3,405 research outputs found
Gravity and Yang-Mills theory
Three of the four forces of Nature are described by quantum Yang-Mills
theories with remarkable precision. The fourth force, gravity, is described
classically by the Einstein-Hilbert theory. There appears to be an inherent
incompatibility between quantum mechanics and the Einstein-Hilbert theory which
prevents us from developing a consistent quantum theory of gravity. The
Einstein-Hilbert theory is therefore believed to differ greatly from Yang-Mills
theory (which does have a sensible quantum mechanical description). It is
therefore very surprising that these two theories actually share close
perturbative ties. This article focuses on these ties between Yang-Mills theory
and the Einstein-Hilbert theory. We discuss the origin of these ties and their
implications for a quantum theory of gravity.Comment: 6 pages, based on contribution to GRF 2010, to appear in a special
edition of IJMP
One qubit almost completely reveals the dynamics of two
From the time dependence of states of one of them, the dynamics of two
interacting qubits is determined to be one of two possibilities that differ
only by a change of signs of parameters in the Hamiltonian. The only exception
is a simple particular case where several parameters in the Hamiltonian are
zero and one of the remaining nonzero parameters has no effect on the time
dependence of states of the one qubit. The mean values that describe the
initial state of the other qubit and of the correlations between the two qubits
also are generally determined to within a change of signs by the time
dependence of states of the one qubit, but with many more exceptions. An
example demonstrates all the results. Feedback in the equations of motion that
allows time dependence in a subsystem to determine the dynamics of the larger
system can occur in both classical and quantum mechanics. The role of quantum
mechanics here is just to identify qubits as the simplest objects to consider
and specify the form that equations of motion for two interacting qubits can
take.Comment: 6 pages with new and updated materia
Lie algebraic noncommuting structures from reparametrisation symmetry
We extend our earlier work of revealing both space-space and space-time
noncommuting structures in various models in particle mechanics exhibiting
reparametrisation symmetry. We show explicitly (in contrast to the earlier
results in our paper \cite{sg}) that for some special choices of the
reparametrisation parameter , one can obtain space-space noncommuting
structures which are Lie-algebraic in form even in the case of the relativistic
free particle. The connection of these structures with the existing models in
the literature is also briefly discussed. Further, there exists some values of
for which the noncommutativity in the space-space sector can be made
to vanish. As a matter of internal consistency of our approach, we also study
the angular momentum algebra in details.Comment: 9 pages Latex, some references adde
Relations Between Quantum Maps and Quantum States
The relation between completely positive maps and compound states is
investigated in terms of the notion of quantum conditional probability
Unital Positive Maps and Quantum States
We analyze the structure of the subset of states generated by unital
completely positive quantum maps, A witness that certifies that a state does
not belong to the subset generated by a given map is constructed. We analyse
the representations of positive maps and their relation to quantum
Perron-Frobenius theory.Comment: 14 page
Momentum and Mass Fluxes in a Gas Confined between Periodically Structured Surfaces at Different Temperatures
It is well known that in a gas-filled duct or channel along which a
temperature gradient is applied, a thermal creep flow is created. Here we show
that a mass and momentum flux can also be induced in a gas confined between two
parallel structured surfaces at different temperatures, i.e.
\textit{orthogonal} to the temperature gradient. We use both analytical and
numerical methods to compute the resulting fluxes. The momentum flux assumes
its maximum value in the free-molecular flow regime, the (normalized) mass flux
in the transition flow regime. The discovered phenomena could find applications
in novel methods for energy-conversion and thermal pumping of gases.Comment: 6 pages, 5 figures, updated fig.5, updated text for the numerical
metho
How state preparation can affect a quantum experiment: Quantum process tomography for open systems
We study the effects of preparation of input states in a quantum tomography
experiment. We show that maps arising from a quantum process tomography
experiment (called process maps) differ from the well know dynamical maps. The
difference between the two is due to the preparation procedure that is
necessary for any quantum experiment. We study two preparation procedures,
stochastic preparation and preparation by measurements. The stochastic
preparation procedure yields process maps that are linear, while the
preparations using von Neumann measurements lead to non-linear processes, and
can only be consistently described by a bi-linear process map. A new process
tomography recipe is derived for preparation by measurement for qubits. The
difference between the two methods is analyzed in terms of a quantum process
tomography experiment. A verification protocol is proposed to differentiate
between linear processes and bi-linear processes. We also emphasize the
preparation procedure will have a non-trivial effect for any quantum experiment
in which the system of interest interacts with its environment.Comment: 13 pages, no figures, submitted to Phys. Rev.
Zeno dynamics and constraints
We investigate some examples of quantum Zeno dynamics, when a system
undergoes very frequent (projective) measurements that ascertain whether it is
within a given spatial region. In agreement with previously obtained results,
the evolution is found to be unitary and the generator of the Zeno dynamics is
the Hamiltonian with hard-wall (Dirichlet) boundary conditions. By using a new
approach to this problem, this result is found to be valid in an arbitrary
-dimensional compact domain. We then propose some preliminary ideas
concerning the algebra of observables in the projected region and finally look
at the case of a projection onto a lower dimensional space: in such a situation
the Zeno ansatz turns out to be a procedure to impose constraints.Comment: 21 page
- …