pinecone/core-2020-05-10-deduplication huggingface dataset:
Generalized Log-Majorization and Multivariate Trace Inequalities

We show that recent multivariate generalizations of the Araki-Lieb-Thirring
inequality and the Golden-Thompson inequality [Sutter, Berta, and Tomamichel,
Comm. Math. Phys. (2016)] for Schatten norms hold more generally for all
unitarily invariant norms and certain variations thereof. The main technical
contribution is a generalization of the concept of log-majorization which
allows us to treat majorization with regards to logarithmic integral averages
of vectors of singular values.Comment: 17 page
Density of States for Random Band Matrices in two dimensions

We consider a two dimensional random band matrix ensemble, in the limit of
infinite volume and fixed but large band width $W$. For this model we
rigorously prove smoothness of the averaged density of states. We also prove
that the resulting expression coincides with Wigner's semicircle law with a
precision $W^{-2+\delta },$ where $\delta\to 0$ when $W\to \infty.$ The proof
uses the supersymmetric approach and extends results by Disertori, Pinson and
Spencer from three to two dimensions.Comment: 41 pages, 2 figure
Finite type modules and Bethe ansatz equations

We introduce and study a category $\text{Fin}$ of modules of the Borel
subalgebra of a quantum affine algebra $U_q\mathfrak{g}$, where the commutative
algebra of Drinfeld generators $h_{i,r}$, corresponding to Cartan currents, has
finitely many characteristic values. This category is a natural extension of
the category of finite-dimensional $U_q\mathfrak{g}$ modules. In particular, we
classify the irreducible objects, discuss their properties, and describe the
combinatorics of the q-characters. We study transfer matrices corresponding to
modules in $\text{Fin}$. Among them we find the Baxter $Q_i$ operators and
$T_i$ operators satisfying relations of the form $T_iQ_i=\prod_j Q_j+ \prod_k
Q_k$. We show that these operators are polynomials of the spectral parameter
after a suitable normalization. This allows us to prove the Bethe ansatz
equations for the zeroes of the eigenvalues of the $Q_i$ operators acting in an
arbitrary finite-dimensional representation of $U_q\mathfrak{g}$.Comment: Latex 33 page
Characterization of the metal-insulator transport transition for the
  two-particle Anderson model

We extend to the two-particle Anderson model the characterization of the
metal-insulator transport transition obtained in the one-particle setting by
Germinet and Klein. We show that, for any fixed number of particles, the slow
spreading of wave packets in time implies the initial estimate of a modified
version of the Bootstrap Multiscale Analysis. In this new version, operators
are restricted to boxes defined with respect to the pseudo-distance in which we
have the slow spreading. At the bottom of the spectrum, within the regime of
one-particle dynamical localization, we show that this modified multiscale
analysis yields dynamical localization for the two-particle Anderson model,
allowing us to obtain a characterization of the metal-insulator transport
transition for the two-particle Anderson model at the bottom of the spectrum
Small Cocycles, Fine Torus Fibrations, and a Z^2 Subshift with Neither

Following an earlier similar conjecture of Kellendonk and Putnam, Giordano, Putnam, and Skau conjectured that all minimal, free  ZdZd  actions on Cantor sets admit “small cocycles.” These represent classes in  H1H1  that are mapped to small vectors in  RdRd  by the Ruelle–Sullivan (RS) map. We show that there exist  Z2Z2  actions where no such small cocycles exist, and where the image of  H1H1  under RS is  Z2Z2 . Our methods involve tiling spaces and shape deformations, and along the way we prove a relation between the image of RS and the set of “virtual eigenvalues,” i.e., elements of  RdRd  that become topological eigenvalues of the tiling flow after an arbitrarily small change in the shapes and sizes of the tiles.Peer-reviewedPublisher Versio
Strings in Singular Space-Times and their Universal Gauge Theory

We study the propagation of bosonic strings in singular target space-times.
For describing this, we assume this target space to be the quotient of a smooth
manifold $M$ by a singular foliation ${\cal F}$ on it. Using the technical tool
of a gauge theory, we propose a smooth functional for this scenario, such that
the propagation is assured to lie in the singular target on-shell, i.e. only
after taking into account the gauge invariant content of the theory. One of the
main new aspects of our approach is that we do not limit ${\cal F}$ to be
generated by a group action. We will show that, whenever it exists, the above
gauging is effectuated by a single geometrical and universal gauge theory,
whose target space is the generalized tangent bundle $TM\oplus T^*M$.Comment: 49 pages, 4 figure
Inequalities Between Size, Mass, Angular Momentum, and Charge for
  Axisymmetric Bodies and the Formation of Trapped Surfaces

