5,917 research outputs found
Cascading Quivers from Decaying D-branes
We use an argument analogous to that of Kachru, Pearson and Verlinde to argue
that cascades in L^{a,b,c} quiver gauge theories always preserve the form of
the quiver, and that all gauge groups drop at each step by the number M of
fractional branes. In particular, we demonstrate that an NS5-brane that sweeps
out the S^3 of the base of L^{a,b,c} destroys M D3-branes.Comment: 11 pages, 1 figure; v2: references adde
Beta-rhythm oscillations and synchronization transition in network models of Izhikevich neurons: effect of topology and synaptic type
Despite their significant functional roles, beta-band oscillations are least
understood. Synchronization in neuronal networks have attracted much attention
in recent years with the main focus on transition type. Whether one obtains
explosive transition or a continuous transition is an important feature of the
neuronal network which can depend on network structure as well as synaptic
types. In this study we consider the effect of synaptic interaction (electrical
and chemical) as well as structural connectivity on synchronization transition
in network models of Izhikevich neurons which spike regularly with beta
rhythms. We find a wide range of behavior including continuous transition,
explosive transition, as well as lack of global order. The stronger electrical
synapses are more conducive to synchronization and can even lead to explosive
synchronization. The key network element which determines the order of
transition is found to be the clustering coefficient and not the small world
effect, or the existence of hubs in a network. These results are in contrast to
previous results which use phase oscillator models such as the Kuramoto model.
Furthermore, we show that the patterns of synchronization changes when one goes
to the gamma band. We attribute such a change to the change in the refractory
period of Izhikevich neurons which changes significantly with frequency.Comment: 7 figures, 1 tabl
Holography as a highly efficient RG flow II: An explicit construction
We complete the reformulation of the holographic correspondence as a
\emph{highly efficient RG flow} that can also determine the UV data in the
field theory in the strong coupling and large limit. We introduce a special
way to define operators at any given scale in terms of appropriate
coarse-grained collective variables, without requiring the use of the
elementary fields. The Wilsonian construction is generalised by promoting the
cut-off to a functional of these collective variables. We impose three criteria
to determine the coarse-graining. The first criterion is that the effective
Ward identities for local conservation of energy, momentum, etc. should
preserve their standard forms, but in new scale-dependent background metric and
sources which are functionals of the effective single trace operators. The
second criterion is that the scale-evolution equations of the operators in the
actual background metric should be state-independent, implying that the
collective variables should not explicitly appear in them. The final criterion
is that the endpoint of the scale-evolution of the RG flow can be transformed
to a fixed point corresponding to familiar non-relativistic equations with a
finite number of parameters, such as incompressible non-relativistic
Navier-Stokes, under a certain universal rescaling of the scale and of the time
coordinate. Using previous work, we explicitly show that in the hydrodynamic
limit each such highly efficient RG flow reproduces a unique classical gravity
theory with precise UV data that satisfy our IR criterion. We obtain the
explicit coarse-graining which reproduces Einstein's equations. In a simple
example, we are also able to compute the beta function. Finally, we show how
our construction can be interpolated with the traditional Wilsonian RG flow at
a suitable scale, and can be used to develop new non-perturbative frameworks
for QCD-like theories.Comment: 1+59 pages; Introduction slightly expanded, Section V on beta
function in highly efficient RG flow added, version accepted in PR
Strong unitary and overlap uncertainty relations: theory and experiment
We derive and experimentally investigate a strong uncertainty relation valid
for any unitary operators, which implies the standard uncertainty relation
as a special case, and which can be written in terms of geometric phases. It is
saturated by every pure state of any -dimensional quantum system, generates
a tight overlap uncertainty relation for the transition probabilities of any
pure states, and gives an upper bound for the out-of-time-order
correlation function. We test these uncertainty relations experimentally for
photonic polarisation qubits, including the minimum uncertainty states of the
overlap uncertainty relation, via interferometric measurements of generalised
geometric phases.Comment: 5 pages of main text, 5 pages of Supplemental Material.
Clarifications added in this updated versio
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