Quantum arrival time measurement and backflow effect

The current density for a freely evolving state without negative momentum components can temporarily be negative. The operational arrival time distribution, defined by the absorption rate of an ideal detector, is calculated for a model detector and compared with recently proposed distributions. Counterintuitive features of the backflow regime are discussed.Comment: LATEX, 9 pages, 2 postscript figure

Spin dependent observable effect for free particles using the arrival time distribution

The mean arrival time of free particles is computed using the quantum probability current. This is uniquely determined in the non-relativistic limit of Dirac equation, although the Schroedinger probability current has an inherent non-uniqueness. Since the Dirac probability current involves a spin-dependent term, an arrival time distribution based on the probability current shows an observable spin-dependent effect, even for free particles. This arises essentially from relativistic quantum dynamics, but persists even in the non-relativistic regime.Comment: 5 Latex pages, 2.eps figures; discussions sharpened and references added; accepted for publication in Physical Review

Time-of-Arrival States

Although one can show formally that a time-of-arrival operator cannot exist, one can modify the low momentum behaviour of the operator slightly so that it is self-adjoint. We show that such a modification results in the difficulty that the eigenstates are drastically altered. In an eigenstate of the modified time-of-arrival operator, the particle, at the predicted time-of-arrival, is found far away from the point of arrival with probability 1/2.Comment: 15 pages, 2 figure

Larmor precession and tunneling time of a relativistic neutral spinning particle through an arbitrary potential barrier

The Larmor precession of a relativistic neutral spin-1/2 particle in a uniform constant magnetic field confined to the region of a one-dimensional arbitrary potential barrier is investigated. The spin precession serves as a clock to measure the time spent by a quantum particle traversing a potential barrier. With the help of general spin coherent state it is explicitly shown that the precession time is equal to the dwell time.Comment: 10 pages, 1 figure. To be published in Phys. Rev. A (01 February 2002

Pseudogap Formation in the Symmetric Anderson Lattice Model

We present self-consistent calculations for the self-energy and magnetic susceptibility of the 2D and 3D symmetric Anderson lattice Hamiltonian, in the fluctuation exchange approximation. At high temperatures, strong f-electron scattering leads to broad quasiparticle spectral functions, a reduced quasiparticle band gap, and a metallic density of states. As the temperature is lowered, the spectral functions narrow and a pseudogap forms at the characteristic temperature $T_x$ at which the width of the quasiparticle spectral function at the gap edge is comparable to the renormalized activation energy. For $T << T_x$, the pseudogap is approximately equal to the hybridization gap in the bare band structure. The opening of the pseudogap is clearly apparent in both the spin susceptibility and the compressibility.Comment: RevTeX - 14 pages and 7 figures (available on request), NRL-JA-6690-94-002

Tunneling Time Distribution by means of Nelson's Quantum Mechanics and Wave-Particle Duality

We calculate a tunneling time distribution by means of Nelson's quantum mechanics and investigate its statistical properties. The relationship between the average and deviation of tunneling time suggests the exsistence of ``wave-particle duality'' in the tunneling phenomena.Comment: 14 pages including 11 figures, the text has been revise

Nonconstant electronic density of states tunneling inversion for A15 superconductors: Nb3Sn

We re-examine the tunneling data on A15 superconductors by performing a generalized McMillan-Rowell tunneling inversion that incorporates a nonconstant electronic density of states obtained from band-structure calculations. For Nb3Sn, we find that the fit to the experimental data can be slightly improved by taking into account the sharp structure in the density of states, but it is likely that such an analysis alone is not enough to completely explain the superconducting tunneling characteristics of this material. Nevertheless, the extracted Eliashberg function displays a number of features expected to be present for the highest quality Nb3Sn samples.Comment: 11 pages, 11 figure

Time of arrival through interacting environments: Tunneling processes

We discuss the propagation of wave packets through interacting environments. Such environments generally modify the dispersion relation or shape of the wave function. To study such effects in detail, we define the distribution function P_{X}(T), which describes the arrival time T of a packet at a detector located at point X. We calculate P_{X}(T) for wave packets traveling through a tunneling barrier and find that our results actually explain recent experiments. We compare our results with Nelson's stochastic interpretation of quantum mechanics and resolve a paradox previously apparent in Nelson's viewpoint about the tunneling time.Comment: Latex 19 pages, 11 eps figures, title modified, comments and references added, final versio

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

The Time-Energy Uncertainty Relation

The time energy uncertainty relation has been a controversial issue since the advent of quantum theory, with respect to appropriate formalisation, validity and possible meanings. A comprehensive account of the development of this subject up to the 1980s is provided by a combination of the reviews of Jammer (1974), Bauer and Mello (1978), and Busch (1990). More recent reviews are concerned with different specific aspects of the subject. The purpose of this chapter is to show that different types of time energy uncertainty relation can indeed be deduced in specific contexts, but that there is no unique universal relation that could stand on equal footing with the position-momentum uncertainty relation. To this end, we will survey the various formulations of a time energy uncertainty relation, with a brief assessment of their validity, and along the way we will indicate some new developments that emerged since the 1990s.Comment: 33 pages, Latex. This expanded version (prepared for the 2nd edition of "Time in quantum mechanics") contains minor corrections, new examples and pointers to some additional relevant literatur