We establish inequalities relating the size of a material body to its mass,
angular momentum, and charge, within the context of axisymmetric initial data
sets for the Einstein equations. These inequalities hold in general without the
assumption of the maximal condition, and use a notion of size which is easily
computable. Moreover, these results give rise to black hole existence criteria
which are meaningful even in the time-symmetric case, and also include certain
boundary effects.Comment: 12 page
Ultra-Weak Time Operators of Schroedinger Operators

In an abstract framework, a new concept on time operator, ultra-weak time
operator, is introduced, which is a concept weaker than that of weak time
operator. Theorems on the existence of an ultra-weak time operator are
established. As an application of the theorems, it is shown that Schroedinger
operators H with potentials V obeying suitable conditions, including the
Hamiltonian of the hydrogen atom, have ultra-weak time operators. Moreover, a
class of Borel measurable functions $f$ such that $f(H)$ has an ultra-weak time
operator is found.Comment: We add Sections 1.1,1.2 and 1.
Revisiting EPRL: All Finite-Dimensional Solutions by Naimark's
  Fundamental Theorem

In this paper we research all possible finite-dimensional representations and
corresponding values of the Barbero-Immirzi parameter contained in EPRL
simplicity constraints by using Naimark's fundamental theorem of the Lorentz
group representation theory. It turns out that for each non-zero pure imaginary
with rational modulus value of the Barbero-Immirzi parameter $\gamma = i
\frac{p}{q}, p, q \in Z, p, q \ne 0$, there is a solution of the simplicity
constraints, such that the corresponding Lorentz representation is finite
dimensional. The converse is also true - for each finite-dimensional Lorentz
representation solution of the simplicity constraints $(n, \rho)$, the
associated Barbero-Immirzi parameter is non-zero pure imaginary with rational
modulus, $\gamma = i \frac{p}{q}, p, q \in Z, p, q \ne 0$. We solve the
simplicity constraints with respect to the Barbero-Immirzi parameter and then
use Naimark's fundamental theorem of the Lorentz group representations to find
all finite-dimensional representations contained in the solutions
Low-energy Fock-space localization for attractive hard-core particles in
  disorder

We study a one-dimensional quantum system with an arbitrary number of
hard-core particles on the lattice, which are subject to a deterministic
attractive interaction as well as a random potential. Our choice of interaction
is suggested by the spectral analysis of the XXZ quantum spin chain. The main
result concerns a version of high-disorder Fock-space localization expressed
here in the configuration space of hard-core particles. The proof relies on an
energetically motivated Combes-Thomas estimate and an effective one-particle
analysis. As an application, we show the exponential decay of the two-point
function in the infinite system uniformly in the particle number.Comment: 24 page
Bounded energy waves on the black hole interior of
  Reissner-Nordstr\"om-de Sitter

Motivated by the Strong Cosmic Censorship Conjecture, in the presence of a
cosmological constant, we consider solutions of the scalar wave equation
$\Box_g\phi=0$ on fixed subextremal Reissner--Nordstr\"om--de Sitter
backgrounds $({\mathcal M}, g)$, without imposing symmetry assumptions on
$\phi$. We provide a sufficient condition, in terms of surface gravities and a
parameter for an exponential decaying Price law, for a local energy of the
waves to remain bounded up to the Cauchy horizon. The energy we consider
controls, in particular, regular transverse derivatives at the Cauchy horizon;
this allows us to extend the solutions with bounded energy, to the Cauchy
horizon, as functions in $C^0\cap H^1_{loc}$. Our results correspond to another
manifestation of the potential breakdown of Strong Cosmic Censorship in the
positive cosmological constant setting.Comment: 21 pages, 5 figure
Hadamard states for quantum Abelian duality

Abelian duality is realized naturally by combining differential cohomology
and locally covariant quantum field theory. This leads to a C$^*$-algebra of
observables, which encompasses the simultaneous discretization of both magnetic
and electric fluxes. We discuss the assignment of physically well-behaved
states to such algebra and the properties of the associated GNS triple. We show
that the algebra of observables factorizes as a suitable tensor product of
three C$^*$-algebras: the first factor encodes dynamical information, while the
other two capture topological data corresponding to electric and magnetic
fluxes. On the former factor we exhibit a state whose two-point correlation
function has the same singular structure of a Hadamard state. Specifying
suitable counterparts also on the topological factors we obtain a state for the
full theory, providing ultimately a unitary implementation of Abelian duality.Comment: 33 page
Hausdorff closed limits and rigidity in Lorentzian geometry

