Abstract:
Dispersion relations for dipolar modes propagating along a chain of metal nanoparticles are calculated by solving the full Maxwell equations, including radiation damping. The nanoparticles are treated as point dipoles, which means the results are valid only for a/d <= 1/3, where a is the particle radius and d the spacing. The discrete modes for a finite chain are first calculated, then these are mapped onto the dispersion relations appropriate for the infinite chain. Computed results are given for a chain of 50-nm diameter Ag spheres spaced by 75 nm. We find large deviations from previous quasistatic results: Transverse modes interact strongly with the light line. Longitudinal modes develop a bandwidth more than twice as large, resulting in a group velocity that is more than doubled. All modes for which k_mode <= w/c show strongly enhanced decay due to radiation damping.

Abstract:
The quantum analog of the joint probability distributions describing a classical stochastic process is introduced. A prescription is given for constructing the quantum distribution associated with a sequence of measurements. For the case of quantum Brownian motion this prescription is illustrated with a number of explicit examples. In particular it is shown how the prescription can be extended in the form of a general formula for the Wigner function of a Brownian particle entangled with a heat bath.

Abstract:
We consider the case of a pair of particles initially in a superposition state corresponding to a separated pair of wave packets. We calculate \emph{exactly} the time development of this non-Gaussian state due to interaction with an \emph{arbitrary} heat bath. We find that coherence decays continuously, as expected. We then investigate entanglement and find that at a finite time the system becomes separable (not entangled). Thus, we see that entanglement sudden death is also prevalent in continuous variable systems which should raise concern for the designers of entangled systems.

Abstract:
We outline an exact approach to decoherence and entanglement problems for continuous variable systems. The method is based on a construction of quantum distribution functions introduced by Ford and Lewis \cite{ford86} in which a system in thermal equilibrium is placed in an initial state by a measurement and then sampled by subsequent measurements. With the Langevin equation describing quantum Brownian motion, this method has proved to be a powerful tool for discussing such problems. After reviewing our previous work on decoherence and our recent work on disentanglement, we apply the method to the problem of a pair of particles in a correlated Gaussian state. The initial state and its time development are explicitly exhibited. For a single relaxation time bath at zero temperature exact numerical results are given. The criterion of Duan et al. \cite{duan00} for such states is used to prove that the state is initially entangled and becomes separable after a finite time (entanglement sudden death).

Abstract:
We present a simple calculation of the Lorentz transformation of the spectral distribution of blackbody radiation at temperature T. Here we emphasize that T is the temperature in the blackbody rest frame and does not change. We thus avoid the confused and confusing question of how temperature transforms. We show by explicit calculation that at zero temperature the spectral distribution is invariant. At finite temperature we find the well known result familiar in discussions of the the 2.7! K cosmic radiation.

Abstract:
A localized free particle is represented by a wave packet and its motion is discussed in most quantum mechanics textbooks. Implicit in these discussions is the assumption of zero temperature. We discuss how the effects of finite temperature and squeezing can be incorporated in an elementary manner. The results show how the introduction of simple tools and ideas can bring the reader into contact with topics at the frontiers of research in quantum mechanics. We discuss the standard quantum limit, which is of interest in the measurement of small forces, and decoherence of a mixed (``Schrodinger cat'') state, which has implications for current research in quantum computation, entanglement, and the quantum-classical interface.

Abstract:
The Hu-Paz-Zhang equation is a master equation for an oscillator coupled to a linear passive bath. It is exact within the assumption that the oscillator and bath are initially uncoupled . Here an exact general solution is obtained in the form of an expression for the Wigner function at time t in terms of the initial Wigner function. The result is applied to the motion of a Gaussian wave packet and to that of a pair of such wave packets. A serious divergence arising from the assumption of an initially uncoupled state is found to be due to the zero-point oscillations of the bath and not removed in a cutoff model. As a consequence, worthwhile results for the equation can only be obtained in the high temperature limit, where zero-point oscillations are neglected. In that limit closed form expressions for wave packet spreading and attenuation of coherence are obtained. These results agree within a numerical factor with those appearing in the literature, which apply for the case of a particle at zero temperature that is suddenly coupled to a bath at high temperature. On the other hand very different results are obtained for the physically consistent case in which the initial particle temperature is arranged to coincide with that of the bath.

Abstract:
The prototypical Schr\"{o}dinger cat state, i.e., an initial state corresponding to two widely separated Gaussian wave packets, is considered. The decoherence time is calculated solely within the framework of elementary quantum mechanics and equilibrium statistical mechanics. This is at variance with common lore that irreversible coupling to a dissipative environment is the mechanism of decoherence. Here, we show that, on the contrary, decoherence can in fact occur at high temperature even for vanishingly small dissipation.

Abstract:
In a letter to Nature (Ford G W and O'Connell R F 1996 Nature 380 113) we presented a formula for the derivative of the hyperbolic cotangent that differs from the standard one in the literature by an additional term proportional to the Dirac delta function. Since our letter was necessarily brief, shortly after its appearance we prepared a more extensive unpublished note giving a detailed explanation of our argument. Since this note has been referenced in a recent article (Estrada R and Fulling S A 2002 J. Phys. A: Math. Gen. 35 3079) we think it appropriate that it now appear in print. We have made no alteration to the original note.

Abstract:
The low temperature solution of the exact master equation for an oscillator coupled to a linear passive heat bath is known to give rise to serious divergences. We now show that, even in the high temperature regime, problems also exist, notably the fact that the density matrix is not necessarily positive.