Stress Tensor of the Hydrogen Molecular Ion

The electronic stress tensor of the hydrogen molecule ion H_2^+ is investigated for the ground state (sigma_g 1s) and the first excited state (sigma_u^* 1s) using their exact wave functions. A map of its largest eigenvalue and corresponding eigenvector is shown to be closely related to the nature of chemical bonding. For the ground state, we also show the spatial distribution of interaction energy density to describe in which part of the molecule stabilization and destabilization take place.Comment: 9 pages, 4 figure

Towards Microscopic Understanding of the Phonon Bottleneck

The problem of the phonon bottleneck in the relaxation of two-level systems (spins) to a narrow group of resonant phonons via emission-absorption processes is investigated from the first principles. It is shown that the kinetic approach based on the Pauli master equation is invalid because of the narrow distribution of the phonons exchanging their energy with the spins. This results in a long-memory effect that can be best taken into account by introducing an additional dynamical variable corresponding to the nondiagonal matrix elements responsible for spin-phonon correlation. The resulting system of dynamical equations describes the phonon-bottleneck plateau in the spin excitation, as well as a gap in the spin-phonon spectrum for any finite concentration of spins. On the other hand, it does not accurately render the lineshape of emitted phonons and still needs improving.Comment: 13 Phys. Rev. pages, 5 figure captions (7 figures

Transient effects on electron spin observation

In an earlier publication we addressed the problem of splitting an electron beam in the Stern-Gerlach experiment. In contrast to arguments put forward in the early days of quantum theory, we concluded that there are no issues of principle preventing the observation of electron spin during free flight. In that paper, however, we considered only a sudden switch off of the separating magnetic field. In this work we consider the possible effects of finite switching times at the beginning and the end of the interaction period. We consider a model where the coupling between the electron and the field is time dependent. As a result of the time dependence, the field also acquires an electric component, but this seems to cause no significant change of our conclusions. On the other hand, the smooth change of the interaction enforces the same longitudinal velocity on the electron both at the beginning and end of the interaction period because of conservation laws; this effect was missing in our earlier calculations. As the electrons are supposed to travel as a beam, this feature helps by restoring the beam quality after the interaction

On Pauli Pairs

The state of a system in classical mechanics can be uniquely reconstructed if we know the positions and the momenta of all its parts. In 1958 Pauli has conjectured that the same holds for quantum mechanical systems. The conjecture turned out to be wrong. In this paper we provide a new set of examples of Pauli pairs, being the pairs of quantum states indistinguishable by measuring the spatial location and momentum. In particular, we construct a new set of spatially localized Pauli pairs.Comment: submitted to JM

Thermopower induced by a supercurrent in superconductor-normal-metal structures

We examine the thermopower Q of a mesoscopic normal-metal (N) wire in contact to superconducting (S) segments and show that even with electron-hole symmetry, Q may become finite due to the presence of supercurrents. Moreover, we show how the dominant part of Q can be directly related to the equilibrium supercurrents in the structure. In general, a finite thermopower appears both between the N reservoirs and the superconductors, and between the N reservoirs themselves. The latter, however, strongly depends on the geometrical symmetry of the structure.Comment: 4 pages, 4 figures; text compacted and material adde

Four-vector vs. four-scalar representation of the Dirac wave function

In a Minkowski spacetime, one may transform the Dirac wave function under the spin group, as one transforms coordinates under the Poincar\'e group. This is not an option in a curved spacetime. Therefore, in the equation proposed independently by Fock and Weyl, the four complex components of the Dirac wave function transform as scalars under a general coordinate transformation. Recent work has shown that a covariant complex four-vector representation is also possible. Using notions of vector bundle theory, we describe these two representations in a unified framework. We prove theorems that relate together the different representations and the different choices of connections within each representation. As a result, either of the two representations can account for a variety of inequivalent, linear, covariant Dirac equations in a curved spacetime that reduce to the original Dirac equation in a Minkowski spacetime. In particular, we show that the standard Dirac equation in a curved spacetime, with any choice of the tetrad field, is equivalent to a particular realization of the covariant Dirac equation for a complex four-vector wave function.Comment: 30 pages (standard 12pt). v2: version accepted for publication in Int. J. Geom. Meth. Mod. Phys. Some emphasis and a clarification in Sect. 2.1. The Appendix now proves that the complex tangent bundle is a spinor bundle according to precisely the definition given in Sect. 2.1. Proof of the main Theorem 2 made easier to follo

A Lorentz-Violating Alternative to Higgs Mechanism?

