1,041 research outputs found
A Quantum-Classical Brackets from p-Mechanics
We provide an answer to the long standing problem of mixing quantum and
classical dynamics within a single formalism. The construction is based on
p-mechanical derivation (quant-ph/0212101, quant-ph/0304023) of quantum and
classical dynamics from the representation theory of the Heisenberg group. To
achieve a quantum-classical mixing we take the product of two copies of the
Heisenberg group which represent two different Planck's constants. In
comparison with earlier guesses our answer contains an extra term of analytical
nature, which was not obtained before in purely algebraic setup.
Keywords: Moyal brackets, Poisson brackets, commutator, Heisenberg group,
orbit method, representation theory, Planck's constant, quantum-classical
mixingComment: LaTeX, 7 pages (EPL style), no figures; v2: example of dynamics with
two different Planck's constants is added, minor corrections; v3: major
revion, a complete example of quantum-classic dynamics is given; v4: few
grammatic correction
A Theoretical Treatment of the Steady-Flow, Linear, Crossed-Field, Direct-Current Plasma Accelerator for Inviscid, Adiabatic, Isothermal, Constant-Area Flow
The theory is developed from the individual equations of motion of the three components of the plasma. The effect of the ion cyclotron angle (omega tau), which is the product of the ion cyclotron frequency and the ion mean free time between collisions with neutral particles and which is proportional to the axial component of the ion slip velocity, on both Joule heating rate and accelerator length is included in the results and is shown to be small only for values of about 10(exp -3) radian or less
Unitarity Restoration in the Presence of Closed Timelike Curves
A proposal is made for a mathematically unambiguous treatment of evolution in
the presence of closed timelike curves. In constrast to other proposals for
handling the naively nonunitary evolution that is often present in such
situations, this proposal is causal, linear in the initial density matrix and
preserves probability. It provides a physically reasonable interpretation of
invertible nonunitary evolution by redefining the final Hilbert space so that
the evolution is unitary or equivalently by removing the nonunitary part of the
evolution operator using a polar decomposition.Comment: LaTeX, 17pp, Revisions: Title change, expanded and clarified
presentation of original proposal, esp. with regard to Heisenberg picture and
remaining in original Hilbert spac
Unitary Equivalence of the Metric and Holonomy Formulations of 2+1 Dimensional Quantum Gravity on the Torus
Recent work on canonical transformations in quantum mechanics is applied to
transform between the Moncrief metric formulation and the Witten-Carlip
holonomy formulation of 2+1-dimensional quantum gravity on the torus. A
non-polynomial factor ordering of the classical canonical transformation
between the metric and holonomy variables is constructed which preserves their
classical modular transformation properties. An extension of the definition of
a unitary transformation is briefly discussed and is used to find the inner
product in the holonomy variables which makes the canonical transformation
unitary. This defines the Hilbert space in the Witten-Carlip formulation which
is unitarily equivalent to the natural Hilbert space in the Moncrief
formulation. In addition, gravitational theta-states arising from ``large''
diffeomorphisms are found in the theory.Comment: 31 pages LaTeX [Important Revision: a section is added constructing
the inner product/Hilbert space for the Witten-Carlip holonomy formulation;
the proof of unitary equivalence of the metric and holonomy formulations is
then completed. Other additions include discussion of relation of canonical
and unitary transformations. Title/abstract change.
Quantum Backreaction on ``Classical'' Variables
A mathematically consistent procedure for coupling quasiclassical and quantum
variables through coupled Hamilton-Heisenberg equations of motion is derived
from a variational principle. During evolution, the quasiclassical variables
become entangled with the quantum variables with the result that the value of
the quasiclassical variables depends on the quantum state. This provides a
formalism to compute the backreaction of any quantum system on a quasiclassical
one. In particular, it leads to a natural candidate for a theory of gravity
coupled to quantized matter in which the gravitational field is not quantized.Comment: LaTeX, 10 pp. title change, minor improvement of presentatio
Einstein and Yang-Mills theories in hyperbolic form without gauge-fixing
The evolution of physical and gauge degrees of freedom in the Einstein and
Yang-Mills theories are separated in a gauge-invariant manner. We show that the
equations of motion of these theories can always be written in
flux-conservative first-order symmetric hyperbolic form. This dynamical form is
ideal for global analysis, analytic approximation methods such as
gauge-invariant perturbation theory, and numerical solution.Comment: 12 pages, revtex3.0, no figure
An Information-Theoretic Measure of Uncertainty due to Quantum and Thermal Fluctuations
We study an information-theoretic measure of uncertainty for quantum systems.
It is the Shannon information of the phase space probability distribution
\la z | \rho | z \ra , where |z \ra are coherent states, and is the
density matrix. The uncertainty principle is expressed in this measure as . For a harmonic oscillator in a thermal state, coincides with von
Neumann entropy, - \Tr(\rho \ln \rho), in the high-temperature regime, but
unlike entropy, it is non-zero at zero temperature. It therefore supplies a
non-trivial measure of uncertainty due to both quantum and thermal
fluctuations. We study as a function of time for a class of non-equilibrium
quantum systems consisting of a distinguished system coupled to a heat bath. We
derive an evolution equation for . For the harmonic oscillator, in the
Fokker-Planck regime, we show that increases monotonically. For more
general Hamiltonians, settles down to monotonic increase in the long run,
but may suffer an initial decrease for certain initial states that undergo
``reassembly'' (the opposite of quantum spreading). Our main result is to
prove, for linear systems, that at each moment of time has a lower bound
, over all possible initial states. This bound is a generalization
of the uncertainty principle to include thermal fluctuations in non-equilibrium
systems, and represents the least amount of uncertainty the system must suffer
after evolution in the presence of an environment for time .Comment: 36 pages (revised uncorrupted version), Report IC 92-93/2
Promoting Positive Youth Development The Miami Youth Development Project (YDP)
The Miami Youth Development Project (YDP) had its beginnings in the early 1990s as a grassroots response to the needs of troubled (multiproblem) young people in the community (Arnett, Kurtines, & Montgomery, 2008, this issue). YDP is an important outcome of efforts to create positive youth development interventions that draw on the strengths of developmental intervention science outreach research in the development of community-supported positive development programs (i.e., an approach that focuses on meeting community needs as well as youth needs by generating innovative knowledge of evidence-based change intervention strategies that are feasible, affordable, and sustainable in âreal worldâ settings, (Kurtines, Ferrer-Wreder, Cass Lorente, Silverman, Montgomery, 2008, this issue). Now completing its second decade, YDP represents an effort to bring together a more empowering model of knowledge development for research involvement in the community, a nuanced and contextualized notion of youth and their development, and methodologies that richly reflect rather than reduce the experiences of the young people whose development the authors seek to promote
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