26,896 research outputs found
Walking in the SU(N)
We study the phase diagram as function of the number of colours and flavours
of asymptotically free non-supersymmetric theories with matter in higher
dimensional representations of arbitrary SU(N) gauge groups. Since matter in
higher dimensional representations screens more than in the fundamental a
general feature is that a lower number of flavours is needed to achieve a
near-conformal theory. We study the spectrum of the theories near the fixed
point and consider possible applications of our analysis to the dynamical
breaking of the electroweak symmetry.Comment: 12 page
Rigorous derivation of nonlinear scalar conservation laws from follow-the-leader type models via many particle limit
We prove that the unique entropy solution to a scalar nonlinear conservation
law with strictly monotone velocity and nonnegative initial condition can be
rigorously obtained as the large particle limit of a microscopic
follow-the-leader type model, which is interpreted as the discrete Lagrangian
approximation of the nonlinear scalar conservation law. More precisely, we
prove that the empirical measure (respectively the discretised density)
obtained from the follow-the-leader system converges in the 1-Wasserstein
topology (respectively in ) to the unique Kruzkov entropy solution
of the conservation law. The initial data are taken in ,
nonnegative, and with compact support, hence we are able to handle densities
with vacuum. Our result holds for a reasonably general class of velocity maps
(including all the relevant examples in the applications, e.g. in the
Lighthill-Whitham-Richards model for traffic flow) with possible degenerate
slope near the vacuum state. The proof of the result is based on discrete BV
estimates and on a discrete version of the one-sided Oleinik-type condition. In
particular, we prove that the regularizing effect
for nonlinear scalar conservation laws is intrinsic of the discrete model
Linear growth of the trace anomaly in Yang-Mills thermodynamics
In the lattice work by Miller [1,2] and in the work by Zwanziger [3] a linear
growth of the trace anomaly for high temperatures was found in pure SU(2) and
SU(3) Yang-Mills theories. These results show the remarkable property that the
corresponding systems are strong interacting even at high temperatures. We show
that within an analytical approach to Yang-Mills thermodynamics this linear
rise is obtained and is directly connected to the presence of a
temperature-dependent ground state, which describes (part of) the
nonperturbative nature of the Yang-Mills system. Our predictions are in
approximate agreement with [1,2,3]Comment: 9 pages and 2 figure
Integrability of the quantum KdV equation at c = -2
We present a simple a direct proof of the complete integrability of the
quantum KdV equation at , with an explicit description of all the
conservation laws.Comment: 9 page
Exact stabilization of entangled states in finite time by dissipative quantum circuits
Open quantum systems evolving according to discrete-time dynamics are
capable, unlike continuous-time counterparts, to converge to a stable
equilibrium in finite time with zero error. We consider dissipative quantum
circuits consisting of sequences of quantum channels subject to specified
quasi-locality constraints, and determine conditions under which stabilization
of a pure multipartite entangled state of interest may be exactly achieved in
finite time. Special emphasis is devoted to characterizing scenarios where
finite-time stabilization may be achieved robustly with respect to the order of
the applied quantum maps, as suitable for unsupervised control architectures.
We show that if a decomposition of the physical Hilbert space into virtual
subsystems is found, which is compatible with the locality constraint and
relative to which the target state factorizes, then robust stabilization may be
achieved by independently cooling each component. We further show that if the
same condition holds for a scalable class of pure states, a continuous-time
quasi-local Markov semigroup ensuring rapid mixing can be obtained. Somewhat
surprisingly, we find that the commutativity of the canonical parent
Hamiltonian one may associate to the target state does not directly relate to
its finite-time stabilizability properties, although in all cases where we can
guarantee robust stabilization, a (possibly non-canonical) commuting parent
Hamiltonian may be found. Beside graph states, quantum states amenable to
finite-time robust stabilization include a class of universal resource states
displaying two-dimensional symmetry-protected topological order, along with
tensor network states obtained by generalizing a construction due to Bravyi and
Vyalyi. Extensions to representative classes of mixed graph-product and thermal
states are also discussed.Comment: 20 + 9 pages, 9 figure
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