John C. Garrison

Canonically Conjugate Pairs, Uncertainty Relations, and Phase Operators

Apparent difficulties that prevent the definition of canonical conjugates for certain observables, e.g., the number operator, are eliminated by distinguishing between the Heisenberg and Weyl forms of the canonical commutation relations (CCRs). Examples are given for which the uncertainty principle does not follow from the CCRs. An operator F is constructed which is canonically conjugate, in the Heisenberg sense, to the number operator; and F is used to define a quantum time operator.

One- and two-dimensional simulations of ultra-short-pulse reflectometry

Ultra-short-pulse reflectometry is studied by means of the numerical integration of one- and two-dimensional full-wave equations for ordinary and extraordinary modes propagating in a plasma. The numerical calculations illustrate the use of the reflection of ultra-short-pulse microwaves as an effective probe of the density or magnetic profile in the presence of density or magnetic fluctuations in the plasma. Bragg resonance effects can be identified in the reflected signals, which give information on fluctuations. It is also demonstrated that ultra-short-pulse reflectometry can be used to perform correlation reflectometry measurements in which correlation lengths for density fluctuations are deduced from the observed cross-correlation function of phase shifts as a function of frequency.

Absence of Long‐Range Order in Thin Films

Thin films are described as idealized systems having finite extent in one direction but infinite extent in the other two. For systems of particles interacting through smooth potentials (e.g., no hard cores), it is shown that an equilibrium state for a homogeneous thin film is necessarily invariant under any continuous internal symmetry group generated by a conserved density. For short‐range interactions it is also shown that equilibrium states are necessarily translation invariant. The absence of long‐range order follows from its relation to broken symmetry. The only properties of the state required for the proof are local normality, spatial translation invariance, and the Kubo‐Martin‐Schwinger boundary condition. The argument employs the Bogoliubov inequality and the techniques of the algebraic approach to statistical mechanics. For inhomogeneous systems, the same argument shows that all order parameters defined by anomalous averages must vanish. Identical results can be obtained for systems with infinit...

GALILEAN RELATIVITY, LOCALITY, AND QUANTUM HYDRODYNAMICS.

In this work we study the consequences of locality and Galilean covariance for the operators that occur in Landaus quantum hydrodynamics. We specifically consider the following requirements: (1) Galilean covariance of the velocity field, (2) locality of the velocity field, and (3) Landaus assumption that the momentum density is a symmetrized product of the velocity and density operators. It is demonstrated that the density‐velocity commutation relation of the Landau theory is essentially a direct consequence of (1) and (2). The addition of (3) is sufficient to determine the velocity‐velocity commutation relation, also in agreement with Laudau. We further show that the density‐velocity commutation relation, independent of (3) or any specific form for the velocity field, is inconsistent with the nonnegative character of the local density.

Quantum spatial propagation of squeezed light in a degenerate parametric amplifier

Abstract Differential equations which describe the steady state spatial evolution of nonclassical light are established using standard quantum field theoretic techniques. A Schrodinger equation for the state vector of the optical field is derived using the quantum analog of the slowly varying envelope approximation (SVEA). The steady state solutions are those that satisfy the time independent Schrodinger equation. The resulting eigenvalue problem then leads to the spatial propagation equations. For the degenerate parametric amplifier this method shows that the squeezed state is an eigenstate of the squeezing hamiltonian. The magnitude and phase of the squeezing parameter obey nonlinear differential equations coupled by the amplifier gain constant and phase mismatch. The solution to these differential equations is equivalent to one obtained from the classical three-wave mixing steady state solution to the parametric amplifier with a nondepleted pump.

Approximate scaling laws for saturation in the fel (1-D theory)

Abstract Approximate scaling laws for the saturation intensity and the saturation length in a free electron laser amplifier are derived by expressing them in terms of naturally defined characteristic values. The characteristic intensity is defined as that for which the power gain of the laser field equals the synchrotron wave number of the electrons. The characteristic length is defined as the gain length at saturation. Comparison with simulation results shows that the scaling laws are accurate to within ±10%.

One- and two-dimensional simulations of ultra-short-pulse reflectometry (abstract)

Ultra-short-pulse reflectometry is studied by means of the numerical integration of one- and two-dimensional full-wave equations for ordinary and extraordinary modes propagating in a plasma. The numerical calculations illustrate the use of the reflection of ultra-short-pulse microwaves as an effective probe of the density or magnetic profile in the presence of density or magnetic fluctuations in the plasma. Bragg resonance effects can be identified in the reflected signals, which give information on fluctuations. It is also demonstrated that ultra-short-pulse reflectometry can be used to perform correlation reflectometry measurements in which correlation lengths for density fluctuations are deduced from the observed cross-correlation function of phase shifts as a function of frequency.

Scaling laws for saturation in free electron lasers

Abstract Saturation in free electron laser amplifiers is described by the critical intensity at which the saturated gain length equals the electron synchrotron wavelength. This yields approximate scaling laws agreeing with simulation results within ±10%.