190 research outputs found
Structure and consequences of vortex-core states in p-wave superfluids
It is now well established that in two-dimensional chiral p-wave paired
superfluids, the vortices carry zero-energy modes which obey non-abelian
exchange statistics and can potentially be used for topological quantum
computation. In such superfluids there may also exist other excitations below
the bulk gap inside the cores of vortices. We study the properties of these
subgap states, and argue that their presence affects the topological protection
of the zero modes. In conventional superconductors where the chemical potential
is of the order of the Fermi energy of a non-interacting Fermi gas, there is a
large number of subgap states and the mini-gap towards the lowest of these
states is a small fraction of the Fermi energy. It is therefore difficult to
cool the system to below the mini-gap and at experimentally available
temperatures, transitions between the subgap states, including the zero modes,
will occur and can alter the quantum states of the zero-modes. We show that
compound qubits involving the zero-modes and the parity of the occupation
number of the subgap states on each vortex are still well defined. However,
practical schemes taking into account all subgap states would nonetheless be
difficult to achieve. We propose to avoid this difficulty by working in the
regime of small chemical potential mu, near the transition to a strongly paired
phase, where the number of subgap states is reduced. We develop the theory to
describe this regime of strong pairing interactions and we show how the subgap
states are ultimately absorbed into the bulk gap. Since the bulk gap vanishes
as mu -> 0 there is an optimum value mu_c which maximises the combined gap. We
propose cold atomic gases as candidate systems where the regime of strong
interactions can be explored, and explicitly evaluate mu_c in a Feshbach
resonant K-40 gas.Comment: 19 pages, 10 figures; v2: main text as published version, additional
detail included as appendice
The averaged null energy condition for general quantum field theories in two dimensions
It is shown that the averaged null energy condition is fulfilled for a dense,
translationally invariant set of vector states in any local quantum field
theory in two-dimensional Minkowski spacetime whenever the theory has a mass
gap and possesses an energy-momentum tensor. The latter is assumed to be a
Wightman field which is local relative to the observables, generates locally
the translations, is divergence-free, and energetically bounded. Thus the
averaged null energy condition can be deduced from completely generic, standard
assumptions for general quantum field theory in two-dimensional flat spacetime.Comment: LateX2e, 16 pages, 1 eps figur
Simple Quantum Systems in Spacetimes with Closed Timelike Curves
Three simple examples illustrate properties of path integral amplitudes in
fixed background spacetimes with closed timelike curves: non-relativistic
potential scattering in the Born approximation is non-unitary, but both an
example with hard spheres and the exact solution of a totally discrete model
are unitary.Comment: 15 pages, CALT-68-180
Design and Synthesis of a Novel Alpha-Methylene Lactone Chemotherapeutic Agent
Goniothalamin, a natural product isolated from the dried stem bark of Malaysian plants of the genus Goniothalamus, has been shown to induce apoptosis in cancer cells. The bioactivity of this molecule is though to be due to its ability to react with thiols. One mechanism involves its reaction with glutathione, a natural antioxidant found in all cells. Using a four step synthetic sequence, a novel gamma-lactone analogue of goniothalamin has been prepared that replaces the endocylic double bond in goniothalamin\u27s lactone core with an exocyclic double bond. It is anticipated that this alteration will allow the compound to react more rapidly with thiols and therefore increase its cytotoxicity towards cancer cells
The averaged null energy condition and difference inequalities in quantum field theory
Recently, Larry Ford and Tom Roman have discovered that in a flat cylindrical
space, although the stress-energy tensor itself fails to satisfy the averaged
null energy condition (ANEC) along the (non-achronal) null geodesics, when the
``Casimir-vacuum" contribution is subtracted from the stress-energy the
resulting tensor does satisfy the ANEC inequality. Ford and Roman name this
class of constraints on the quantum stress-energy tensor ``difference
inequalities." Here I give a proof of the difference inequality for a minimally
coupled massless scalar field in an arbitrary two-dimensional spacetime, using
the same techniques as those we relied on to prove ANEC in an earlier paper
with Robert Wald. I begin with an overview of averaged energy conditions in
quantum field theory.Comment: 20 page
Quantum interest in two dimensions
The quantum interest conjecture of Ford and Roman asserts that any