We begin with a basic exploration of the (point-set topological) notion of
Hausdorff closed limits in the spacetime setting. Specifically, we show that
this notion of limit is well suited to sequences of achronal sets, and use this
to generalize the `achronal limits' introduced in [12]. This, in turn, allows
for a broad generalization of the notion of Lorentzian horosphere introduced in
[12]. We prove a new rigidity result for such horospheres, which in a sense
encodes various spacetime splitting results, including the basic Lorentzian
splitting theorem. We use this to give a partial proof of the Bartnik splitting
conjecture, under a new condition involving past and future Cauchy horospheres,
which is weaker than those considered in [10] and [12]. We close with some
observations on spacetimes with spacelike causal boundary, including a rigidity
result in the positive cosmological constant case.Comment: 29 pages, 5 figure
Integrable differential systems of topological type and reconstruction
  by the topological recursion

Starting from a $d\times d$ rational Lax pair system of the form $\hbar
\partial_x \Psi= L\Psi$ and $\hbar \partial_t \Psi=R\Psi$ we prove that, under
certain assumptions (genus $0$ spectral curve and additional conditions on $R$
and $L$), the system satisfies the "topological type property". A consequence
is that the formal $\hbar$-WKB expansion of its determinantal correlators,
satisfy the topological recursion. This applies in particular to all $(p,q)$
minimal models reductions of the KP hierarchy, or to the six Painlev\'e
systems.Comment: Published version in Annales Henri Poincar\'
Central Limit Theorem and Large Deviation Principle for Continuous Time
  Open Quantum Walks

Open Quantum Walks (OQWs), originally introduced by S. Attal, are quantum
generalizations of classical Markov chains. Recently, natural continuous time
models of OQW have been developed by C. Pellegrini. These models, called
Continuous Time Open Quantum Walks (CTOQWs), appear as natural continuous time
limits of discrete time OQWs. In particular they are quantum extensions of
continuous time Markov chains. This article is devoted to the study of
homogeneous CTOQW on $\mathbb{Z}^d$. We focus namely on their associated
quantum trajectories which allow us to prove a Central Limit Theorem for the
"position" of the walker as well as a Large Deviation Principle.Comment: 31 pages, 5 figure
Fock representation of gravitational boundary modes and the discreteness
  of the area spectrum

In this article, we study the quantum theory of gravitational boundary modes
on a null surface. These boundary modes are given by a spinor and a
spinor-valued two-form, which enter the gravitational boundary term for
self-dual gravity. Using a Fock representation, we quantise the boundary
fields, and show that the area of a two-dimensional cross section turns into
the difference of two number operators. The spectrum is discrete, and it agrees
with the one known from loop quantum gravity with the correct dependence on the
Barbero--Immirzi parameter. No discrete structures (such as spin network
functions, or triangulations of space) are ever required---the entire
derivation happens at the level of the continuum theory. In addition, the area
spectrum is manifestly Lorentz invariant.Comment: 27 pages, two figure
On Scattering for Small Data of 2+1 Dimensional Equivariant
  Einstein-Wave Map System

We consider the Cauchy problem of 2+1 equivariant wave maps coupled to
Einstein's equations of general relativity and prove that two separate
(nonlinear) subclasses of the system disperse to their corresponding linearized
equations in the large. Global asymptotic behaviour of 2+1 Einstein-wave map
system is relevant because the system occurs naturally in 3+1 vacuum Einstein's
equations.Comment: Error from a previous work (Lemma 9.1 in Ref[1]) rectified. Original
  problem reduced to two special case
Area Operator in Loop Quantum Gravity

