2,271 research outputs found
Stackelberg strategies in linear-quadratic stochastic differential games
This paper obtains the Stackelberg solution to a class of two-player stochastic differential games described by linear state dynamics and quadratic objective functionals. The information structure of the problem is such that the players make independent noisy measurements of the initial state and are permitted to utilize only this information in constructing their controls. Furthermore, by the very nature of the Stackelberg solution concept, one of the players is assumed to know, in advance, the strategy of the other player (the leader). For this class of problems, we first establish existence and uniqueness of the Stackelberg solution and then relate the derivation of the leader's Stackelberg solution to the optimal solution of a nonstandard stochastic control problem. This stochastic control problem is solved in a more general context, and its solution is utilized in constructing the Stackelberg strategy of the leader. For the special case Gaussian statistics, it is shown that this optimal strategy is affine in observation of the leader. The paper also discusses numerical aspects of the Stackelberg solution under general statistics and develops algorithms which converge to the unique Stackelberg solution
Generating Complex Potentials with Real Eigenvalues in Supersymmetric Quantum Mechanics
In the framework of SUSYQM extended to deal with non-Hermitian Hamiltonians,
we analyze three sets of complex potentials with real spectra, recently derived
by a potential algebraic approach based upon the complex Lie algebra sl(2, C).
This extends to the complex domain the well-known relationship between SUSYQM
and potential algebras for Hermitian Hamiltonians, resulting from their common
link with the factorization method and Darboux transformations. In the same
framework, we also generate for the first time a pair of elliptic partner
potentials of Weierstrass type, one of them being real and the other
imaginary and PT symmetric. The latter turns out to be quasiexactly solvable
with one known eigenvalue corresponding to a bound state. When the Weierstrass
function degenerates to a hyperbolic one, the imaginary potential becomes PT
non-symmetric and its known eigenvalue corresponds to an unbound state.Comment: 20 pages, Latex 2e + amssym + graphics, 2 figures, accepted in Int.
J. Mod. Phys.
Flat-Space Chiral Gravity
We provide the first evidence for a holographic correspondence between a
gravitational theory in flat space and a specific unitary field theory in one
dimension lower. The gravitational theory is a flat-space limit of
topologically massive gravity in three dimensions at Chern-Simons level k=1.
The field theory is a chiral two-dimensional conformal field theory with
central charge c=24.Comment: 5 pages, v2: minor rearrangement
High-density Skyrmion matter and Neutron Stars
We examine neutron star properties based on a model of dense matter composed
of B=1 skyrmions immersed in a mesonic mean field background. The model
realizes spontaneous chiral symmetry breaking non-linearly and incorporates
scale-breaking of QCD through a dilaton VEV that also affects the mean fields.
Quartic self-interactions among the vector mesons are introduced on grounds of
naturalness in the corresponding effective field theory. Within a plausible
range of the quartic couplings, the model generates neutron star masses and
radii that are consistent with a preponderance of observational constraints,
including recent ones that point to the existence of relatively massive neutron
stars with mass M 1.7 Msun and radius R (12-14) km. If the existence of neutron
stars with such dimensions is confirmed, matter at supra-nuclear density is
stiffer than extrapolations of most microscopic models suggest.Comment: 27 pages, 5 figures, AASTeX style; to be published in The
Astrophysical Journa
Holography of 3d Flat Cosmological Horizons
We provide a first derivation of the Bekenstein-Hawking entropy of 3d flat
cosmological horizons in terms of the counting of states in a dual field
theory. These horizons appear in the shifted-boost orbifold of R^{1,2}, the
flat limit of non-extremal rotating BTZ black holes. These 3d geometries carry
non-zero charges under the asymptotic symmetry algebra of R^{1,2}, the 3d
Bondi-Metzner-Sachs (BMS3) algebra. The dual theory has the symmetries of the
2d Galilean Conformal Algebra, a contraction of two copies of the Virasoro
algebra, which is isomorphic to BMS3. We study flat holography as a limit of
AdS3/CFT2 to semi-classically compute the density of states in the dual,
exactly reproducing the bulk entropy in the limit of large charges. Our flat
horizons, remnants of the BTZ inner horizons also satisfy a first law of
thermodynamics. We comment on how the dual theory reproduces the bulk first law
and how cosmological bulk excitations are matched with boundary quantum
numbers.Comment: 5 pages; v2: Typos corrected, references update
Pseudo-Hermiticity and some consequences of a generalized quantum condition
We exploit the hidden symmetry structure of a recently proposed non-Hermitian
Hamiltonian and of its Hermitian equivalent one. This sheds new light on the
pseudo-Hermitian character of the former and allows access to a generalized
quantum condition. Special cases lead to hyperbolic and Morse-like potentials
in the framework of a coordinate-dependent mass model.Comment: 10 pages, no figur
Inductive algebras and homogeneous shifts
Inductive algebras for the irreducible unitary representations of the
universal cover of the group of unimodular two by two matrices are classified.
The classification of homogeneous shift operators is obtained as a direct
consequence. This gives a new approach to the results of Bagchi and Misra
Shape-invariant quantum Hamiltonian with position-dependent effective mass through second order supersymmetry
Second order supersymmetric approach is taken to the system describing motion
of a quantum particle in a potential endowed with position-dependent effective
mass. It is shown that the intertwining relations between second order partner
Hamiltonians may be exploited to obtain a simple shape-invariant condition.
Indeed a novel relation between potential and mass functions is derived, which
leads to a class of exactly solvable model. As an illustration of our
procedure, two examples are given for which one obtains whole spectra
algebraically. Both shape-invariant potentials exhibit harmonic-oscillator-like
or singular-oscillator-like spectra depending on the values of the
shape-invariant parameter.Comment: 16 pages, 5 figs; Present e-mail of AG: [email protected]
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