Spectral singularities and Bragg scattering in complex crystals

Spectral singularities that spoil the completeness of Bloch-Floquet states may occur in non-Hermitian Hamiltonians with complex periodic potentials. Here an equivalence is established between spectral singularities in complex crystals and secularities that arise in Bragg diffraction patterns. Signatures of spectral singularities in a scattering process with wave packets are elucidated for a PT-symmetric complex crystal.Comment: 6 pages, 5 figures, to be published in Phys. Rev.

On the negative spectrum of two-dimensional Schr\"odinger operators with radial potentials

For a two-dimensional Schr\"odinger operator $H_{\alpha V}=-\Delta-\alpha V$ with the radial potential $V(x)=F(|x|), F(r)\ge 0$, we study the behavior of the number $N_-(H_{\alpha V})$ of its negative eigenvalues, as the coupling parameter $\alpha$ tends to infinity. We obtain the necessary and sufficient conditions for the semi-classical growth $N_-(H_{\alpha V})=O(\alpha)$ and for the validity of the Weyl asymptotic law.Comment: 13 page

A naked singularity stable under scalar field perturbations

We prove the stability of a spacetime with a naked singularity under scalar field perturbations, where the perturbations are regular at the singularity. This spacetime, found by Janis, Newman and Winicour, and independently by Wyman, is sourced by a massless scalar field and also arises as a certain limit of a class of charged dilatonic solutions in string theory. This stability result opens up specific questions for investigation related to the cosmic censorship conjecture and the mechanism by which it is implemented in nature.Comment: 19 pages, version to appear in IJMPD, references adde

Quasiprobabilistic Interpretation of Weak measurements in Mesoscopic Junctions

The impossibility of measuring noncommuting quantum mechanical observables is one of the most fascinating consequences of the quantum mechanical postulates. Hence, to date the investigation of quantum measurement and projection is a fundamentally interesting topic. We propose to test the concept of weak measurement of noncommuting observables in mesoscopic transport experiments, using a quasiprobablistic description. We derive an inequality for current correlators, which is satisfied by every classical probability but violated by high-frequency fourth-order cumulants in the quantum regime for experimentally feasible parameters.Comment: 4 pages, published versio

Explicit solution for vibrating bar with viscous boundaries and internal damper

We investigate longitudinal vibrations of a bar subjected to viscous boundary conditions at each end, and an internal damper at an arbitrary point along the bar's length. The system is described by four independent parameters and exhibits a variety of behaviors including rigid motion, super stability/instability and zero damping. The solution is obtained by applying the Laplace transform to the equation of motion and computing the Green's function of the transformed problem. This leads to an unconventional eigenvalue-like problem with the spectral variable in the boundary conditions. The eigenmodes of the problem are necessarily complex-valued and are not orthogonal in the usual inner product. Nonetheless, in generic cases we obtain an explicit eigenmode expansion for the response of the bar to initial conditions and external force. For some special values of parameters the system of eigenmodes may become incomplete, or no non-trivial eigenmodes may exist at all. We thoroughly analyze physical and mathematical reasons for this behavior and explicitly identify the corresponding parameter values. In particular, when no eigenmodes exist, we obtain closed form solutions. Theoretical analysis is complemented by numerical simulations, and analytic solutions are compared to computations using finite elements.Comment: 29 pages, 6 figure

Intertwining Operator Realization of the AdS/CFT Correspondence

We give a group-theoretic interpretation of the AdS/CFT correspondence as relation of representation equivalence between representations of the conformal group describing the bulk AdS fields $\phi$ and the coupled boundary fields $\phi_0$ and ${\cal O}$. We use two kinds of equivalences. The first kind is equivalence between bulk fields and boundary fields and is established here. The second kind is the equivalence between coupled boundary fields. Operators realizing the first kind of equivalence for special cases were given by Witten and others - here they are constructed in a more general setting from the requirement that they are intertwining operators. The intertwining operators realizing the second kind of equivalence are provided by the standard conformal two-point functions. Using both equivalences we find that the bulk field has in fact two boundary fields, namely, the coupled boundary fields. Thus, from the viewpoint of the bulk-boundary correspondence the coupled fields are on an equal footing. Our setting is more general since our bulk fields are described by representations of the Euclidean conformal group $G=SO(d+1,1)$, induced from representations $\tau$ of the maximal compact subgroup $SO(d+1)$ of $G$. From these large reducible representations we can single out representations which are equivalent to conformal boundary representations labelled by the conformal weight and by arbitrary representations $\mu$ of the Euclidean Lorentz group $M=SO(d)$, such that $\mu$ is contained in the restriction of $\tau$ to $M$. Thus, our boundary-to-bulk operators can be compared with those in the literature only when for a fixed $\mu$ we consider a 'minimal' representation $\tau=\tau(\mu)$ containing $\mu$.Comment: 25 pages, TEX file using harvmac.tex; v2: misprints corrected; to appear in Nuclear Physics

