161 research outputs found
An SU(2) Analog of the Azbel--Hofstadter Hamiltonian
Motivated by recent findings due to Wiegmann and Zabrodin, Faddeev and
Kashaev concerning the appearence of the quantum U_q(sl(2)) symmetry in the
problem of a Bloch electron on a two-dimensional magnetic lattice, we introduce
a modification of the tight binding Azbel--Hofstadter Hamiltonian that is a
specific spin-S Euler top and can be considered as its ``classical'' analog.
The eigenvalue problem for the proposed model, in the coherent state
representation, is described by the S-gap Lam\'e equation and, thus, is
completely solvable. We observe a striking similarity between the shapes of the
spectra of the two models for various values of the spin S.Comment: 19 pages, LaTeX, 4 PostScript figures. Relation between Cartan and
Cartesian deformation of SU(2) and numerical results added. Final version as
will appear in J. Phys. A: Math. Ge
Topology at the Planck Length
A basic arbitrariness in the determination of the topology of a manifold at
the Planck length is discussed. An explicit example is given of a `smooth'
change in topology from the 2-sphere to the 2-torus through a sequence of
noncommuting geometries. Applications are considered to the theory of D-branes
within the context of the proposed (atrix) theory.Comment: Orsay Preprint 97/34, 17 pages, Late
Nambu Quantum Mechanics on Discrete 3-Tori
We propose a quantization of linear, volume preserving, maps on the discrete
and finite 3-torus T_N^3 represented by elements of the group SL(3,Z_N). These
flows can be considered as special motions of the Nambu dynamics (linear Nambu
flows) in the three dimensional toroidal phase space and are characterized by
invariant vectors, a, of T_N^3. We quantize all such flows which are
necessarily restricted on a planar two-dimensional phase space, embedded in the
3-torus, transverse to the vector a . The corresponding maps belong to the
little group of the vector a in SL(3,Z_N) which is an SL(2,Z_N) subgroup. The
associated linear Nambu maps are generated by a pair of linear and quadratic
Hamiltonians (Clebsch-Monge potentials of the flow) and the corresponding
quantum maps, realize the metaplectic representation of SL(3,Z_N) on the
discrete group of three dimensional magnetic translations i.e. the
non-commutative 3-torus with deformation parameter the N-th root of unity.
Other potential applications of our construction are related to the
quantization of deterministic chaos in turbulent maps as well as to quantum
tomography of three dimensional objects.Comment: 13 pages, LaTeX2
Holomorphic Quantization on the Torus and Finite Quantum Mechanics
We construct explicitly the quantization of classical linear maps of on toroidal phase space, of arbitrary modulus, using the holomorphic
(chiral) version of the metaplectic representation. We show that Finite Quantum
Mechanics (FQM) on tori of arbitrary integer discretization, is a consistent
restriction of the holomorphic quantization of to the subgroup
, being the principal congruent subgroup mod l,
on a finite dimensional Hilbert space. The generators of the ``rotation group''
mod l, , for arbitrary values of l are determined as
well as their quantum mechanical eigenvalues and eigenstates.Comment: 12 pages LaTeX (needs amssymb.sty). Version as will appear in J.
Phys.
Strange Attractors in Dissipative Nambu Mechanics : Classical and Quantum Aspects
We extend the framework of Nambu-Hamiltonian Mechanics to include dissipation
in phase space. We demonstrate that it accommodates the phase space
dynamics of low dimensional dissipative systems such as the much studied Lorenz
and R\"{o}ssler Strange attractors, as well as the more recent constructions of
Chen and Leipnik-Newton. The rotational, volume preserving part of the flow
preserves in time a family of two intersecting surfaces, the so called {\em
Nambu Hamiltonians}. They foliate the entire phase space and are, in turn,
deformed in time by Dissipation which represents their irrotational part of the
flow. It is given by the gradient of a scalar function and is responsible for
the emergence of the Strange Attractors.
Based on our recent work on Quantum Nambu Mechanics, we provide an explicit
quantization of the Lorenz attractor through the introduction of
Non-commutative phase space coordinates as Hermitian matrices in
. They satisfy the commutation relations induced by one of the two
Nambu Hamiltonians, the second one generating a unique time evolution.
Dissipation is incorporated quantum mechanically in a self-consistent way
having the correct classical limit without the introduction of external degrees
of freedom. Due to its volume phase space contraction it violates the quantum
commutation relations. We demonstrate that the Heisenberg-Nambu evolution
equations for the Quantum Lorenz system give rise to an attracting ellipsoid in
the dimensional phase space.Comment: 35 pages, 4 figures, LaTe
Analytic Representation of Finite Quantum Systems
A transform between functions in R and functions in Zd is used to define the
analogue of number and coherent states in the context of finite d-dimensional
quantum systems. The coherent states are used to define an analytic
representation in terms of theta functions. All states are represented by
entire functions with growth of order 2, which have exactly d zeros in each
cell. The analytic function of a state is constructed from its zeros. Results
about the completeness of finite sets of coherent states within a cell are
derived
Phase Effect of A General Two-Higgs-Doublet Model in
In a general two-Higgs-doublet model (2HDM), without the {\it ad hoc}
discrete symmetries to prevent tree-level flavor-changing-neutral currents, an
extra phase angle in the charged-Higgs-fermion coupling is allowed. We show
that the charged-Higgs amplitude interferes destructively or constructively
with the standard model amplitude depending crucially on this phase angle. The
popular model I and II are special cases of our analysis. As a result of this
phase angle the severe constraint on the charged-Higgs boson mass imposed by
the inclusive rate of from CLEO can be relaxed. We also examine
the effects of this phase angle on the neutron electric dipole moment.
Furthermore, we also discuss other constraints on the charged-Higgs-fermion
couplings coming from measurements of mixing, , and
.Comment: LaTeX 17 pages, 3 figure
New Physics in CP Asymmetries and Rare B Decays
We review and update the effects of physics beyond the standard model on CP
asymmetries in B decays. These asymmetries can be significantly altered if
there are important new-physics contributions to \bqbqbar mixing. This same new
physics will therefore also contribute to rare, flavor-changing B decays.
Through a study of such decays, we show that it is possible to partially
distinguish the different models of new physics.Comment: 42 pages, plain TeX (macros included), 1 figure (included). A few
sentences added, references updated. Present manuscript is now identical to
the version accepted for publication in Phys. Rev.
Probing the charged Higgs boson at the LHC in the CP-violating type-II 2HDM
We present a phenomenological study of a CP-violating two-Higgs-doublet Model
with type-II Yukawa couplings at the Large Hadron Collider (LHC). In the light
of recent LHC data, we focus on the parameter space that survives the current
and past experimental constraints as well as theoretical bounds on the model.
Once the phenomenological scenario is set, we analyse the scope of the LHC in
exploring this model through the discovery of a charged Higgs boson produced in
association with a W boson, with the former decaying into the lightest neutral
Higgs and a second W state, altogether yielding a b\bar b W^+W^- signature, of
which we exploit the W^+W^- semileptonic decays.Comment: 37 pages, 16 figures; v2 updated treatment of LHC constraint
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