Probability backflow for a Dirac particle

The phenomenon of probability backflow, previously quantified for a free nonrelativistic particle, is considered for a free particle obeying Dirac's equation. It is known that probability backflow can occur in the opposite direction to the momentum; that is to say, there exist positive-energy states in which the particle certainly has a positive momentum in a given direction, but for which the component of the probability flux vector in that direction is negative. It is shown thar the maximum possible amount of probability that can flow backwards, over a given time interval of duration T, depends on the dimensionless parameter epsilon = root 4h/mc(2)T, where m is the mass of the particle and c is the speed of light. At epsilon = 0, the nonrelativistic value of approximately 0.039 for this maximum is recovered. Numerical studies suggest that the maximum decreases monotonically as epsilon increases from 0, and show that it depends on the size of m, h, and T, unlike the nonrelativistic case.

New integrable boundary conditions for the q-deformed supersymmetric U model and Bethe ansatz equations

New classes of integrable boundary conditions for the q-deformed (or two-parameter) supersymmetric U model are presented. The boundary systems are solved by using the coordinate space Bethe ansatz technique and Bethe ansatz equations are derived. (C) 1998 Elsevier Science B.V.

Nine classes of integrable boundary conditions for the eight-state supersymmetric fermion model

Nine classes of integrable boundary conditions for the eight-state supersymmetric model of strongly correlated fermions are presented. The boundary systems are solved by using the coordinate Bethe ansatz method and the Bethe ansatz equations for all nine cases are given.

Spectral linewidth narrowing by a weak squeezed field of an arbitrary bandwidth

We study the spectral and noise properties of the fluorescence field emitted from a two-level atom driven by a beam of squeezed light. For a weak driving field we derive simple analytical formulae for the fluorescence and quadrature-noise spectra which are valid for an arbitrary bandwidth of the squeezed field. We analyse the spectra in the regime where the squeezing bandwidth is smaller or comparable to the atomic linewidth, the area where non-Markovian effects are important. We emphasize that there is a noticable difference between the fluorescence spectra for the thermal and squeezed field excitations. In both cases the spectrum can be narrower than any bandwidth involved in the process. However, as we point out for the squeezed driving field the linewidth narrowing, being much larger than in the thermal-field case, can be attributed to the squeezing of the fluctuations in the driving held. We also calculate the quadrature-noise spectrum of the emitted fluorescence, and find that for a detuned squeezed field the fluorescence spectrum does not reveal the quadrature-noise spectrum. In contrast to the fluorescence spectrum having two peaks, the quadrature-noise spectrum exhibits three peaks. We explain this difference as arising from the competiting three-photon scattering processes. (C) 1998 Elsevier Science B.V. All rights reserved.

Coherent molecular solitons in Bose-Einstein condensates

We analyze the coherent formation of molecular Bose-Einstein condensate (BEC) from an atomic BEG, using a parametric field theory approach. We point out the transition between a quantum soliton regime, where atoms couple in a local way to a classical soliton domain, where a stable coupled-condensate soliton can form in three dimensions. This gives the possibility of an intense, stable atom-laser output. [S0031-9007(98)07283-4].

Characterizing Greenberger-Horne-Zeilinger correlations in nondegenerate parametric oscillation via phase measurements

We present a potential realization of the Greenberger-Horne-Zeilinger all or nothing contradiction of quantum mechanics with local realism using phase measurement techniques in a simple photon number triplet. Such a triplet could be generated using nondegenerate parametric oscillation. [S0031-9007(98)07671-6].

Incoherent interlayer transport and angular-dependent magnetoresistance oscillations in layered metals

The effect of incoherent interlayer transport on the interlayer resistance of a layered metal is considered. We find that for both quasi-one-dimensional and quasi-two-dimensional Fermi liquids the angular dependence of the magnetoresistance is essentially the same for coherent and incoherent transport. Consequently, the existence of a three-dimensional Fermi surface is not necessary to explain the oscillations in the magnetoresistance that are seen in many organic conductors as the field direction is varied. [S0031-9007(98)07660-1].

Measurements on trapped laser-cooled ions using quantum computations

There are some interesting connections between the theory of quantum computation and quantum measurement. As an illustration, we present a scheme in which an ion trap quantum computer can be used to make arbitrarily accurate measurements of the quadrature phase variables for the collective vibrational motion of the ion. We also discuss some more general aspects of quantum computation and measurement in terms of the Feynman-Deutsch principle.

