78 research outputs found
Sr2V3O9 and Ba2V3O9: quasi one-dimensional spin-systems with an anomalous low temperature susceptibility
The magnetic behaviour of the low-dimensional Vanadium-oxides Sr2V3O9 and
Ba2V3O9 was investigated by means of magnetic susceptibility and specific heat
measurements. In both compounds, the results can be very well described by an
S=1/2 Heisenberg antiferromagnetic chain with an intrachain exchange of J = 82
K and J = 94 K in Sr2V3O9 and Ba2V3O9, respectively. In Sr2V3O9,
antiferromagnetic ordering at T_N = 5.3 K indicate a weak interchain exchange
of the order of J_perp ~ 2 K. In contrast, no evidence for magnetic order was
found in Ba2V3O9 down to 0.5 K, pointing to an even smaller interchain
coupling. In both compounds, we observe a pronounced Curie-like increase of the
susceptibility below 30 K, which we tentatively attribute to a staggered field
effect induced by the applied magnetic field. Results of LDA calculations
support the quasi one-dimensional character and indicate that in Sr2V3O9, the
magnetic chain is perpendicular to the structural one with the magnetic
exchange being transferred through VO4 tetrahedra.Comment: Submitted to Phy. Rev.
A topos for algebraic quantum theory
The aim of this paper is to relate algebraic quantum mechanics to topos
theory, so as to construct new foundations for quantum logic and quantum
spaces. Motivated by Bohr's idea that the empirical content of quantum physics
is accessible only through classical physics, we show how a C*-algebra of
observables A induces a topos T(A) in which the amalgamation of all of its
commutative subalgebras comprises a single commutative C*-algebra. According to
the constructive Gelfand duality theorem of Banaschewski and Mulvey, the latter
has an internal spectrum S(A) in T(A), which in our approach plays the role of
a quantum phase space of the system. Thus we associate a locale (which is the
topos-theoretical notion of a space and which intrinsically carries the
intuitionistic logical structure of a Heyting algebra) to a C*-algebra (which
is the noncommutative notion of a space). In this setting, states on A become
probability measures (more precisely, valuations) on S(A), and self-adjoint
elements of A define continuous functions (more precisely, locale maps) from
S(A) to Scott's interval domain. Noting that open subsets of S(A) correspond to
propositions about the system, the pairing map that assigns a (generalized)
truth value to a state and a proposition assumes an extremely simple
categorical form. Formulated in this way, the quantum theory defined by A is
essentially turned into a classical theory, internal to the topos T(A).Comment: 52 pages, final version, to appear in Communications in Mathematical
Physic
Geometric Approach to Pontryagin's Maximum Principle
Since the second half of the 20th century, Pontryagin's Maximum Principle has
been widely discussed and used as a method to solve optimal control problems in
medicine, robotics, finance, engineering, astronomy. Here, we focus on the
proof and on the understanding of this Principle, using as much geometric ideas
and geometric tools as possible. This approach provides a better and clearer
understanding of the Principle and, in particular, of the role of the abnormal
extremals. These extremals are interesting because they do not depend on the
cost function, but only on the control system. Moreover, they were discarded as
solutions until the nineties, when examples of strict abnormal optimal curves
were found. In order to give a detailed exposition of the proof, the paper is
mostly self\textendash{}contained, which forces us to consider different areas
in mathematics such as algebra, analysis, geometry.Comment: Final version. Minors changes have been made. 56 page
Defects and glassy dynamics in solid He-4: Perspectives and current status
We review the anomalous behavior of solid He-4 at low temperatures with
particular attention to the role of structural defects present in solid. The
discussion centers around the possible role of two level systems and structural
glassy components for inducing the observed anomalies. We propose that the
origin of glassy behavior is due to the dynamics of defects like dislocations
formed in He-4. Within the developed framework of glassy components in a solid,
we give a summary of the results and predictions for the effects that cover the
mechanical, thermodynamic, viscoelastic, and electro-elastic contributions of
the glassy response of solid He-4. Our proposed glass model for solid He-4 has
several implications: (1) The anomalous properties of He-4 can be accounted for
by allowing defects to freeze out at lowest temperatures. The dynamics of solid
He-4 is governed by glasslike (glassy) relaxation processes and the
distribution of relaxation times varies significantly between different
torsional oscillator, shear modulus, and dielectric function experiments. (2)
Any defect freeze-out will be accompanied by thermodynamic signatures
consistent with entropy contributions from defects. It follows that such
entropy contribution is much smaller than the required superfluid fraction, yet
it is sufficient to account for excess entropy at lowest temperatures. (3) We
predict a Cole-Cole type relation between the real and imaginary part of the
response functions for rotational and planar shear that is occurring due to the
dynamics of defects. Similar results apply for other response functions. (4)
Using the framework of glassy dynamics, we predict low-frequency yet to be
measured electro-elastic features in defect rich He-4 crystals. These
predictions allow one to directly test the ideas and very presence of glassy
contributions in He-4.Comment: 33 pages, 13 figure
Spectroscopic fingerprint of charge order melting driven by quantum fluctuations in a cuprate
Theoretical Physic
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