661 research outputs found
Gap equation in scalar field theory at finite temperature
We investigate the two-loop gap equation for the thermal mass of hot massless
theory and find that the gap equation itself has a non-zero finite
imaginary part. This indicates that it is not possible to find the real thermal
mass as a solution of the gap equation beyond order in perturbation
theory. We have solved the gap equation and obtain the real and the imaginary
part of the thermal mass which are correct up to order in perturbation
theory.Comment: 13 pages, Latex with axodraw, Minor corrections, Appendix adde
Putting competing orders in their place near the Mott transition
We describe the localization transition of superfluids on two-dimensional
lattices into commensurate Mott insulators with average particle density p/q
(p, q relatively prime integers) per lattice site. For bosons on the square
lattice, we argue that the superfluid has at least q degenerate species of
vortices which transform under a projective representation of the square
lattice space group (a PSG). The formation of a single vortex condensate
produces the Mott insulator, which is required by the PSG to have density wave
order at wavelengths of q/n lattice sites (n integer) along the principle axes;
such a second-order transition is forbidden in the Landau-Ginzburg-Wilson
framework. We also discuss the superfluid-insulator transition in the direct
boson representation, and find that an interpretation of the quantum
criticality in terms of deconfined fractionalized bosons is only permitted at
special values of q for which a permutative representation of the PSG exists.
We argue (and demonstrate in detail in a companion paper: L. Balents et al.,
cond-mat/0409470) that our results apply essentially unchanged to electronic
systems with short-range pairing, with the PSG determined by the particle
density of Cooper pairs. We also describe the effect of static impurities in
the superfluid: the impurities locally break the degeneracy between the q
vortex species, and this induces density wave order near each vortex. We
suggest that such a theory offers an appealing rationale for the local density
of states modulations observed by Hoffman et al. (cond-mat/0201348) in STM
studies of the vortex lattice of BSCCO, and allows a unified description of the
nucleation of density wave order in zero and finite magnetic fields. We note
signatures of our theory that may be tested by future STM experiments.Comment: 35 pages, 16 figures; (v2) part II is cond-mat/0409470; (v3) added
new appendix and clarifying remarks; (v4) corrected typo
Competing orders II: the doped quantum dimer model
We study the phases of doped spin S=1/2 quantum antiferromagnets on the
square lattice, as they evolve from paramagnetic Mott insulators with valence
bond solid (VBS) order at zero doping, to superconductors at moderate doping.
The interplay between density wave/VBS order and superconductivity is
efficiently described by the quantum dimer model, which acts as an effective
theory for the total spin S=0 sector. We extend the dimer model to include
fermionic S=1/2 excitations, and show that its mean-field, static gauge field
saddle points have projective symmetries (PSGs) similar to those of `slave'
particle U(1) and SU(2) gauge theories. We account for the non-perturbative
effects of gauge fluctuations by a duality mapping of the S=0 dimer model. The
dual theory of vortices has a PSG identical to that found in a previous paper
(L. Balents et al., cond-mat/0408329) by a duality analysis of bosons on the
square lattice. The previous theory therefore also describes fluctuations
across superconducting, supersolid and Mott insulating phases of the present
electronic model. Finally, with the aim of describing neutron scattering
experiments, we present a phenomenological model for collective S=1 excitations
and their coupling to superflow and density wave fluctuations.Comment: 22 pages, 10 figures; part I is cond-mat/0408329; (v2) changed title
and added clarification
Constraining mass of the graviton with GW170817
We consider the massive graviton phenomenological model based on the graviton's dispersion terms included into phase of gravitational wave's waveform. Such model was already considered in many works but it was based on a single leading-order dispersion term only. Here we derive a relation between relativistic gravitons emission and absorption time intervals computed up to , where is the Lorentz factor. Including the dispersion terms into the phase of gravitational wave's waveform results in two non-GR parameters of the and the post-Newtonian orders whose posteriors are used to put a constraint on the graviton's rest mass. We use the TaylorF2 waveform model to analyse the event GW170817 and report the following -confidence upper bounds on the graviton's rest mass: g and g for the high and low spin priors
Certified Policy Verification and Synthesis for MDPs under Distributional Reach-avoidance Properties
Markov Decision Processes (MDPs) are a classical model for decision making in
the presence of uncertainty. Often they are viewed as state transformers with
planning objectives defined with respect to paths over MDP states. An
increasingly popular alternative is to view them as distribution transformers,
giving rise to a sequence of probability distributions over MDP states. For
instance, reachability and safety properties in modeling robot swarms or
chemical reaction networks are naturally defined in terms of probability
distributions over states. Verifying such distributional properties is known to
be hard and often beyond the reach of classical state-based verification
techniques.
In this work, we consider the problems of certified policy (i.e. controller)
verification and synthesis in MDPs under distributional reach-avoidance
specifications. By certified we mean that, along with a policy, we also aim to
synthesize a (checkable) certificate ensuring that the MDP indeed satisfies the
property. Thus, given the target set of distributions and an unsafe set of
distributions over MDP states, our goal is to either synthesize a certificate
for a given policy or synthesize a policy along with a certificate, proving
that the target distribution can be reached while avoiding unsafe
distributions. To solve this problem, we introduce the novel notion of
distributional reach-avoid certificates and present automated procedures for
(1) synthesizing a certificate for a given policy, and (2) synthesizing a
policy together with the certificate, both providing formal guarantees on
certificate correctness. Our experimental evaluation demonstrates the ability
of our method to solve several non-trivial examples, including a multi-agent
robot-swarm model, to synthesize certified policies and to certify existing
policies.Comment: Extended version of a paper accepted at IJCAI 202
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