A relative gradient theory for layered materials

It is possible to remedy certain difficulties with the description of short wave length phenomena and interfacial slip in standard models of a laminated material by considering the bending stiffness of the layers. If the couple or moment stresses are assumed to be proportional to the relative deformation gradient, then the bending effect disappears for vanishing interface slip, and the model correctly reduces to an isotropic standard continuum. In earlier Cosserat-type models this was not the case. Laminated materials of the kind considered here occur naturally as layered rock, or at a different scale, in synthetic layered materials and composites. Similarities to the situation in regular dislocation structures with couple stresses, also make these ideas relevant to single slip in crystalline materials. Application of the theory to a one-dimensional model for layered beams demonstrates agreement with exact results at the extremes of zero and infinite interface stiffness. Moreover, comparison with finite element calculations confirm the accuracy of the prediction for intermediate interfacial stiffness.

The velocity of probability transport in quantum mechanics

In his study of the 'time of arrival' problem in the nonrelativistic quantum mechanics of a single particle, Allcock [1] noted that the direction of the probability flux vector is not necessarily the same as that of the mean momentum of a wave packet, even when the packet is composed entirely of plane waves with a common direction of momentum. Packets can be constructed, for example for a particle moving under a constant force, in which probability flows for a finite time in the opposite direction to the momentum. A similar phenomenon occurs for the Dirac electron. The maximum amount of probabilitiy backflow which can occur over a given time interval can be calculated in each case.

Search for time variation of the fine structure constant

An order of magnitude sensitivity gain is described for using quasar spectra to investigate possible time or space variation in the fine structure constant alpha. Applied to a sample of 30 absorption systems, spanning redshifts 0.5 < z < 1.6, we derive limits on variations in alpha over a wide range of epochs. For the whole sample, Delta alpha/alpha = (-1.1 +/- 0.4) x 10(-5). This deviation is dominated by measurements at z > 1, where Delta alpha/alpha = (-1.9 +/- 0.5) x 10(-5). For z < 1, Delta alpha/alpha = (-0.2 +/- 0.4) x 10(-5). While this is consistent with a time-varying alpha, further work is required to explore possible systematic errors in the data, although careful searches have so far revealed none.

Algebraic Bethe ansatz for integrable Kondo impurities in the one-dimensional supersymmetric t-J model

An integrable Kondo problem in the one-dimensional supersymmetric t-J model is studied by means of the boundary supersymmetric quantum inverse scattering method. The boundary K matrices depending on the local moments of the impurities are presented as a nontrivial realization of the graded reflection equation algebras in a two-dimensional impurity Hilbert space. Further, the model is solved by using the algebraic Bethe ansatz method and the Bethe ansatz equations are obtained. (C) 1999 Elsevier Science B.V.

Integrability of a t - J model with impurities

A t - J model for correlated electrons with impurities is proposed. The impurities are introduced in such a way that integrability of the model in one dimension is not violated. The algebraic Bethe ansatz solution of the model is also given and it is shown that the Bethe states are highest weight states with respect to the supersymmetry algebra gl(2/1).

Eigenvalues of Casimir operators for gl(m/infinity)

A full set of Casimir operators for the Lie superalgebra gl(m/infinity) is constructed and shown to be well defined in the category O-FS generated by the highest-weight irreducible representations with only a finite number of non-zero weight components. The eigenvalues of these Casimir operators are determined explicitly in terms of the highest weight. Characteristic identities satisfied by certain (infinite) matrices with entries from gl(m/infinity) are also determined.

Integrable Kondo impurities in the one-dimensional supersymmetric U model of strongly correlated electrons

Integrable Kondo impurities in the one-dimensional supersymmetric U model of strongly correlated electrons are studied by means of the boundary graded quantum inverse scattering method. The boundary K-matrices depending on the local magnetic moments of the impurities are presented as non-trivial realizations of the reflection equation algebras in an impurity Hilbert space. Furthermore, the model Hamiltonian is diagonalized and the Bethe ansatz equations are derived. It is interesting to note that our model exhibits a free parameter in the bulk Hamiltonian but no free parameter exists on the boundaries. This is in sharp contrast to the impurity models arising from the supersymmetric t-J and extended Hubbard models where there is no free parameter in the bulk but there is a free parameter on each boundary.