. We present a criterion which can be used to determine the degree of...

When gas bubbles rise in a surface-contaminated liquid, the upper parts of their surfaces may be almost free of contaminant and shear stress, while on the remainder of their surfaces there is enough contaminant to prevent tangential motion. Sadhal & Johnson solved the problem of Stokes flow of a uniform stream past a single spherical bubble. We ext...

The calculation of hadron distributions ine + e –4-jets using the 4-parton matrix element diverges unless cuts are imposed on the parton phase space. Experimentally cuts can be applied only on the hadron spectrum and not at the 4-parton level. Test observables for the three gluon vertex relying on jet-jet angular correlations are found to be partic...

The amplitude of a 4-jet process ine +e − annihilation can be used to compute the associated flux of low energy particles due to the emission of soft gluons. I calculate the radiation pattern for the two contributing process, $e^ + e^ - \to q\bar qgg$ and $e^ + e^ - \to q\bar qq'\bar q'$ , in a form suitable for comparison with the experimental...

Thesis (Ph. D.)--University of Cambridge, 1989.

Thesis (M.Sc.)--Victoria University of Wellington, 1985. Bibliography: leaves 104-105.