41,457 research outputs found
Crystal properties of eigenstates for quantum cat maps
Using the Bargmann-Husimi representation of quantum mechanics on a torus
phase space, we study analytically eigenstates of quantized cat maps. The
linearity of these maps implies a close relationship between classically
invariant sublattices on the one hand, and the patterns (or `constellations')
of Husimi zeros of certain quantum eigenstates on the other hand. For these
states, the zero patterns are crystals on the torus. As a consequence, we can
compute explicit families of eigenstates for which the zero patterns become
uniformly distributed on the torus phase space in the limit . This
result constitutes a first rigorous example of semi-classical equidistribution
for Husimi zeros of eigenstates in quantized one-dimensional chaotic systems.Comment: 43 pages, LaTeX, including 7 eps figures Some amendments were made in
order to clarify the text, mainly in the 4 first sections. Figures are
unchanged. To be published in: Nonlinearit
New Chiral Fermions, a New Gauge Interaction, Dirac Neutrinos, and Dark Matter
We propose that all light fermionic degrees of freedom, including the
Standard Model (SM) fermions and all possible light beyond-the-standard-model
fields, are chiral with respect to some spontaneously broken abelian gauge
symmetry. Hypercharge, for example, plays this role for the SM fermions. We
introduce a new symmetry, , for all new light fermionic states.
Anomaly cancellations mandate the existence of several new fermion fields with
nontrivial charges. We develop a concrete model of this type, for
which we show that (i) some fermions remain massless after
breaking -- similar to SM neutrinos -- and (ii) accidental global symmetries
translate into stable massive particles -- similar to SM protons. These
ingredients provide a solution to the dark matter and neutrino mass puzzles
assuming one also postulates the existence of heavy degrees of freedom that act
as "mediators" between the two sectors. The neutrino mass mechanism described
here leads to parametrically small Dirac neutrino masses, and the model also
requires the existence of at least four Dirac sterile neutrinos. Finally, we
describe a general technique to write down chiral-fermions-only models that are
at least anomaly-free under a gauge symmetry
New upper bounds on sphere packings I
We develop an analogue for sphere packing of the linear programming bounds
for error-correcting codes, and use it to prove upper bounds for the density of
sphere packings, which are the best bounds known at least for dimensions 4
through 36. We conjecture that our approach can be used to solve the sphere
packing problem in dimensions 8 and 24.Comment: 26 pages, 1 figur
Holographic Probes of Anti-de Sitter Spacetimes
We describe probes of anti-de Sitter spacetimes in terms of conformal field
theories on the AdS boundary. Our basic tool is a formula that relates bulk and
boundary states -- classical bulk field configurations are dual to expectation
values of operators on the boundary. At the quantum level we relate the
operator expansions of bulk and boundary fields. Using our methods, we discuss
the CFT description of local bulk probes including normalizable wavepackets,
fundamental and D-strings, and D-instantons. Radial motions of probes in the
bulk spacetime are related to motions in scale on the boundary, demonstrating a
scale-radius duality. We discuss the implications of these results for the
holographic description of black hole horizons in the boundary field theory.Comment: 28 pages, LaTex. References adde
Discreteness Corrections to the Effective Hamiltonian of Isotropic Loop Quantum Cosmology
One of the qualitatively distinct and robust implication of Loop Quantum
Gravity (LQG) is the underlying discrete structure. In the cosmological context
elucidated by Loop Quantum Cosmology (LQC), this is manifested by the
Hamiltonian constraint equation being a (partial) difference equation. One
obtains an effective Hamiltonian framework by making the continuum
approximation followed by a WKB approximation. In the large volume regime,
these lead to the usual classical Einstein equation which is independent of
both the Barbero-Immirzi parameter as well as . In this work we
present an alternative derivation of the effective Hamiltonian by-passing the
continuum approximation step. As a result, the effective Hamiltonian is
obtained as a close form expression in . These corrections to the
Einstein equation can be thought of as corrections due to the underlying
discrete (spatial) geometry with controlling the size of these
corrections. These corrections imply a bound on the rate of change of the
volume of the isotropic universe. In most cases these are perturbative in
nature but for cosmological constant dominated isotropic universe, there are
significant deviations.Comment: Revtex4, 24 pages, 3 figures. In version 2, one reference and a para
pertaining to it are added. In the version 3, some typos are corrected and
remark 4 in section III is revised. Final version to appear in Class. Quantum
Gra
Exact mass-coupling relation for the homogeneous sine-Gordon model
We derive the exact mass-coupling relation of the simplest multi-scale
quantum integrable model, i.e., the homogeneous sine-Gordon model with two mass
scales. The relation is obtained by comparing the perturbed conformal field
theory description of the model valid at short distances to the large distance
bootstrap description based on the model's integrability. In particular, we
find a differential equation for the relation by constructing conserved tensor
currents which satisfy a generalization of the sum rule Ward identity.
The mass-coupling relation is written in terms of hypergeometric functions.Comment: 6 pages, 2 figures. (v2) references and clarifications added;
original title "Exact mass-coupling relation of the simplest multi-scale
quantum integrable model" changed for journa
No unique solution to the seismological problem of standing kink MHD waves
The aim of this paper is to point out that the classic seismological problem
using observations and theoretical expressions for the periods and damping
times of transverse standing magnetohydrodynamic (MHD) waves in coronal loops
is better referred to as a reduced seismological problem. Reduced emphasises
the fact that only a small number of characteristic quantities of the
equilibrium profiles can be determined. Reduced also implies that there is no
unique solution to the full seismological problem. Even the reduced
seismological problem does not allow a unique solution. Bayesian inference
results support our mathematical arguments and offer insight into the
relationship between the algebraic and the probabilistic inversions.Comment: 10 pages, accepted in A&
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