349 research outputs found
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
with the radial potential , we study the behavior of
the number of its negative eigenvalues, as the coupling
parameter tends to infinity. We obtain the necessary and sufficient
conditions for the semi-classical growth 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 and the coupled boundary fields
and . 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 , induced from
representations of the maximal compact subgroup of . 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 of the Euclidean Lorentz group
, such that is contained in the restriction of to .
Thus, our boundary-to-bulk operators can be compared with those in the
literature only when for a fixed we consider a 'minimal' representation
containing .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
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