negative-energy pulse must necessarily be followed by an over-compensating
positive-energy one within a certain maximum time delay. Furthermore, the
minimum amount of over-compensation increases with the separation between the
pulses. In this paper, we first study the case of a negative-energy square
pulse followed by a positive-energy one for a minimally coupled, massless
scalar field in two-dimensional Minkowski space. We obtain explicit expressions
for the maximum time delay and the amount of over-compensation needed, using a
previously developed eigenvalue approach. These results are then used to give a
proof of the quantum interest conjecture for massless scalar fields in two
dimensions, valid for general energy distributions.Comment: 17 pages, 4 figures; final version to appear in PR
From wormhole to time machine: Comments on Hawking's Chronology Protection Conjecture
The recent interest in ``time machines'' has been largely fueled by the
apparent ease with which such systems may be formed in general relativity,
given relatively benign initial conditions such as the existence of traversable
wormholes or of infinite cosmic strings. This rather disturbing state of
affairs has led Hawking to formulate his Chronology Protection Conjecture,
whereby the formation of ``time machines'' is forbidden. This paper will use
several simple examples to argue that the universe appears to exhibit a
``defense in depth'' strategy in this regard. For appropriate parameter regimes
Casimir effects, wormhole disruption effects, and gravitational back reaction
effects all contribute to the fight against time travel. Particular attention
is paid to the role of the quantum gravity cutoff. For the class of model
problems considered it is shown that the gravitational back reaction becomes
large before the Planck scale quantum gravity cutoff is reached, thus
supporting Hawking's conjecture.Comment: 43 pages,ReV_TeX,major revision
Open and Closed Universes, Initial Singularities and Inflation
The existence of initial singularities in expanding universes is proved
without assuming the timelike convergence condition. The assumptions made in
the proof are ones likely to hold both in open universes and in many closed
ones. (It is further argued that at least some of the expanding closed
universes that do not obey a key assumption of the theorem will have initial
singularities on other grounds.) The result is significant for two reasons:
(a)~previous closed-universe singularity theorems have assumed the timelike
convergence condition, and (b)~the timelike convergence condition is known to
be violated in inflationary spacetimes. An immediate consequence of this
theorem is that a recent result on initial singularities in open,
future-eternal, inflating spacetimes may now be extended to include many closed
universes. Also, as a fringe benefit, the time-reverse of the theorem may be
applied to gravitational collapse.Comment: 27 pages, Plain TeX (figures are embedded in the file itself and they
will emerge if it is processed according to the instructions at the top of
the file
Averaged Energy Conditions in 4D Evaporating Black Hole Backgrounds
Using Visser's semi-analytical model for the stress-energy tensor
corresponding to the conformally coupled massless scalar field in the Unruh
vacuum, we examine, by explicitly evaluating the relevant integrals over
half-complete geodesics, the averaged weak (AWEC) and averaged null (ANEC)
energy conditions along with Ford-Roman quantum inequality-type restrictions on
negative energy in the context of four dimensional evaporating black hole
backgrounds. We find that in all cases where the averaged energy conditions
fail, there exist quantum inequality bounds on the magnitude and duration of
negative energy densities.Comment: Revtex, 13 pages, to appear in Phy. Rev.
Restrictions on negative energy density in a curved spacetime
Recently a restriction ("quantum inequality-type relation") on the
(renormalized) energy density measured by a static observer in a "globally
static" (ultrastatic) spacetime has been formulated by Pfenning and Ford for
the minimally coupled scalar field, in the extension of quantum inequality-type
relation on flat spacetime of Ford and Roman. They found negative lower bounds
for the line integrals of energy density multiplied by a sampling (weighting)
function, and explicitly evaluate them for some specific spacetimes. In this
paper, we study the lower bound on spacetimes whose spacelike hypersurfaces are
compact and without boundary. In the short "sampling time" limit, the bound has
asymptotic expansion. Although the expansion can not be represented by locally
invariant quantities in general due to the nonlocal nature of the integral, we
explicitly evaluate the dominant terms in the limit in terms of the invariant
quantities. We also make an estimate for the bound in the long sampling time
limit.Comment: LaTex, 23 Page
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