10,496 research outputs found
Pseudo-unitary symmetry and the Gaussian pseudo-unitary ensemble of random matrices
Employing the currently discussed notion of pseudo-Hermiticity, we define a
pseudo-unitary group. Further, we develop a random matrix theory which is
invariant under such a group and call this ensemble of pseudo-Hermitian random
matrices as the pseudo-unitary ensemble. We obtain exact results for the
nearest-neighbour level spacing distribution for (2 X 2) PT-symmetric
Hamiltonian matrices which has a novel form, s log (1/s) near zero spacing.
This shows a level repulsion in marked distinction with an algebraic form in
the Wigner surmise. We believe that this paves way for a description of varied
phenomena in two-dimensional statistical mechanics, quantum chromodynamics, and
so on.Comment: 9 pages, 2 figures, LaTeX, submitted to the Physical Review Letters
on August 20, 200
Normalization procedure for relaxation studies in NMR quantum information processing
NMR quantum information processing studies rely on the reconstruction of the
density matrix representing the so-called pseudo-pure states (PPS). An
initially pure part of a PPS state undergoes unitary and non-unitary
(relaxation) transformations during a computation process, causing a "loss of
purity" until the equilibrium is reached. Besides, upon relaxation, the nuclear
polarization varies in time, a fact which must be taken into account when
comparing density matrices at different instants. Attempting to use time-fixed
normalization procedures when relaxation is present, leads to various anomalies
on matrices populations. On this paper we propose a method which takes into
account the time-dependence of the normalization factor. From a generic form
for the deviation density matrix an expression for the relaxing initial pure
state is deduced. The method is exemplified with an experiment of relaxation of
the concurrence of a pseudo-entangled state, which exhibits the phenomenon of
sudden death, and the relaxation of the Wigner function of a pseudo-cat state.Comment: 9 pages, 5 figures, to appear in QI
Congruences and Canonical Forms for a Positive Matrix: Application to the Schweinler-Wigner Extremum Principle
It is shown that a real symmetric [complex hermitian] positive
definite matrix is congruent to a diagonal matrix modulo a
pseudo-orthogonal [pseudo-unitary] matrix in [ ], for any
choice of partition . It is further shown that the method of proof in
this context can easily be adapted to obtain a rather simple proof of
Williamson's theorem which states that if is even then is congruent
also to a diagonal matrix modulo a symplectic matrix in
[]. Applications of these results considered include a
generalization of the Schweinler-Wigner method of `orthogonalization based on
an extremum principle' to construct pseudo-orthogonal and symplectic bases from
a given set of linearly independent vectors.Comment: 7 pages, latex, no figure
Different instances of time as different quantum modes: quantum states across space-time for continuous variables
Space-time is one of the most essential, yet most mysterious concepts in
physics. In quantum mechanics it is common to understand time as a marker of
instances of evolution and define states around all the space but at one time;
while in general relativity space-time is taken as a combinator, curved around
mass. Here we present a unified approach on both space and time in quantum
theory, and build quantum states across spacetime instead of only on spatial
slices. We no longer distinguish measurements on the same system at different
times with measurements on different systems at one time and construct
spacetime states upon these measurement statistics. As a first step towards
non-relativistic quantum field theory, we consider how to approach this in the
continuous-variable multi-mode regime. We propose six possible definitions for
spacetime states in continuous variables, based on four different measurement
processes: quadratures, displaced parity operators, position measurements and
weak measurements. The basic idea is to treat different instances of time as
different quantum modes. They are motivated by the pseudo-density matrix
formulation among indefinite causal structures and the path integral formalism.
We show that these definitions lead to desirable properties, and raise the
differences and similarities between spatial and temporal correlations. An
experimental proposal for tomography is presented, construing the operational
meaning of the spacetime states.Comment: 28 pages, comments welcom
Spindensities in Pseudo-classical kinetic theory
In this paper the classical limit of relativistic transport theories for spin
1/2 fermions is examined through a comparison with the classical kinetic theory
derived from N=1 supersymmetric classical mechanics. The conclusion is that in
the classical limit spindensities, i.e. the axial-vector contribution to the
relativistic Wigner-function, vanishes and dipole-densities, i.e. the
spin-tensor contributions to the relativistic Wigner function, may survive.Comment: Latex 22 pages, 63628 bytes. No figure
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