327 research outputs found
Uncertainty relation and non-dispersive states in Finite Quantum Mechanics
In this letter, we provide evidence for a classical sector of states in the
Hilbert space of Finite Quantum Mechanics (FQM). We construct a subset of
states whose the minimum bound of position -momentum uncertainty (equivalent to
an effective ) vanishes. The classical regime, contrary to standard
Quantum Mechanical Systems of particles and fields, but also of strings and
branes appears in short distances of the order of the lattice spacing. {}For
linear quantum maps of long periods, we observe that time evolution leads to
fast decorrelation of the wave packets, phenomenon similar to the behavior of
wave packets in t' Hooft and Susskind holographic picture. Moreoever, we
construct explicitly a non - dispersive basis of states in accordance with t'
Hooft's arguments about the deterministic behavior of FQM.Comment: Latex file, 16pages, 3 ps-figures, version to appear in Phys.Lett.
Square-integrability of multivariate metaplectic wave-packet representations
This paper presents a systematic study for harmonic analysis of metaplectic wave-packet representations on the Hilbert function space L2(Rd). The abstract notions of symplectic wave-packet groups and metaplectic wave-packet representations will be introduced. We then present an admissibility condition on closed subgroups of the real symplectic group Sp(Rd), which guarantees the square-integrability of the associated metaplectic wave-packet representation on L2(Rd)
Implementation of group-covariant POVMs by orthogonal measurements
We consider group-covariant positive operator valued measures (POVMs) on a
finite dimensional quantum system. Following Neumark's theorem a POVM can be
implemented by an orthogonal measurement on a larger system. Accordingly, our
goal is to find an implementation of a given group-covariant POVM by a quantum
circuit using its symmetry. Based on representation theory of the symmetry
group we develop a general approach for the implementation of group-covariant
POVMs which consist of rank-one operators. The construction relies on a method
to decompose matrices that intertwine two representations of a finite group. We
give several examples for which the resulting quantum circuits are efficient.
In particular, we obtain efficient quantum circuits for a class of POVMs
generated by Weyl-Heisenberg groups. These circuits allow to implement an
approximative simultaneous measurement of the position and crystal momentum of
a particle moving on a cyclic chain.Comment: latex, 25 pages, 3 figure
Phase-averaged transport for quasi-periodic Hamiltonians
For a class of discrete quasi-periodic Schroedinger operators defined by
covariant re- presentations of the rotation algebra, a lower bound on
phase-averaged transport in terms of the multifractal dimensions of the density
of states is proven. This result is established under a Diophantine condition
on the incommensuration parameter. The relevant class of operators is
distinguished by invariance with respect to symmetry automorphisms of the
rotation algebra. It includes the critical Harper (almost-Mathieu) operator. As
a by-product, a new solution of the frame problem associated with
Weyl-Heisenberg-Gabor lattices of coherent states is given
- …