357 research outputs found
Recent Results Regarding Affine Quantum Gravity
Recent progress in the quantization of nonrenormalizable scalar fields has
found that a suitable non-classical modification of the ground state wave
function leads to a result that eliminates term-by-term divergences that arise
in a conventional perturbation analysis. After a brief review of both the
scalar field story and the affine quantum gravity program, examination of the
procedures used in the latter surprisingly shows an analogous formulation which
already implies that affine quantum gravity is not plagued by divergences that
arise in a standard perturbation study. Additionally, guided by the projection
operator method to deal with quantum constraints, trial reproducing kernels are
introduced that satisfy the diffeomorphism constraints. Furthermore, it is
argued that the trial reproducing kernels for the diffeomorphism constraints
may also satisfy the Hamiltonian constraint as well.Comment: 32 pages, new features in this alternative approach to quantize
gravity, minor typos plus an improved argument in Sec. 9 suggested by Karel
Kucha
A de Finetti Representation Theorem for Quantum Process Tomography
In quantum process tomography, it is possible to express the experimenter's
prior information as a sequence of quantum operations, i.e., trace-preserving
completely positive maps. In analogy to de Finetti's concept of exchangeability
for probability distributions, we give a definition of exchangeability for
sequences of quantum operations. We then state and prove a representation
theorem for such exchangeable sequences. The theorem leads to a simple
characterization of admissible priors for quantum process tomography and solves
to a Bayesian's satisfaction the problem of an unknown quantum operation.Comment: 10 page
Note: Energy convexity and density matrices in molecular systems
A novel appropriate definition for the density matrix for an interacting Coulombic driven atomic or molecular system with non-integer number of particles is given. Our approach leads to a direct derivation of the proposal reported by Perdew et al. [Phys. Rev. Lett. 49, 1691 (1982)]10.1103/PhysRevLett.49.1691 and points out its suitability and perspective advances.Fil: Bochicchio, Roberto Carlos. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de FĂsica; Argentina. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas; ArgentinaFil: Rial, Diego Fernando. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas. Oficina de CoordinaciĂłn Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. SantalĂł". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. SantalĂł"; Argentin
On the computation of quantum characteristic exponents
A quantum characteristic exponent may be defined, with the same operational
meaning as the classical Lyapunov exponent when the latter is expressed as a
functional of densities. Existence conditions and supporting measure properties
are discussed as well as the problems encountered in the numerical computation
of the quantum exponents. Although an example of true quantum chaos may be
exhibited, the taming effect of quantum mechanics on chaos is quite apparent in
the computation of the quantum exponents. However, even when the exponents
vanish, the functionals used for their definition may still provide a
characterization of distinct complexity classes for quantum behavior.Comment: 11 pages Latex, 4 ps-figures. Phys. Lett. A, to appea
Reduction of Lie-Jordan Banach algebras and quantum states
A theory of reduction of Lie-Jordan Banach algebras with respect to either a
Jordan ideal or a Lie-Jordan subalgebra is presented. This theory is compared
with the standard reduction of C*-algebras of observables of a quantum system
in the presence of quantum constraints. It is shown that the later corresponds
to the particular instance of the reduction of Lie-Jordan Banach algebras with
respect to a Lie-Jordan subalgebra as described in this paper. The space of
states of the reduced Lie-Jordan Banach algebras is described in terms of
equivalence classes of extensions to the full algebra and their GNS
representations are characterized in the same way. A few simple examples are
discussed that illustrates some of the main results
Distillability and positivity of partial transposes in general quantum field systems
Criteria for distillability, and the property of having a positive partial
transpose, are introduced for states of general bipartite quantum systems. The
framework is sufficiently general to include systems with an infinite number of
degrees of freedom, including quantum fields. We show that a large number of
states in relativistic quantum field theory, including the vacuum state and
thermal equilibrium states, are distillable over subsystems separated by
arbitrary spacelike distances. These results apply to any quantum field model.
It will also be shown that these results can be generalized to quantum fields
in curved spacetime, leading to the conclusion that there is a large number of
quantum field states which are distillable over subsystems separated by an
event horizon.Comment: 25 pages, 2 figures. v2: Typos removed, references and comments
added. v3: Expanded introduction and reference list. To appear in Rev. Math.
Phy
Quantum control without access to the controlling interaction
In our model a fixed Hamiltonian acts on the joint Hilbert space of a quantum
system and its controller. We show under which conditions measurements, state
preparations, and unitary implementations on the system can be performed by
quantum operations on the controller only.
It turns out that a measurement of the observable A and an implementation of
the one-parameter group exp(iAr) can be performed by almost the same sequence
of control operations. Furthermore measurement procedures for A+B, for (AB+BA),
and for i[A,B] can be constructed from measurements of A and B. This shows that
the algebraic structure of the set of observables can be explained by the Lie
group structure of the unitary evolutions on the joint Hilbert space of the
measuring device and the measured system.
A spin chain model with nearest neighborhood coupling shows that the border
line between controller and system can be shifted consistently.Comment: 10 pages, Revte
Noncommutative Thermofield Dynamics
The real-time operator formalism for thermal quantum field theories,
thermofield dynamics, is formulated in terms of a path-integral approach in
non-commutative spaces. As an application, the two-point function for a thermal
non-commutative theory is derived at the one-loop level. The
effect of temperature and the non-commutative parameter, competing with one
another, is analyzed.Comment: 13 pages; to be published in IJMP-A
Family of solvable generalized random-matrix ensembles with unitary symmetry
We construct a very general family of characteristic functions describing
Random Matrix Ensembles (RME) having a global unitary invariance, and
containing an arbitrary, one-variable probability measure which we characterize
by a `spread function'. Various choices of the spread function lead to a
variety of possible generalized RMEs, which show deviations from the well-known
Gaussian RME originally proposed by Wigner. We obtain the correlation functions
of such generalized ensembles exactly, and show examples of how particular
choices of the spread function can describe ensembles with arbitrary eigenvalue
densities as well as critical ensembles with multifractality.Comment: 4 pages, to be published in Phys. Rev. E, Rapid Com
Are buffers around home representative of physical activity spaces among adults?
Residential buffers are frequently used to assess built environment characteristics relevant to physical activity (PA), yet little is known about how well they represent the spatial areas in which individuals undertake PA. We used System for Observing Play and Recreation in Communities data for 217 adults from five US states who wore an accelerometer and a GPS for three weeks to create newly defined PA-specific activity spaces. These PA spaces were based on PA occurring in bouts of ≥10min and were defined as 1) the single minimum convex polygon (MCP) containing all of a participant's PA bout minutes and 2) the combination of many MCPs constructed using each PA bout independently. Participants spent a large proportion of their PA bout time outside of 0.5, 1, and 5 mile residential buffers, and these residential buffers were a poor approximation of the spatial areas in which PA bouts occurred. The newly proposed GPS-based PA spaces can be used in future studies in place of the more general concept of activity space to better approximate built environments experienced during PA
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