832 research outputs found
Uses of a small field value which falls from a metastable maximum over cosmological times
We consider a small, metastable maximum vacuum expectation value of
order of a few eV, for a pseudoscalar Goldstone-like field, which is related to
the scalar inflaton field in an idealized model of a cosmological,
spontaneously-broken chiral symmetry. The b field allows for relating
semi-quantitatively three distinct quantities in a cosmological context.
(1) A very small, residual vacuum energy density or effective cosmological
constant of ~ lambda b_0^4 ~ 2.7 x 10^{-47}GeV^4, for lambda ~ 3 x 10^{-14},
the same as an empirical inflaton self-coupling.
(2) A tiny neutrino mass, less then b_0.
(3) A possible small variation downward of the proton to electron mass ratio
over cosmological time. The latter arises from the motion downward of the
field over cosmological time, toward a nonzero limiting value as . Such behavior is consistent with an equation of motion.
We argue that hypothetical b quanta, potentially inducing new long-range
forces, are absent, because of negative, effective squared mass in an equation
of motion for -field fluctuations.Comment: version accepted for publication in Mod.Phys.Lett.
Anomaly Cancellation in 2+1 dimensions in the presence of a domainwall mass
A Fermion in 2+1 dimensions, with a mass function which depends on one
spatial coordinate and passes through a zero ( a domain wall mass), is
considered. In this model, originally proposed by Callan and Harvey, the gauge
variation of the effective gauge action mainly consists of two terms. One comes
from the induced Chern-Simons term and the other from the chiral fermions,
bound to the 1+1 dimensional wall, and they are expected to cancel each other.
Though there exist arguments in favour of this, based on the possible forms of
the effective action valid far from the wall and some facts about theories of
chiral fermions in 1+1 dimensions, a complete calculation is lacking. In this
paper we present an explicit calculation of this cancellation at one loop valid
even close to the wall. We show that, integrating out the ``massive'' modes of
the theory does produce the Chern-Simons term, as appreciated previously. In
addition we show that it generates a term that softens the high energy
behaviour of the 1+1 dimensional effective chiral theory thereby resolving an
ambiguity present in a general 1+1 dimensional theory.Comment: 17 pages, LaTex file, CU-TP-61
A Hardy inequality in twisted waveguides
We show that twisting of an infinite straight three-dimensional tube with
non-circular cross-section gives rise to a Hardy-type inequality for the
associated Dirichlet Laplacian. As an application we prove certain stability of
the spectrum of the Dirichlet Laplacian in locally and mildly bent tubes.
Namely, it is known that any local bending, no matter how small, generates
eigenvalues below the essential spectrum of the Laplacian in the tubes with
arbitrary cross-sections rotated along a reference curve in an appropriate way.
In the present paper we show that for any other rotation some critical strength
of the bending is needed in order to induce a non-empty discrete spectrum.Comment: LaTeX, 20 page
Quantum Adiabatic Algorithms, Small Gaps, and Different Paths
We construct a set of instances of 3SAT which are not solved efficiently using the simplestquantum adiabatic algorithm. These instances are obtained by picking randomclauses all consistent with two disparate planted solutions and then penalizing one ofthem with a single additional clause. We argue that by randomly modifying the beginningHamiltonian, one obtains (with substantial probability) an adiabatic path thatremoves this difficulty. This suggests that the quantum adiabatic algorithm should ingeneral be run on each instance with many different random paths leading to the problemHamiltonian. We do not know whether this trick will help for a random instance of3SAT (as opposed to an instance from the particular set we consider), especially if theinstance has an exponential number of disparate assignments that violate few clauses.We use a continuous imaginary time Quantum Monte Carlo algorithm in a novel way tonumerically investigate the ground state as well as the first excited state of our system.Our arguments are supplemented by Quantum Monte Carlo data from simulations withup to 150 spins.United States. Dept. of Energy (Cooperative Research Agreement DE-FG02-94ER40818)W. M. Keck Foundation Center for Extreme Quantum Information TheoryU.S. Army Research Laboratory (Grant W911NF-09-1-0438)National Science Foundation (U.S.) (Grant CCF-0829421
Robustness of adiabatic passage trough a quantum phase transition
We analyze the crossing of a quantum critical point based on exact results
for the transverse XY model. In dependence of the change rate of the driving
field, the evolution of the ground state is studied while the transverse
magnetic field is tuned through the critical point with a linear ramping. The
excitation probability is obtained exactly and is compared to previous studies
and to the Landau-Zener formula, a long time solution for non-adiabatic
transitions in two-level systems. The exact time dependence of the excitations
density in the system allows to identify the adiabatic and diabatic regions
during the sweep and to study the mesoscopic fluctuations of the excitations.
The effect of white noise is investigated, where the critical point transmutes
into a non-hermitian ``degenerate region''. Besides an overall increase of the
excitations during and at the end of the sweep, the most destructive effect of
the noise is the decay of the state purity that is enhanced by the passage
through the degenerate region.Comment: 16 pages, 15 figure
Spectrum of the Schr\"odinger operator in a perturbed periodically twisted tube
We study Dirichlet Laplacian in a screw-shaped region, i.e. a straight
twisted tube of a non-circular cross section. It is shown that a local
perturbation which consists of "slowing down" the twisting in the mean gives
rise to a non-empty discrete spectrum.Comment: LaTeX2e, 10 page
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
Chiral Symmetry Breaking and Pion Wave Function
We consider here chiral symmetry breaking through nontrivial vacuum structure
with quark antiquark condensates. We then relate the condensate function to the
wave function of pion as a Goldstone mode. This simultaneously yields the pion
also as a quark antiquark bound state as a localised zero mode in vacuum. We
illustrate the above with Nambu Jona-Lasinio model to calculate different
pionic properties in terms of the vacuum structure for breaking of exact or
approximate chiral symmetry, as well as the condensate fluctuations giving rise
to mesons.Comment: latex, revtex, 16 page
Fluctuation-dissipation theorem and quantum tunneling with dissipation
We suggest to take the fluctuation-dissipation theorem of Callen and Welton
as a basis to study quantum dissipative phenomena (such as macroscopic quantum
tunneling) in a manner analogous to the Nambu-Goldstone theorem for spontaneous
symmetry breakdown. It is shown that the essential physical contents of the
Caldeira-Leggett model such as the suppression of quantum coherence by Ohmic
dissipation are derived from general principles only, namely, the
fluctuation-dissipation theorem and unitarity and causality (i.e., dispersion
relations), without referring to an explicit form of the Lagrangian. An
interesting connection between quantum tunneling with Ohmic dissipation and the
Anderson's orthogonality theorem is also noted.Comment: To appear in Phys. Rev.
Effective Hamiltonian approach to adiabatic approximation in open systems
The adiabatic approximation in open systems is formulated through the
effective Hamiltonian approach. By introducing an ancilla, we embed the open
system dynamics into a non-Hermitian quantum dynamics of a composite system,
the adiabatic evolution of the open system is then defined as the adiabatic
dynamics of the composite system. Validity and invalidity conditions for this
approximation are established and discussed. A High-order adiabatic
approximation for open systems is introduced. As an example, the adiabatic
condition for an open spin- particle in time-dependent magnetic
fields is analyzed.Comment: 6 pages, 2 figure
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