4,972 research outputs found
Reconstructing the thermal Green functions at real times from those at imaginary times
By exploiting the analyticity and boundary value properties of the thermal
Green functions that result from the KMS condition in both time and energy
complex variables, we treat the general (non-perturbative) problem of
recovering the thermal functions at real times from the corresponding functions
at imaginary times, introduced as primary objects in the Matsubara formalism.
The key property on which we rely is the fact that the Fourier transforms of
the retarded and advanced functions in the energy variable have to be the
`unique Carlsonian analytic interpolations' of the Fourier coefficients of the
imaginary-time correlator, the latter being taken at the discrete Matsubara
imaginary energies, respectively in the upper and lower half-planes. Starting
from the Fourier coefficients regarded as `data set', we then develop a method
based on the Pollaczek polynomials for constructing explicitly their analytic
interpolations.Comment: 23 pages, 2 figure
An equivariant isomorphism theorem for mod reductions of arboreal Galois representations
Let be a quadratic, monic polynomial with coefficients in , where is a localization of a number ring . In this paper, we first prove that if is non-square and non-isotrivial, then there exists an absolute, effective constant with the following property: for all primes such that the reduced polynomial is non-square and non-isotrivial, the squarefree Zsigmondy set of is bounded by . Using this result, we prove that if is non-isotrivial and geometrically stable then outside a finite, effective set of primes of the geometric part of the arboreal representation of is isomorphic to that of . As an application of our results we prove R. Jones' conjecture on the arboreal Galois representation attached to the polynomial
A superfluid-droplet crystal and a free-space supersolid in a dipole-blockaded gas
A novel supersolid phase is predicted for an ensemble of Rydberg atoms in the
dipole-blockade regime, interacting via a repulsive dipolar potential
"softened" at short distances. Using exact numerical techniques, we study the
low temperature phase diagram of this system, and observe an intriguing phase
consisting of a crystal of mesoscopic superfluid droplets. At low temperature,
phase coherence throughout the whole system, and the ensuing bulk
superfluidity, are established through tunnelling of identical particles
between neighbouring droplets.Comment: 4 pages, 4 figure
Strongly correlated gases of Rydberg-dressed atoms: quantum and classical dynamics
We discuss techniques to generate long-range interactions in a gas of
groundstate alkali atoms, by weakly admixing excited Rydberg states with laser
light. This provides a tool to engineer strongly correlated phases with reduced
decoherence from inelastic collisions and spontaneous emission. As an
illustration, we discuss the quantum phases of dressed atoms with dipole-dipole
interactions confined in a harmonic potential, as relevant to experiments. We
show that residual spontaneous emission from the Rydberg state acts as a
heating mechanism, leading to a quantum-classical crossover.Comment: 4 pages, 4 figure
What is a Gene? A Two Sided View
The need to account for all currently available experimental observations
concerning the gene nature, has reshaped the concept of gene turning it from the
essentially mechanistic unit, predominant during the '70s, into a quite abstract
open and generalized entity, whose contour appears less defined as compared to the
past. Here we propose the essence of the gene to be considered double faced. In
this respect genotypic and phenotypic entities of a gene would coexist and mix
reciprocally. This harmonizes present knowledge with current definitions and
predisposes for remodelling of our thinking as a consequence of future discoveries.
A two sided view of the gene also allows to combine the genetic and epigenetic
aspects in a unique solution, being structural and functional at the same time and
simultaneously able to include the different levels in an overlapping unicum
Molecular Dipolar Crystals as High Fidelity Quantum Memory for Hybrid Quantum Computing
We study collective excitations of rotational and spin states of an ensemble
of polar molecules, which are prepared in a dipolar crystalline phase, as a
candidate for a high fidelity quantum memory. While dipolar crystals are formed
in the high density limit of cold clouds of polar molecules under 1D and 2D
trapping conditions, the crystalline structure protects the molecular qubits
from detrimental effects of short range collisions. We calculate the lifetime
of the quantum memory by identifying the dominant decoherence mechanisms, and
estimate their effects on gate operations, when a molecular ensemble qubit is
transferred to a superconducting strip line cavity (circuit QED). In the case
rotational excitations coupled by dipole-dipole interactions we identify
phonons as the main limitation of the life time of qubits. We study specific
setups and conditions, where the coupling to the phonon modes is minimized.
Detailed results are presented for a 1D dipolar chain
Designing spin-1 lattice models using polar molecules
We describe how to design a large class of always on spin-1 interactions
between polar molecules trapped in an optical lattice. The spin degrees of
freedom correspond to the hyperfine levels of a ro-vibrational ground state
molecule. Interactions are induced using a microwave field to mix ground states
in one hyperfine manifold with the spin entangled dipole-dipole coupled excited
states. Using multiple fields anistropic models in one, two, or three
dimensions, can be built with tunable spatial range. An illustrative example in
one dimension is the generalized Haldane model, which at a specific parameter
has a gapped valence bond solid ground state. The interaction strengths are
large compared to decoherence rates and should allow for probing the rich phase
structure of strongly correlated systems, including dimerized and gapped
phases.Comment: 24 pages, 5 figure
Nature-Inspired Interconnects for Self-Assembled Large-Scale Network-on-Chip Designs
Future nano-scale electronics built up from an Avogadro number of components
needs efficient, highly scalable, and robust means of communication in order to
be competitive with traditional silicon approaches. In recent years, the
Networks-on-Chip (NoC) paradigm emerged as a promising solution to interconnect
challenges in silicon-based electronics. Current NoC architectures are either
highly regular or fully customized, both of which represent implausible
assumptions for emerging bottom-up self-assembled molecular electronics that
are generally assumed to have a high degree of irregularity and imperfection.
Here, we pragmatically and experimentally investigate important design
trade-offs and properties of an irregular, abstract, yet physically plausible
3D small-world interconnect fabric that is inspired by modern network-on-chip
paradigms. We vary the framework's key parameters, such as the connectivity,
the number of switch nodes, the distribution of long- versus short-range
connections, and measure the network's relevant communication characteristics.
We further explore the robustness against link failures and the ability and
efficiency to solve a simple toy problem, the synchronization task. The results
confirm that (1) computation in irregular assemblies is a promising and
disruptive computing paradigm for self-assembled nano-scale electronics and (2)
that 3D small-world interconnect fabrics with a power-law decaying distribution
of shortcut lengths are physically plausible and have major advantages over
local 2D and 3D regular topologies
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