1,653 research outputs found
A fully-discrete Semi-Lagrangian scheme for a first order mean field game problem
In this work we propose a fully-discrete Semi-Lagrangian scheme for a {\it
first order mean field game system}. We prove that the resulting discretization
admits at least one solution and, in the scalar case, we prove a convergence
result for the scheme. Numerical simulations and examples are also discussed.Comment: 28 pages,16 figure
Time-optimal Unitary Operations in Ising Chains II: Unequal Couplings and Fixed Fidelity
We analytically determine the minimal time and the optimal control laws
required for the realization, up to an assigned fidelity and with a fixed
energy available, of entangling quantum gates () between
indirectly coupled qubits of a trilinear Ising chain. The control is coherent
and open loop, and it is represented by a local and continuous magnetic field
acting on the intermediate qubit. The time cost of this local quantum operation
is not restricted to be zero. When the matching with the target gate is perfect
(fidelity equal to one) we provide exact solutions for the case of equal Ising
coupling. For the more general case when some error is tolerated (fidelity
smaller than one) we give perturbative solutions for unequal couplings.
Comparison with previous numerical solutions for the minimal time to generate
the same gates with the same Ising Hamiltonian but with instantaneous local
controls shows that the latter are not time-optimal.Comment: 11 pages, no figure
The Hughes model for pedestrian dynamics and congestion modelling
In this paper we present a numerical study of some variations of the Hughes
model for pedestrian flow under different types of congestion effects. The
general model consists of a coupled non-linear PDE system involving an eikonal
equation and a first order conservation law, and it intends to approximate the
flow of a large pedestrian group aiming to reach a target as fast as possible,
while taking into account the congestion of the crowd.
We propose an efficient semi-Lagrangian scheme (SL) to approximate the
solution of the PDE system and we investigate the macroscopic effects of
different penalization functions modelling the congestion phenomena.Comment: 6 page
Brachistochrone of Entanglement for Spin Chains
We analytically investigate the role of entanglement in time-optimal state
evolution as an appli- cation of the quantum brachistochrone, a general method
for obtaining the optimal time-dependent Hamiltonian for reaching a target
quantum state. As a model, we treat two qubits indirectly cou- pled through an
intermediate qubit that is directly controllable, which represents a typical
situation in quantum information processing. We find the time-optimal unitary
evolution law and quantify residual entanglement by the two-tangle between the
indirectly coupled qubits, for all possible sets of initial pure quantum states
of a tripartite system. The integrals of the motion of the brachistochrone are
determined by fixing the minimal time at which the residual entanglement is
maximized. Entan- glement plays a role for W and GHZ initial quantum states,
and for the bi-separable initial state in which the indirectly coupled qubits
have a nonzero value of the 2-tangle.Comment: 9 pages, 4 figure
A fully-discrete scheme for systems of nonlinear Fokker-Planck-Kolmogorov equations
We consider a system of Fokker-Planck-Kolmogorov (FPK) equations, where the
dependence of the coefficients is nonlinear and nonlocal in time with respect
to the unknowns. We extend the numerical scheme proposed and studied recently
by the authors for a single FPK equation of this type. We analyse the
convergence of the scheme and we study its applicability in two examples. The
first one concerns a population model involving two interacting species and the
second one concerns two populations Mean Field Games
Square Root Actions, Metric Signature, and the Path-Integral of Quantum Gravity
We consider quantization of the Baierlein-Sharp-Wheeler form of the
gravitational action, in which the lapse function is determined from the
Hamiltonian constraint. This action has a square root form, analogous to the
actions of the relativistic particle and Nambu string. We argue that
path-integral quantization of the gravitational action should be based on a
path integrand rather than the familiar Feynman expression
, and that unitarity requires integration over manifolds of both
Euclidean and Lorentzian signature. We discuss the relation of this path
integral to our previous considerations regarding the problem of time, and
extend our approach to include fermions.Comment: 32 pages, latex. The revision is a more general treatment of the
regulator. Local constraints are now derived from a requirement of regulator
independenc
Time-Optimal Transfer of Coherence
We provide exact analytical solutions for the problem of time-optimal
transfer of coherence from one spin polarization to a three-fold coherence in a
trilinear Ising chain with a fixed energy available and subject to local
controls with a non negligible time cost. The time of transfer is optimal and
consistent with a previous numerical result obtained assuming instantaneous
local controls.Comment: Published version (with typos in eqs. (25)-(27) corrected
Testing the Standard Model by precision measurement of the weak charges of quarks
In a global analysis of the latest parity-violating electron scattering
measurements on nuclear targets, we demonstrate a significant improvement in
the experimental knowledge of the weak neutral-current lepton-quark
interactions at low energy. The precision of this new result, combined with
earlier atomic parity-violation measurements, places tight constraints on the
size of possible contributions from physics beyond the Standard Model.
Consequently, this result improves the lower-bound on the scale of relevant new
physics to ~1 TeV.Comment: 4 pages, 3 figures; v2: further details on extraction of electroweak
parameters, new figur
The mass shell of the universe
The classical field equations of general relativity can be expressed as a single geodesic equation, describing the free fall of a point particle in superspace. Based on this formulation, a ``worldline'' quantization of gravity, analogous to the Feynman-Schwinger treatment of particle propagation, is proposed, and a hidden mass-shell parameter is identified. We consider the effective action for the supermetric, which would be induced at one loop. In certain minisuperspace models, we find that this effective action is stationary for vanishing cosmological constant
Extracting nucleon strange and anapole form factors from world data
The complete world set of parity violating electron scattering data up to
Q^2~0.3 GeV^2 is analysed. We extract the current experimental determination of
the strange electric and magnetic form factors of the proton, as well as the
weak axial form factors of the proton and neutron, at Q^2 = 0.1 GeV^2. Within
experimental uncertainties, we find that the strange form factors are
consistent with zero, as are the anapole contributions to the axial form
factors. Nevertheless, the correlation between the strange and anapole
contributions suggest that there is only a small probability that these form
factors all vanish simultaneously.Comment: 4 pages, 3 figs; v2: version to appear in PR
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