Entropy of a Quantum Oscillator coupled to a Heat Bath and implications for Quantum Thermodynamics

The free energy of a quantum oscillator in an arbitrary heat bath at a temperature T is given by a "remarkable formula" which involves only a single integral. This leads to a corresponding simple result for the entropy. The low temperature limit is examined in detail and we obtain explicit results both for the case of an Ohmic heat bath and a radiation heat bath. More general heat bath models are also examined. This enables us to determine the entropy at zero temperature in order to check the third law of thermodynamics in the quantum regimeComment: International Conference on "Frontiers of Quantum and Mesoscopic Thermodynamics

Entanglement without Dissipation: A Touchstone for an exact Comparison of Entanglement Measures

Entanglement, which is an essential characteristic of quantum mechanics, is the key element in potential practical quantum information and quantum communication systems. However, there are many open and fundamental questions (relating to entanglement measures, sudden death, etc.) that require a deeper understanding. Thus, we are motivated to investigate a simple but non-trivial correlated two-body continuous variable system in the absence of a heat bath, which facilitates an \underline{exact} measure of the entanglement at all times. In particular, we find that the results obtained from all well-known existing entanglement measures agree with each other but that, in practice, some are more straightforward to use than others

Covariant Calculation of General Relativistic Effects in an Orbiting Gyroscope Experiment

We carry out a covariant calculation of the measurable relativistic effects in an orbiting gyroscope experiment. The experiment, currently known as Gravity Probe B, compares the spin directions of an array of spinning gyroscopes with the optical axis of a telescope, all housed in a spacecraft that rolls about the optical axis. The spacecraft is steered so that the telescope always points toward a known guide star. We calculate the variation in the spin directions relative to readout loops rigidly fixed in the spacecraft, and express the variations in terms of quantities that can be measured, to sufficient accuracy, using an Earth-centered coordinate system. The measurable effects include the aberration of starlight, the geodetic precession caused by space curvature, the frame-dragging effect caused by the rotation of the Earth and the deflection of light by the Sun.Comment: 7 pages, 1 figure, to be submitted to Phys. Rev.

Adiabatic Pair Creation

We give here the proof that pair creation in a time dependent potentials is possible. It happens with probability one if the potential changes adiabatically in time and becomes overcritical, that is when an eigenvalue enters the upper spectral continuum. The potential may be assumed to be zero at large negative and positive times. The rigorous treatment of this effect has been lacking since the pioneering work of Beck, Steinwedel and Suessmann in 1963 and Gershtein and Zeldovich in 1970.Comment: 53 pages, 1 figure. Editorial changes on page 22 f

Time-of-arrival distributions from position-momentum and energy-time joint measurements

The position-momentum quasi-distribution obtained from an Arthurs and Kelly joint measurement model is used to obtain indirectly an ``operational'' time-of-arrival (TOA) distribution following a quantization procedure proposed by Kocha\'nski and W\'odkiewicz [Phys. Rev. A 60, 2689 (1999)]. This TOA distribution is not time covariant. The procedure is generalized by using other phase-space quasi-distributions, and sufficient conditions are provided for time covariance that limit the possible phase-space quasi-distributions essentially to the Wigner function, which, however, provides a non-positive TOA quasi-distribution. These problems are remedied with a different quantization procedure which, on the other hand, does not guarantee normalization. Finally an Arthurs and Kelly measurement model for TOA and energy (valid also for arbitrary conjugate variables when one of the variables is bounded from below) is worked out. The marginal TOA distribution so obtained, a distorted version of Kijowski's distribution, is time covariant, positive, and normalized

Quantitative Treatment of Decoherence

We outline different approaches to define and quantify decoherence. We argue that a measure based on a properly defined norm of deviation of the density matrix is appropriate for quantifying decoherence in quantum registers. For a semiconductor double quantum dot qubit, evaluation of this measure is reviewed. For a general class of decoherence processes, including those occurring in semiconductor qubits, we argue that this measure is additive: It scales linearly with the number of qubits.Comment: Revised version, 26 pages, in LaTeX, 3 EPS figure