524 research outputs found
Huber's theorem for hyperbolic orbisurfaces
We show that for compact orientable hyperbolic orbisurfaces, the Laplace spectrum determines the length spectrum as well as the number of singular points of a given order. The converse also holds, giving a full generalization of Huber's theorem to the setting of compact orientable hyperbolic orbisurfaces
Lifetime of double occupancies in the Fermi-Hubbard model
We investigate the decay of artificially created double occupancies in a
repulsive Fermi-Hubbard system in the strongly interacting limit using
diagrammatic many-body theory and experiments with ultracold fermions on
optical lattices. The lifetime of the doublons is found to scale exponentially
with the ratio of the on-site repulsion to the bandwidth. We show that the
dominant decay process in presence of background holes is the excitation of a
large number of particle hole pairs to absorb the energy of the doublon. We
also show that the strongly interacting nature of the background state is
crucial in obtaining the correct estimate of the doublon lifetime in these
systems. The theoretical estimates and the experimental data are in fair
quantitative agreement
Anomalous Expansion of Attractively Interacting Fermionic Atoms in an Optical Lattice
Strong correlations can dramatically modify the thermodynamics of a quantum
many-particle system. Especially intriguing behaviour can appear when the
system adiabatically enters a strongly correlated regime, for the interplay
between entropy and strong interactions can lead to counterintuitive effects. A
well known example is the so-called Pomeranchuk effect, occurring when liquid
3He is adiabatically compressed towards its crystalline phase. Here, we report
on a novel anomalous, isentropic effect in a spin mixture of attractively
interacting fermionic atoms in an optical lattice. As we adiabatically increase
the attraction between the atoms we observe that the gas, instead of
contracting, anomalously expands. This expansion results from the combination
of two effects induced by pair formation in a lattice potential: the
suppression of quantum fluctuations as the attraction increases, which leads to
a dominant role of entropy, and the progressive loss of the spin degree of
freedom, which forces the gas to excite additional orbital degrees of freedom
and expand to outer regions of the trap in order to maintain the entropy. The
unexpected thermodynamics we observe reveal fundamentally distinctive features
of pairing in the fermionic Hubbard model.Comment: 6 pages (plus appendix), 6 figure
Estimating the nuclear level density with the Monte Carlo shell model
A method for making realistic estimates of the density of levels in even-even
nuclei is presented making use of the Monte Carlo shell model (MCSM). The
procedure follows three basic steps: (1) computation of the thermal energy with
the MCSM, (2) evaluation of the partition function by integrating the thermal
energy, and (3) evaluating the level density by performing the inverse Laplace
transform of the partition function using Maximum Entropy reconstruction
techniques. It is found that results obtained with schematic interactions,
which do not have a sign problem in the MCSM, compare well with realistic
shell-model interactions provided an important isospin dependence is accounted
for.Comment: 14 pages, 3 postscript figures. Latex with RevTex. Submitted as a
rapid communication to Phys. Rev.
On the Reeh-Schlieder Property in Curved Spacetime
We attempt to prove the existence of Reeh-Schlieder states on curved
spacetimes in the framework of locally covariant quantum field theory using the
idea of spacetime deformation and assuming the existence of a Reeh-Schlieder
state on a diffeomorphic (but not isometric) spacetime. We find that physically
interesting states with a weak form of the Reeh-Schlieder property always exist
and indicate their usefulness. Algebraic states satisfying the full
Reeh-Schlieder property also exist, but are not guaranteed to be of physical
interest.Comment: 13 pages, 2 figure
Local covariant quantum field theory over spectral geometries
A framework which combines ideas from Connes' noncommutative geometry, or
spectral geometry, with recent ideas on generally covariant quantum field
theory, is proposed in the present work. A certain type of spectral geometries
modelling (possibly noncommutative) globally hyperbolic spacetimes is
introduced in terms of so-called globally hyperbolic spectral triples. The
concept is further generalized to a category of globally hyperbolic spectral
geometries whose morphisms describe the generalization of isometric embeddings.
Then a local generally covariant quantum field theory is introduced as a
covariant functor between such a category of globally hyperbolic spectral
geometries and the category of involutive algebras (or *-algebras). Thus, a
local covariant quantum field theory over spectral geometries assigns quantum
fields not just to a single noncommutative geometry (or noncommutative
spacetime), but simultaneously to ``all'' spectral geometries, while respecting
the covariance principle demanding that quantum field theories over isomorphic
spectral geometries should also be isomorphic. It is suggested that in a
quantum theory of gravity a particular class of globally hyperbolic spectral
geometries is selected through a dynamical coupling of geometry and matter
compatible with the covariance principle.Comment: 21 pages, 2 figure
Thermometry with spin-dependent lattices
We propose a method for measuring the temperature of strongly correlated
phases of ultracold atom gases confined in spin-dependent optical lattices. In
this technique, a small number of "impurity" atoms--trapped in a state that
does not experience the lattice potential--are in thermal contact with atoms
bound to the lattice. The impurity serves as a thermometer for the system
because its temperature can be straightforwardly measured using time-of-flight
expansion velocity. This technique may be useful for resolving many open
questions regarding thermalization in these isolated systems. We discuss the
theory behind this method and demonstrate proof-of-principle experiments,
including the first realization of a 3D spin-dependent lattice in the strongly
correlated regime.Comment: 22 pages, 8 figures v2: Several references added; Section on heating
rates updated to include dipole fluctuation terms; Section added on the
limitations of the proposed method. To appear in New Journal of Physic
Dirac field on Moyal-Minkowski spacetime and non-commutative potential scattering
The quantized free Dirac field is considered on Minkowski spacetime (of
general dimension). The Dirac field is coupled to an external scalar potential
whose support is finite in time and which acts by a Moyal-deformed
multiplication with respect to the spatial variables. The Moyal-deformed
multiplication corresponds to the product of the algebra of a Moyal plane
described in the setting of spectral geometry. It will be explained how this
leads to an interpretation of the Dirac field as a quantum field theory on
Moyal-deformed Minkowski spacetime (with commutative time) in a setting of
Lorentzian spectral geometries of which some basic aspects will be sketched.
The scattering transformation will be shown to be unitarily implementable in
the canonical vacuum representation of the Dirac field. Furthermore, it will be
indicated how the functional derivatives of the ensuing unitary scattering
operators with respect to the strength of the non-commutative potential induce,
in the spirit of Bogoliubov's formula, quantum field operators (corresponding
to observables) depending on the elements of the non-commutative algebra of
Moyal-Minkowski spacetime.Comment: 60 pages, 1 figur
A geometrical origin for the covariant entropy bound
Causal diamond-shaped subsets of space-time are naturally associated with
operator algebras in quantum field theory, and they are also related to the
Bousso covariant entropy bound. In this work we argue that the net of these
causal sets to which are assigned the local operator algebras of quantum
theories should be taken to be non orthomodular if there is some lowest scale
for the description of space-time as a manifold. This geometry can be related
to a reduction in the degrees of freedom of the holographic type under certain
natural conditions for the local algebras. A non orthomodular net of causal
sets that implements the cutoff in a covariant manner is constructed. It gives
an explanation, in a simple example, of the non positive expansion condition
for light-sheet selection in the covariant entropy bound. It also suggests a
different covariant formulation of entropy bound.Comment: 20 pages, 8 figures, final versio
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