Nonclassical time correlation functions in continuous quantum measurement

A continuous projective measurement of a quantum system often leads to a suppression of the dynamics, known as the Zeno effect. Alternatively, generalized nonprojective, so-called "weak" measurements can be carried out. Such a measurement is parameterized by its strength parameter that can interpolate continuously between the ideal strong measurement with no dynamics-the strict Zeno effect, and a weak measurement characterized by almost free dynamics but blurry observations. Here we analyze the stochastic properties of this uncertainty component in the resulting observation trajectory. The observation uncertainty results from intrinsic quantum uncertainty, the effect of measurement on the system (backaction) and detector noise. It is convenient to separate the latter, system-independent contribution from the system-dependent uncertainty, and this paper shows how to accomplish this separation. The system-dependent uncertainty is found in terms of a quasi-probability, which, despite its weaker properties, is shown to satisfy a weak positivity condition. We discuss the basic properties of this quasi-probability with special emphasis on its time correlation functions as well as their relationship to the full correlation functions along the observation trajectory, and illustrate our general results with simple examples.We demonstrate a violation of classical macrorealism using the fourth-order time correlation functions with respect to the quasi-probability in the twolevel system.Comment: 20 pages, 1 figure, published version (open access

Theoretical framework for quantum networks

We present a framework to treat quantum networks and all possible transformations thereof, including as special cases all possible manipulations of quantum states, measurements, and channels, such as, e.g., cloning, discrimination, estimation, and tomography. Our framework is based on the concepts of quantum comb-which describes all transformations achievable by a given quantum network-and link product-the operation of connecting two quantum networks. Quantum networks are treated both from a constructive point of view-based on connections of elementary circuits-and from an axiomatic one-based on a hierarchy of admissible quantum maps. In the axiomatic context a fundamental property is shown, which we call universality of quantum memory channels: any admissible transformation of quantum networks can be realized by a suitable sequence of memory channels. The open problem whether this property fails for some nonquantum theory, e.g., for no-signaling boxes, is posed.Comment: 23 pages, revtex

q-Deformed de Sitter/Conformal Field Theory Correspondence

Unitary principal series representations of the conformal group appear in the dS/CFT correspondence. These are infinite dimensional irreducible representations, without highest weights. In earlier work of Guijosa and the author it was shown for the case of two-dimensional de Sitter, there was a natural q-deformation of the conformal group, with q a root of unity, where the unitary principal series representations become finite-dimensional cyclic unitary representations. Formulating a version of the dS/CFT correspondence using these representations can lead to a description with a finite-dimensional Hilbert space and unitary evolution. In the present work, we generalize to the case of quantum-deformed three-dimensional de Sitter spacetime and compute the entanglement entropy of a quantum field across the cosmological horizon.Comment: 18 pages, 2 figures, revtex, (v2 reference added

Realization schemes for quantum instruments in finite dimensions

We present a general dilation scheme for quantum instruments with continuous outcome space in finite dimensions, in terms of an indirect POVM measurement performed on a finite dimensional ancilla. The general result is then applied to a large class of instruments generated by operator frames, which contains group-covariant instruments as a particular case, and allows to construct dilation schemes based on a measurement on the ancilla followed by a conditional feed-forward operation on the output. In the case of tight operator frames our construction generalizes quantum teleportation and telecloning, producing a whole family of generalized teleportation schemes in which the instrument is realized via a joint POVM at the sender combined with a conditional feed-forward operation at the receiver.Comment: 22 pages, no figures, published versio