We consider a four-dimensional field-theory model with two massless fermions, coupled to an Abelian vector field without flavour mixing, and to another Abelian vector field with flavour mixing. Both Abelian vectors have a Lorentz-violating kinetic term, introducing a Lorentz-violation mass scale $M$, from which fermions and the flavour-mixing vector get their dynamical masses, whereas the vector coupled without flavour mixing remains massless. When the two coupling constants have similar values in order of magnitude, a mass hierarchy pattern emerges, in which one fermion is very light compared to the other, whilst the vector mass is larger than the mass of the heavy fermion. The work presented here may be considered as a Lorentz-symmetry-Violating alternative to the Higgs mechanism, in the sense that no scalar particle (fundamental or composite) is necessary for the generation of the vector-meson mass. However, the model is not realistic given that, as a result of Lorentz Violation, the maximal (light-cone) speed seen by the fermions is smaller than that of the massless gauge boson (which equals the speed of light in vacuo) by an amount which is unacceptably large to be compatible with the current tests of Lorentz Invariance, unless the gauge couplings assume unnaturally small values. Possible ways out of this phenomenological drawback are briefly discussed, postponing a detailed construction of more realistic models for future work.Comment: 16 pages revtex, three eps figures incorporate

Sequential measurement of conjugate variables as an alternative quantum state tomography

It is shown how it is possible to reconstruct the initial state of a one-dimensional system by measuring sequentially two conjugate variables. The procedure relies on the quasi-characteristic function, the Fourier-transform of the Wigner quasi-probability. The proper characteristic function obtained by Fourier-transforming the experimentally accessible joint probability of observing "position" then "momentum" (or vice versa) can be expressed as a product of the quasi-characteristic function of the two detectors and that, unknown, of the quantum system. This allows state reconstruction through the sequence: data collection, Fourier-transform, algebraic operation, inverse Fourier-transform. The strength of the measurement should be intermediate for the procedure to work.Comment: v2, 5 pages, no figures, substantial improvements in the presentation, thanks to an anonymous referee. v3, close to published versio

On Simulating Liouvillian Flow From Quantum Mechanics Via Wigner Functions

The interconnection between quantum mechanics and probabilistic classical mechanics for a free relativistic particle is derived in terms of Wigner functions (WF) for both Dirac and Klein-Gordon (K-G) equations. Construction of WF is achieved by first defining a bilocal 4-current and then taking its Fourier transform w.r.t. the relative 4-coordinate. The K-G and Proca cases also lend themselves to a closely parallel treatment provided the Kemmer- Duffin beta-matrix formalism is employed for the former. Calculation of WF is carried out in a Lorentz-covariant fashion by standard `trace' techniques. The results are compared with a recent derivation due to Bosanac.Comment: 9 pages, Latex; email: [email protected]

Quantum Continuum Mechanics Made Simple

In this paper we further explore and develop the quantum continuum mechanics (CM) of [Tao \emph{et al}, PRL{\bf 103},086401] with the aim of making it simpler to use in practice. Our simplifications relate to the non-interacting part of the CM equations, and primarily refer to practical implementations in which the groundstate stress tensor is approximated by its Kohn-Sham version. We use the simplified approach to directly prove the exactness of CM for one-electron systems via an orthonormal formulation. This proof sheds light on certain physical considerations contained in the CM theory and their implication on CM-based approximations. The one-electron proof then motivates an approximation to the CM (exact under certain conditions) expanded on the wavefunctions of the Kohn-Sham (KS) equations. Particular attention is paid to the relationships between transitions from occupied to unoccupied KS orbitals and their approximations under the CM. We also demonstrate the simplified CM semi-analytically on an example system