Quantum energy inequalities and local covariance II: Categorical formulation

We formulate Quantum Energy Inequalities (QEIs) in the framework of locally covariant quantum field theory developed by Brunetti, Fredenhagen and Verch, which is based on notions taken from category theory. This leads to a new viewpoint on the QEIs, and also to the identification of a new structural property of locally covariant quantum field theory, which we call Local Physical Equivalence. Covariant formulations of the numerical range and spectrum of locally covariant fields are given and investigated, and a new algebra of fields is identified, in which fields are treated independently of their realisation on particular spacetimes and manifestly covariant versions of the functional calculus may be formulated.Comment: 27 pages, LaTeX. Further discussion added. Version to appear in General Relativity and Gravitatio

On the spin-statistics connection in curved spacetimes

The connection between spin and statistics is examined in the context of locally covariant quantum field theory. A generalization is proposed in which locally covariant theories are defined as functors from a category of framed spacetimes to a category of $*$-algebras. This allows for a more operational description of theories with spin, and for the derivation of a more general version of the spin-statistics connection in curved spacetimes than previously available. The proof involves a "rigidity argument" that is also applied in the standard setting of locally covariant quantum field theory to show how properties such as Einstein causality can be transferred from Minkowski spacetime to general curved spacetimes.Comment: 17pp. Contribution to the proceedings of the conference "Quantum Mathematical Physics" (Regensburg, October 2014

Quantum interest in two dimensions

The quantum interest conjecture of Ford and Roman asserts that any negative-energy pulse must necessarily be followed by an over-compensating positive-energy one within a certain maximum time delay. Furthermore, the minimum amount of over-compensation increases with the separation between the pulses. In this paper, we first study the case of a negative-energy square pulse followed by a positive-energy one for a minimally coupled, massless scalar field in two-dimensional Minkowski space. We obtain explicit expressions for the maximum time delay and the amount of over-compensation needed, using a previously developed eigenvalue approach. These results are then used to give a proof of the quantum interest conjecture for massless scalar fields in two dimensions, valid for general energy distributions.Comment: 17 pages, 4 figures; final version to appear in PR

Crystal truncation rods in kinematical and dynamical x-ray diffraction theories

Crystal truncation rods calculated in the kinematical approximation are shown to quantitatively agree with the sum of the diffracted waves obtained in the two-beam dynamical calculations for different reflections along the rod. The choice and the number of these reflections are specified. The agreement extends down to at least $\sim 10^{-7}$ of the peak intensity. For lower intensities, the accuracy of dynamical calculations is limited by truncation of the electron density at a mathematically planar surface, arising from the Fourier series expansion of the crystal polarizability

On the spin-statistics connection in curved spacetimes

The connection between spin and statistics is examined in the context of locally covariant quantum field theory. A generalization is proposed in which locally covariant theories are defined as functors from a category of framed spacetimes to a category of ∗-algebras. This allows for a more operational description of theories with spin, and for the derivation of a more general version of the spin-statistics connection in curved spacetimes than previously available. The proof involves a "rigidity argument" that is also applied in the standard setting of locally covariant quantum field theory to show how properties such as Einstein causality can be transferred from Minkowski spacetime to general curved spacetimes

The split property for quantum field theories in flat and curved spacetimes

The split property expresses a strong form of independence of spacelike separated regions in algebraic quantum field theory. In Minkowski spacetime, it can be proved under hypotheses of nuclearity. An expository account is given of nuclearity and the split property, and connections are drawn to the theory of quantum energy inequalities. In addition, a recent proof of the split property for quantum field theory in curved spacetimes is outlined, emphasising the essential ideas

Monte Carlo Simulation of Sinusoidally Modulated Superlattice Growth

The fabrication of ZnSe/ZnTe superlattices grown by the process of rotating the substrate in the presence of an inhomogeneous flux distribution instead of successively closing and opening of source shutters is studied via Monte Carlo simulations. It is found that the concentration of each compound is sinusoidally modulated along the growth direction, caused by the uneven arrival of Se and Te atoms at a given point of the sample, and by the variation of the Te/Se ratio at that point due to the rotation of the substrate. In this way we obtain a ZnSe$_{1-x}$Te$_x$ alloy in which the composition $x$ varies sinusoidally along the growth direction. The period of the modulation is directly controlled by the rate of the substrate rotation. The amplitude of the compositional modulation is monotonous for small angular velocities of the substrate rotation, but is itself modulated for large angular velocities. The average amplitude of the modulation pattern decreases as the angular velocity of substrate rotation increases and the measurement position approaches the center of rotation. The simulation results are in good agreement with previously published experimental measurements on superlattices fabricated in this manner

In-plane uniaxial anisotropy rotations in (Ga,Mn)As thin films

We show, by SQUID magnetometry, that in (Ga,Mn)As films the in-plane uniaxial magnetic easy axis is consistently associated with particular crystallographic directions and that it can be rotated from the [-110] direction to the [110] direction by low temperature annealing. We show that this behavior is hole-density-dependent and does not originate from surface anisotropy. The presence of uniaxial anisotropy as well its dependence on the hole-concentration and temperature can be explained in terms of the p-d Zener model of the ferromagnetism assuming a small trigonal distortion.Comment: 4 pages, 6 Postscript figures, uses revtex

Self sustained traversable wormholes and the equation of state

We compute the graviton one loop contribution to a classical energy in a \textit{traversable} wormhole background. The form of the shape function considered is obtained by the equation of state $p=\omega\rho$. We investigate the size of the wormhole as a function of the parameter $\omega$. The investigation is evaluated by means of a variational approach with Gaussian trial wave functionals. A zeta function regularization is involved to handle with divergences. A renormalization procedure is introduced and the finite one loop energy is considered as a \textit{self-consistent} source for the traversable wormhole.The case of the phantom region is briefly discussed.Comment: Uses RevTeX 4. 21 pages. Submitted to Classical and Quantum Gravity. Extended version of the talk given at ERE2006 (Palma de Mallorca, September 4-8, 2006) and of the talk given at MG11-GT5, Berlin, 23-29 July, 200