A hyperlink is a finite set of non-intersecting simple closed curves in
$\mathbb{R} \times \mathbb{R}^3$. Let $S$ be an orientable surface in
$\mathbb{R}^3$. The dynamical variables in General Relativity are the vierbein
$e$ and a $\mathfrak{su}(2)\times\mathfrak{su}(2)$-valued connection $\omega$.
Together with Minkowski metric, $e$ will define a metric $g$ on the manifold.
Denote $A_S(e)$ as the area of $S$, for a given choice of $e$.
  The Einstein-Hilbert action $S(e,\omega)$ is defined on $e$ and $\omega$. We
will quantize the area of the surface $S$ by integrating $A_S(e)$ against a
holonomy operator of a hyperlink $L$, disjoint from $S$, and the exponential of
the Einstein-Hilbert action, over the space of vierbeins $e$ and
$\mathfrak{su}(2)\times\mathfrak{su}(2)$-valued connections $\omega$. Using our
earlier work done on Chern-Simons path integrals in $\mathbb{R}^3$, we will
write this infinite dimensional path integral as the limit of a sequence of
Chern-Simons integrals. Our main result shows that the area operator can be
computed from a link-surface diagram between $L$ and $S$. By assigning an
irreducible representation of $\mathfrak{su}(2)\times\mathfrak{su}(2)$ to each
component of $L$, the area operator gives the total net momentum impact on the
surface $S$.Comment: arXiv admin note: text overlap with arXiv:1701.04397,
  arXiv:1705.0039
Quantum graphs which optimize the spectral gap

A finite discrete graph is turned into a quantum (metric) graph once a finite
length is assigned to each edge and the one-dimensional Laplacian is taken to
be the operator. We study the dependence of the spectral gap (the first
positive Laplacian eigenvalue) on the choice of edge lengths. In particular,
starting from a certain discrete graph, we seek the quantum graph for which an
optimal (either maximal or minimal) spectral gap is obtained. We fully solve
the minimization problem for all graphs. We develop tools for investigating the
maximization problem and solve it for some families of graphs
Some Remarks on the $C^0$-(in)extendibility of Spacetimes

The existence, established over the past number of years and supporting
earlier work of Ori [14], of physically relevant black hole spacetimes that
admit $C^0$ metric extensions beyond the future Cauchy horizon, while being
$C^2$-inextendible, has focused attention on fundamental issues concerning the
strong cosmic censorship conjecture. These issues were recently discussed in
the work of Jan Sbierski [17], in which he established the (nonobvious) fact
that the Schwarschild solution in global Kruskal-Szekeres coordinates is
$C^0$-inextendible. In this paper we review aspects of Sbierski's methodology
in a general context, and use similar techniques, along with some new
observations, to consider the $C^0$-inextendibility of open FLRW cosmological
models. We find that a certain special class of open FLRW spacetimes, which we
have dubbed `Milne-like,' actually admit $C^0$ extensions through the big bang.
For spacetimes that are not Milne-like, we prove some inextendibility results
within the class of spherically symmetric spacetimes.Comment: 22 pages, v2: minor changes and clarifications; reference added. To
  appear in Annales Henri Poincar
Local vs. global temperature under a positive curvature condition

For a massless free scalar field in a globally hyperbolic space-time we
compare the global temperature T, defined for the KMS states $\omega^T$, with
the local temperature $T_{\omega}(x)$ introduced by Buchholz and Schlemmer. We
prove the following claims: (1) Whenever $T_{\omega^T}(x)$ is defined, it is a
continuous, monotonically increasing function of T at every point x. (2)
$T_{\omega}(x)$ is defined when the space-time is ultra-static with compact
Cauchy surface and non-trivial scalar curvature $R\ge 0$, $\omega$ is
stationary and a few other assumptions are satisfied. Our proof of (2) relies
on the positive mass theorem. We discuss the necessity of its assumptions,
providing counter-examples in an ultra-static space-time with non-compact
Cauchy surface and R<0 somewhere. We interpret the result in terms of a
violation of the weak energy condition in the background space-time.Comment: 19 pages; v2 accepted for publicatio
Universality of single qudit gates

We consider the problem of deciding if a set of quantum one-qudit gates
$\mathcal{S}=\{g_1,\ldots,g_n\}\subset G$ is universal, i.e if the closure
$\overline{<\mathcal{S}>}$ is equal to $G$, where $G$ is either the special
unitary or the special orthogonal group. To every gate $g$ in $\mathcal{S}$ we
asign its image under the adjoint representation $\mathrm{Ad}_g$, where
$\mathrm{Ad}:G\rightarrow SO(\mathfrak{g})$ and $\mathfrak{g}$ is the Lie
algebra of $G$. The necessary condition for the universality of $\mathcal{S}$
is that the only matrices that commute with all $\mathrm{Ad}_{g_i}$'s are
proportional to the identity. If in addition there is an element in
$<\mathcal{S}>$ whose Hilbert-Schmidt distance from the centre of $G$ belongs
to $]0,\frac{1}{\sqrt{2}}]$, then $\mathcal{S}$ is universal. Using these we
provide a simple algorithm that allows deciding the universality of any set of
$d$-dimensional gates in a finite number of steps and formulate the general
classification theorem.Comment: Significantly improved universality criteria and presentation. A
  simple algorithm that allows deciding the universality of any set of gates in
  a finite number of steps added and discussed. Accepted in AH
A geometric invariant characterising initial data for the Kerr-Newman
  spacetime

