16 research outputs found
Local tuning of Coupling Constants allows for Quantum Fields in Curved Spacetime in the Lab
In this paper we will investigate how one can create emergent curved
spacetimes by locally tuning the coupling constants of condensed matter
systems. In the continuum limit we thus obtain continuous effective quantum
fields living on curved spacetimes. In particular, using Stingnet condensates
we can obtain effective electromagnetism. We will show for example how we
obtain quantum electromagnetism (U(1)-Yang-Mills) in a black hole
(Schwarzschild) spacetime.Comment: 11 page
Emission spectra of self-dual black holes
We calculate the particle spectra of evaporating self-dual black holes that
are potential dark matter candidates. We first estimate the relevant mass and
temperature range and find that the masses are below the Planck mass, and the
temperature of the black holes is small compared to their mass. In this limit,
we then derive the number-density of the primary emission particles, and, by
studying the wave-equation of a scalar field in the background metric of the
black hole, show that we can use the low energy approximation for the greybody
factors. We finally arrive at the expression for the spectrum of secondary
particle emission from a dark matter halo constituted of self-dual black holes.Comment: 15 pages, 6 figures, typos corrected, reference adde
Conserved Topological Defects in Non-Embedded Graphs in Quantum Gravity
We follow up on previous work which found that commonly used graph evolution
moves lead to conserved quantities that can be expressed in terms of the
braiding of the graph in its embedding space. We study non-embedded graphs
under three distinct sets of dynamical rules and find non-trivial conserved
quantities that can be expressed in terms of topological defects in the dual
geometry. For graphs dual to 2-dimensional simplicial complexes we identify all
the conserved quantities of the evolution. We also indicate expected results
for graphs dual to 3-dimensional simplicial complexes.Comment: 42 pages, 34 figure
Lieb-Robinson bounds with dependence on interaction strengths
We propose new Lieb-Robinson bounds (bounds on the speed of propagation of
information in quantum systems) with an explicit dependence on the interaction
strengths of the Hamiltonian. For systems with more than two interactions it is
found that the Lieb-Robinson speed is not always algebraic in the interaction
strengths. We consider Hamiltonians with any finite number of bounded operators
and also a certain class of unbounded operators. We obtain bounds and
propagation speeds for quantum systems on lattices and also general graphs
possessing a kind of homogeneity and isotropy. One area for which this
formalism could be useful is the study of quantum phase transitions which occur
when interactions strengths are varied.Comment: 19 pages, 1 figure, minor modification
A Simple Guard for Learned Optimizers
If the trend of learned components eventually outperforming their
hand-crafted version continues, learned optimizers will eventually outperform
hand-crafted optimizers like SGD or Adam. Even if learned optimizers (L2Os)
eventually outpace hand-crafted ones in practice however, they are still not
provably convergent and might fail out of distribution. These are the questions
addressed here. Currently, learned optimizers frequently outperform generic
hand-crafted optimizers (such as gradient descent) at the beginning of learning
but they generally plateau after some time while the generic algorithms
continue to make progress and often overtake the learned algorithm as Aesop's
tortoise which overtakes the hare. L2Os also still have a difficult time
generalizing out of distribution. Heaton et al. proposed Safeguarded L2O (GL2O)
which can take a learned optimizer and safeguard it with a generic learning
algorithm so that by conditionally switching between the two, the resulting
algorithm is provably convergent. We propose a new class of Safeguarded L2O,
called Loss-Guarded L2O (LGL2O), which is both conceptually simpler and
computationally less expensive. The guarding mechanism decides solely based on
the expected future loss value of both optimizers. Furthermore, we show
theoretical proof of LGL2O's convergence guarantee and empirical results
comparing to GL2O and other baselines showing that it combines the best of both
L2O and SGD and that in practice converges much better than GL2O.Comment: 8 pages main article, 19 figures total, 2 pages of references, 7
pages of appendix. ICML 2022. Added Appendix Section H with extra experiments
about stabilit
Lieb-Robinson bounds for commutator-bounded operators
We generalize the Lieb-Robinson theorem to systems whose Hamiltonian is the
sum of local operators whose commutators are bounded.Comment: 5 pages, minor editorial change
Generalized Uncertainty Principle and Self-dual Black Holes
The Generalized Uncertainty Principle suggests corrections to the Uncertainty
Principle as the energy increases towards the Planck value. It provides a
natural transition between the expressions for the Compton wavelength below the
Planck mass and the black hole event horizon size above this mass. It also
suggests corrections to the the event horizon size as the black hole mass falls
towards the Planck value, leading to the concept of a Generalized Event
Horizon. Extrapolating below the Planck mass suggests the existence of a new
class of black holes, whose size is of order the Compton wavelength for their
mass. Such sub-Planckian black holes have recently been discovered in the
context of loop quantum gravity and it is possible that this applies more
generally. This suggests an intriguing connection between black holes, the
Uncertainty Principle and quantum gravity.Comment: 13 Pages, 6 figure