3,706 research outputs found
Brownian semistationary processes and conditional full support
In this note, we study the infinite-dimensional conditional laws of Brownian
semistationary processes. Motivated by the fact that these processes are
typically not semimartingales, we present sufficient conditions ensuring that a
Brownian semistationary process has conditional full support, a property
introduced by Guasoni, R\'asonyi, and Schachermayer [Ann. Appl. Probab., 18
(2008) pp. 491--520]. By the results of Guasoni, R\'asonyi, and Schachermayer,
this property has two important implications. It ensures, firstly, that the
process admits no free lunches under proportional transaction costs, and
secondly, that it can be approximated pathwise (in the sup norm) by
semimartingales that admit equivalent martingale measures.Comment: 7 page
Fundamental Limits on the Speed of Evolution of Quantum States
This paper reports on some new inequalities of
Margolus-Levitin-Mandelstam-Tamm-type involving the speed of quantum evolution
between two orthogonal pure states. The clear determinant of the qualitative
behavior of this time scale is the statistics of the energy spectrum. An
often-overlooked correspondence between the real-time behavior of a quantum
system and the statistical mechanics of a transformed (imaginary-time)
thermodynamic system appears promising as a source of qualitative insights into
the quantum dynamics.Comment: 6 pages, 1 eps figur
Generalized Complex Spherical Harmonics, Frame Functions, and Gleason Theorem
Consider a finite dimensional complex Hilbert space \cH, with dim(\cH)
\geq 3, define \bS(\cH):= \{x\in \cH \:|\: ||x||=1\}, and let \nu_\cH be
the unique regular Borel positive measure invariant under the action of the
unitary operators in \cH, with \nu_\cH(\bS(\cH))=1. We prove that if a
complex frame function f : \bS(\cH)\to \bC satisfies f \in \cL^2(\bS(\cH),
\nu_\cH), then it verifies Gleason's statement: There is a unique linear
operator A: \cH \to \cH such that for every u \in
\bS(\cH). is Hermitean when is real. No boundedness requirement is
thus assumed on {\em a priori}.Comment: 9 pages, Accepted for publication in Ann. H. Poincar\'
On the tensor convolution and the quantum separability problem
We consider the problem of separability: decide whether a Hermitian operator
on a finite dimensional Hilbert tensor product is separable or entangled. We
show that the tensor convolution defined for certain mappings on an almost
arbitrary locally compact abelian group, give rise to formulation of an
equivalent problem to the separability one.Comment: 13 pages, two sections adde
Continuous slice functional calculus in quaternionic Hilbert spaces
The aim of this work is to define a continuous functional calculus in
quaternionic Hilbert spaces, starting from basic issues regarding the notion of
spherical spectrum of a normal operator. As properties of the spherical
spectrum suggest, the class of continuous functions to consider in this setting
is the one of slice quaternionic functions. Slice functions generalize the
concept of slice regular function, which comprises power series with
quaternionic coefficients on one side and that can be seen as an effective
generalization to quaternions of holomorphic functions of one complex variable.
The notion of slice function allows to introduce suitable classes of real,
complex and quaternionic --algebras and to define, on each of these
--algebras, a functional calculus for quaternionic normal operators. In
particular, we establish several versions of the spectral map theorem. Some of
the results are proved also for unbounded operators. However, the mentioned
continuous functional calculi are defined only for bounded normal operators.
Some comments on the physical significance of our work are included.Comment: 71 pages, some references added. Accepted for publication in Reviews
in Mathematical Physic
Effects of two dimensional plasmons on the tunneling density of states
We show that gapless plasmons lead to a universal
correction to the tunneling
density of states of a clean two dimensional Coulomb interacting electron gas.
We also discuss a counterpart of this effect in the "composite fermion metal"
which forms in the presence of a quantizing perpendicular magnetic field
corresponding to the half-filled Landau level. We argue that the latter
phenomenon might be relevant for deviations from a simple scaling observed by
A.Chang et al in the tunneling characteristics of Quantum Hall liquids.Comment: 12 pages, Latex, NORDITA repor
Entanglement witness operator for quantum teleportation
The ability of entangled states to act as resource for teleportation is
linked to a property of the fully entangled fraction. We show that the set of
states with their fully entangled fraction bounded by a threshold value
required for performing teleportation is both convex and compact. This feature
enables for the existence of hermitian witness operators the measurement of
which could distinguish unknown states useful for performing teleportation. We
present an example of such a witness operator illustrating it for different
classes of states.Comment: Minor revisions to match the published version. Accepted for
publication in Physical Review Letter
Macroscopic objects in quantum mechanics: A combinatorial approach
Why we do not see large macroscopic objects in entangled states? There are
two ways to approach this question. The first is dynamic: the coupling of a
large object to its environment cause any entanglement to decrease
considerably. The second approach, which is discussed in this paper, puts the
stress on the difficulty to observe a large scale entanglement. As the number
of particles n grows we need an ever more precise knowledge of the state, and
an ever more carefully designed experiment, in order to recognize entanglement.
To develop this point we consider a family of observables, called witnesses,
which are designed to detect entanglement. A witness W distinguishes all the
separable (unentangled) states from some entangled states. If we normalize the
witness W to satisfy |tr(W\rho)| \leq 1 for all separable states \rho, then the
efficiency of W depends on the size of its maximal eigenvalue in absolute
value; that is, its operator norm ||W||. It is known that there are witnesses
on the space of n qbits for which ||W|| is exponential in n. However, we
conjecture that for a large majority of n-qbit witnesses ||W|| \leq O(\sqrt{n
logn}). Thus, in a non ideal measurement, which includes errors, the largest
eigenvalue of a typical witness lies below the threshold of detection. We prove
this conjecture for the family of extremal witnesses introduced by Werner and
Wolf (Phys. Rev. A 64, 032112 (2001)).Comment: RevTeX, 14 pages, some additions to the published version: A second
conjecture added, discussion expanded, and references adde
Quantum graphs as holonomic constraints
We consider the dynamics on a quantum graph as the limit of the dynamics
generated by a one-particle Hamiltonian in R^2 with a potential having a deep
strict minimum on the graph, when the width of the well shrinks to zero. For a
generic graph we prove convergence outside the vertices to the free dynamics on
the edges. For a simple model of a graph with two edges and one vertex, we
prove convergence of the dynamics to the one generated by the Laplacian with
Dirichlet boundary conditions in the vertex.Comment: 28 pages, 3 figure
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