We describe the construction of a geometric invariant characterising initial
data for the Kerr-Newman spacetime. This geometric invariant vanishes if and
only if the initial data set corresponds to exact Kerr-Newman initial data, and
so characterises this type of data. We first illustrate the characterisation of
the Kerr-Newman spacetime in terms of Killing spinors. The space spinor
formalism is then used to obtain a set of four independent conditions on an
initial Cauchy hypersurface that guarantee the existence of a Killing spinor on
the development of the initial data. Following a similar analysis in the vacuum
case, we study the properties of solutions to the approximate Killing spinor
equation and use them to construct the geometric invariant.Comment: 34 page
Veiled singularities for the spherically symmetric massless
  Einstein-Vlasov system

This paper continues the investigation of the formation of naked
singularities in the collapse of collisionless matter initiated in [RV]. There
the existence of certain classes of non-smooth solutions of the Einstein-Vlasov
system was proved. Those solutions are self-similar and hence not
asymptotically flat. To obtain solutions which are more physically relevant it
makes sense to attempt to cut off these solutions in a suitable way so as to
make them asymptotically flat. This task, which turns out to be technically
challenging, will be carried out in this paper.
  [RV] A. D. Rendall and J. J. L. Vel\'{a}zquez, A class of dust-like
self-similar solutions of the massless Einstein-Vlasov system. Annales Henri
Poincare 12, 919-964, (2011).Comment: 67 pages, 1 figur
Efimov effect for a three-particle system with two identical fermions

We consider a three-particle quantum system in dimension three composed of
two identical fermions of mass one and a different particle of mass $m$. The
particles interact via two-body short range potentials. We assume that the
Hamiltonians of all the two-particle subsystems do not have bound states with
negative energy and, moreover, that the Hamiltonians of the two subsystems made
of a fermion and the different particle have a zero-energy resonance. Under
these conditions and for $m<m^* = (13.607)^{-1}$, we give a rigorous proof of
the occurrence of the Efimov effect, i.e., the existence of infinitely many
negative eigenvalues for the three-particle Hamiltonian $H$. More precisely, we
prove that for $m>m^*$ the number of negative eigenvalues of $H$ is finite and
for $m<m^*$ the number $N(z)$ of negative eigenvalues of $H$ below $z<0$ has
the asymptotic behavior $N(z) \sim \mathcal C(m) |\log|z||$ for $z \rightarrow
0^-$. Moreover, we give an upper and a lower bound for the positive constant
$\mathcal C(m)$.Comment: 26 page
The Complexity of Translationally-Invariant Spin Chains with Low Local
  Dimension

We prove that estimating the ground state energy of a
translationally-invariant, nearest-neighbour Hamiltonian on a 1D spin chain is
QMAEXP-complete, even for systems of low local dimension (roughly 40). This is
an improvement over the best previously-known result by several orders of
magnitude, and it shows that spin-glass-like frustration can occur in
translationally-invariant quantum systems with a local dimension comparable to
the smallest-known non-translationally-invariant systems with similar
behaviour.
  While previous constructions of such systems rely on standard models of
quantum computation, we construct a new model that is particularly well-suited
for encoding quantum computation into the ground state of a
translationally-invariant system. This allows us to shift the proof burden from
optimizing the Hamiltonian encoding a standard computational model to proving
universality of a simple model.
  Previous techniques for encoding quantum computation into the ground state of
a local Hamiltonian allow only a linear sequence of gates, hence only a linear
(or nearly linear) path in the graph of all computational states. We extend
these techniques by allowing significantly more general paths, including
branching and cycles, thus enabling a highly efficient encoding of our
computational model. However, this requires more sophisticated techniques for
analysing the spectrum of the resulting Hamiltonian. To address this, we
introduce a framework of graphs with unitary edge labels. After relating our
Hamiltonian to the Laplacian of such a unitary labelled graph, we analyse its
spectrum by combining matrix analysis and spectral graph theory techniques.Comment: 69 page