491 research outputs found
Shimura curve computations via K3 surfaces of Neron-Severi rank at least 19
It is known that K3 surfaces S whose Picard number rho (= rank of the
Neron-Severi group of S) is at least 19 are parametrized by modular curves X,
and these modular curves X include various Shimura modular curves associated
with congruence subgroups of quaternion algebras over Q. In a family of such K3
surfaces, a surface has rho=20 if and only if it corresponds to a CM point on
X. We use this to compute equations for Shimura curves, natural maps between
them, and CM coordinates well beyond what could be done by working with the
curves directly as we did in ``Shimura Curve Computations'' (1998) =
Comment: 16 pages (1 figure drawn with the LaTeX picture environment); To
appear in the proceedings of ANTS-VIII, Banff, May 200
Critical and tricritical exponents of the Gross-Neveu model in the large- limit
The critical and the tricritical exponents of the Gross-Neveu model are
calculated in the large- limit.
Our results indicate that these exponents are given by the mean-field values.Comment: 8 pages, 8 figure
Stabilizer notation for Spekkens' toy theory
Spekkens has introduced a toy theory [Phys. Rev. A, 75, 032110 (2007)] in
order to argue for an epistemic view of quantum states. I describe a notation
for the theory (excluding certain joint measurements) which makes its
similarities and differences with the quantum mechanics of stabilizer states
clear. Given an application of the qubit stabilizer formalism, it is often
entirely straightforward to construct an analogous application of the notation
to the toy theory. This assists calculations within the toy theory, for example
of the number of possible states and transformations, and enables
superpositions to be defined for composite systems.Comment: 7+4 pages, 5 tables. v2: Clarifications added and typos fixed in
response to referee comment
Revised Phase Diagram of the Gross-Neveu Model
We confirm earlier hints that the conventional phase diagram of the discrete
chiral Gross-Neveu model in the large N limit is deficient at non-zero chemical
potential. We present the corrected phase diagram constructed in mean field
theory. It has three different phases, including a kink-antikink crystal phase.
All transitions are second order. The driving mechanism for the new structure
of baryonic matter in the Gross-Neveu model is an Overhauser type instability
with gap formation at the Fermi surface.Comment: Revtex, 12 pages, 15 figures; v2: Axis labelling in Fig. 9 correcte
Superconducting fluctuations in the Luther-Emery liquid
The single-particle superconducting Green's functions of a Luther-Emery
liquid is computed by bosonization techniques. Using a formulation introduced
by Poilblanc and Scalapino [Phys. Rev. B v. 66, art. 052513 (2002)], an
asymptotic expression of the superconducting gap is deduced in the long
wavelength and small frequency limit. Due to superconducting phase
fluctuations, the gap exhibits as a function of size L a (1/L)^{1/2K_\rho}
power-law decay as well as an interesting singularity at the spectral gap
energy. Similarities and differences with the 2-leg t-J ladder are outlined.Comment: RevTeX 4, 3 pages, 2 EPS figure
Asymptotically Free Non-Abelian Gauge Theories With Fermions and Scalars As Alternatives to QCD
In this paper we construct non-Abelian gauge theories with fermions and
scalars that nevertheless possess asymptotic freedom.The scalars are taken to
be in a chiral multiplet transforming as under
and transforming as singlets under the colour SU(3) group. We consider two
distinct scenarios, one in which the additional scalars are light and another
in which they are heavier than half the Z-boson mass. It is shown that
asymptotic freedom is obtained without requiring that all additional couplings
keep fixed ratios with each other. It is also shown that both scenarios can not
be ruled out by what are considered standard tests of QCD like R- parameter,
g-2 for muons or deep inelastic phenomena. The light mass scenario is however
ruled out by high precision Z-width data (and only by that one data).The heavy
mass scenario is still viable and is shown to naturally pass the test of
flavour changing neutral currents. It also is not ruled out by precision
electroweak oblique parameters. Many distinctive experimental signatures of
these models are also discussed.Comment: 37 pages in LATEX with 10 fig
The Weakly Coupled Gross-Neveu Model with Wilson Fermions
The nature of the phase transition in the lattice Gross-Neveu model with
Wilson fermions is investigated using a new analytical technique. This involves
a new type of weak coupling expansion which focuses on the partition function
zeroes of the model. Its application to the single flavour Gross-Neveu model
yields a phase diagram whose structure is consistent with that predicted from a
saddle point approach. The existence of an Aoki phase is confirmed and its
width in the weakly coupled region is determined. Parity, rather than chiral
symmetry breaking naturally emerges as the driving mechanism for the phase
transition.Comment: 15 pages including 1 figur
Three-qubit entangled embeddings of CPT and Dirac groups within E8 Weyl group
In quantum information context, the groups generated by Pauli spin matrices,
and Dirac gamma matrices, are known as the single qubit Pauli group P, and
two-qubit Pauli group P2, respectively. It has been found [M. Socolovsky, Int.
J. Theor. Phys. 43, 1941 (2004)] that the CPT group of the Dirac equation is
isomorphic to P. One introduces a two-qubit entangling orthogonal matrix S
basically related to the CPT symmetry. With the aid of the two-qubit swap gate,
the S matrix allows the generation of the three-qubit real Clifford group and,
with the aid of the Toffoli gate, the Weyl group W(E8) is generated (M. Planat,
Preprint 0904.3691). In this paper, one derives three-qubit entangling groups ?
P and ? P2, isomorphic to the CPT group P and to the Dirac group P2, that are
embedded into W(E8). One discovers a new class of pure theequbit quantum states
with no-vanishing concurrence and three-tangle that we name CPT states. States
of the GHZ and CPT families, and also chain-type states, encode the new
representation of the Dirac group and its CPT subgroup.Comment: 12 page
A model for spin-polarized transport in perovskite manganite bi-crystal grain boundaries
We have studied the temperature dependence of low-field magnetoresistance and
current-voltage characteristics of a low-angle bi-crystal grain boundary
junction in perovskite manganite La_{2/3}Sr_{1/3}MnO_3 thin film. By gradually
trimming the junction we have been able to reveal the non-linear behavior of
the latter. With the use of the relation M_{GB} \propto M_{bulk}\sqrt{MR^*} we
have extracted the grain boundary magnetization. Further, we demonstrate that
the built-in potential barrier of the grain boundary can be modelled by
V_{bi}\propto M_{bulk}^2 - M_{GB}^2. Thus our model connects the
magnetoresistance with the potential barrier at the grain boundary region. The
results indicate that the band-bending at the grain boundary interface has a
magnetic origin.Comment: 9 pages, 5 figure
A Two-Dimensional Model with Chiral Condensates and Cooper Pairs Having QCD-like Phase Structure
We describe how a generalization of the original Gross-Neveu model from U(N)
to O(N) flavor symmetry leads to the appearance of a pairing condensate at high
density, in agreement with the conjectured phenomenon of color
superconductivity in -dimensional QCD. Moreover, the model displays a
rich phase structure which closely resembles the one expected in two-flavor
QCD.Comment: 11 pages, 1 fugure, Presented at TMU-Yale Symposium on Dynamics of
Gauge Fields: An External Activity of APCTP, Tokyo, Japan, 13-15 Dec 199
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