3,753 research outputs found
Classical and nonclassical randomness in quantum measurements
The space of positive operator-valued measures on the Borel sets of a compact
(or even locally compact) Hausdorff space with values in the algebra of linear
operators acting on a d-dimensional Hilbert space is studied from the
perspectives of classical and non-classical convexity through a transform
that associates any positive operator-valued measure with a certain
completely positive linear map of the homogeneous C*-algebra
into . This association is achieved by using an operator-valued integral
in which non-classical random variables (that is, operator-valued functions)
are integrated with respect to positive operator-valued measures and which has
the feature that the integral of a random quantum effect is itself a quantum
effect. A left inverse for yields an integral representation,
along the lines of the classical Riesz Representation Theorem for certain
linear functionals on , of certain (but not all) unital completely
positive linear maps . The extremal and
C*-extremal points of the space of POVMS are determined.Comment: to appear in Journal of Mathematical Physic
Nambu-Goldstone Mechanism in Real-Time Thermal Field Theory
In a one-generation fermion condensate scheme of electroweak symmetry
breaking, it is proven based on Schwinger-Dyson equation in the real-time
thermal field theory in the fermion bubble diagram approximation that, at
finite temperature below the symmetry restoration temperature , a
massive Higgs boson and three massless Nambu-Goldstone bosons could emerge from
the spontaneous breaking of electroweak group
if the two fermion flavors in the one generation are mass-degenerate, thus
Goldstone Theorem is rigorously valid in this case. However, if the two fermion
flavors have unequal masses, owing to "thermal flactuation", the Goldstone
Theorem will be true only approximately for a very large momentum cut-off
in zero temperature fermion loop or for low energy scales. All
possible pinch singularities are proven to cancel each other, as is expected in
a real-time thermal field theory.Comment: 11 pages, revtex, no figure, Phys. Rev. D, to appea
Kondo Problem and Related One-Dimensional Quantum Systems: Bethe Ansatz Solution and Boundary Conformal Field Theory
We review some exact results on Kondo impurity systems derived from
Bethe-ansatz solutions and boundary conformal field theory with particular
emphasis on universal aspects of the phenomenon. The finite-size spectra
characterizing the low-energy fixed point are computed from the Bethe-ansatz
solutions of various models related to the Kondo problem. Using the finite-size
scaling argument, we investigate their exact critical properties. We also
discuss that a universal relation between the Kondo effect and the impurity
effect in one-dimensional quantum systems usefully expedites our understanding
of these different phenomena.Comment: 6 pages, no figure
Exact Critical Properties of the Multi-Component Interacting Fermion Model with Boundaries
Exact critical properties of the one-dimensional SU() interacting fermion
model with open boundaries are studied by using the Bethe ansatz method. We
derive the surface critical exponents of various correlation functions using
boundary conformal field theory. They are classified into two types, i.e. the
exponents for the chiral SU() Tomonaga-Luttinger liquid and those related to
the orthogonality catastrophe. We discuss a possible application of the results
to the photoemission (absorption) in the edge state of the fractional quantum
Hall effect.Comment: 17 pages, RevTe
Boundary susceptibility in the spin-1/2 chain: Curie like behavior without magnetic impurities
We investigate the low-temperature thermodynamics of the spin-1/2 Heisenberg
chain with open ends. On the basis of boundary conformal field theory arguments
and numerical density matrix renormalization group calculations, it is
established that in the isotropic case the impurity susceptibility exhibits a
Curie-like divergent behavior as the temperature decreases, even in the absence
of magnetic impurities. A similar singular temperature dependence is also found
in the boundary contributions of the specific heat coefficient. In the
anisotropic case, for , these boundary quantities still show
singular temperature dependence obeying a power law with an anomalous
dimension. Experimental consequences will be discussed.Comment: 5 pages, 1 figure, final versio
Zeta functions, renormalization group equations, and the effective action
We demonstrate how to extract all the one-loop renormalization group
equations for arbitrary quantum field theories from knowledge of an appropriate
Seeley--DeWitt coefficient. By formally solving the renormalization group
equations to one loop, we renormalization group improve the classical action,
and use this to derive the leading-logarithms in the one-loop effective action
for arbitrary quantum field theories.Comment: 4 pages, ReV-TeX 3.
Exact finite-size spectrum for the multi-channel Kondo model and Kac-Moody fusion rules
The finite-size spectrum for the multi-channel Kondo model is derived
analytically from the exact solution, by mapping the nontrivial Z part of
the Kondo scattering into that for the RSOS model coupled with the impurity.
The analysis is performed for the case of , where is the number of
channel and is the impurity spin. The result obtained is in accordance with
the Kac-Moody fusion hypothesis proposed by Affleck and Ludwig.Comment: RevTex, 4 page
Effects of anisotropic spin-exchange interactions in spin ladders
We investigate the effects of the Dzialoshinskii-Moriya (DM) and
Kaplan-Shekhtman-Entin-Wohlman-Aharony (KSEA) interactions on various
thermodynamic and magnetic properties of a spin 1/2 ladder. Using the Majorana
fermion representation, we derive the spectrum of low energy excitations for a
pure DM interaction and in presence of a superimposed KSEA interaction. We
calculate the various correlation functions for both cases and discuss how they
are modified with respect to the case of an isotropic ladder. We also discuss
the electron spin resonance (ESR) spectrum of the system and show that it is
strongly influenced by the orientation of the magnetic field with respect to
the Dzialoshinskii-Moriya vector. Implications of our calculations for NMR and
ESR experiments on ladder systems are discussed.Comment: 14 pages, 4 eps figures, corrected calculation of NMR rate (v3
Geometrical frustration induced (semi-)metal to insulator transition
We study the low-energy properties of the geometrically frustrated Hubbard
model on a three-dimensional pyrochlore lattice and a two-dimensional
checkerboard lattice on the basis of the renormalization group method and mean
field analysis. It is found that in the half-filling case, a (semi-)metal to
insulator transition (MIT) occurs. Also, in the insulating phase, which has a
spin gap, the spin rotational symmetry is not broken, while charge ordering
exists. The results are applied to the description of the MIT observed in the
pyrochlore system .Comment: 4 pages, 5 figure
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