1,889 research outputs found
A Formal Sociologic Study of Free Will
We make a formal sociologic study of the concept of free will. By using the
language of mathematics and logic, we define what we call everlasting
societies. Everlasting societies never age: persons never age, and the goods of
the society are indestructible. The infinite history of an everlasting society
unfolds by following deterministic and probabilistic laws that do their best to
satisfy the free will of all the persons of the society.
We define three possible kinds of histories for everlasting societies:
primitive histories, good histories, and golden histories. In primitive
histories, persons are inherently selfish, and they use their free will to
obtain the personal ownerships of all the goods of the society. In good
histories, persons are inherently good, and they use their free will to
distribute the goods of the society. In good histories, a person is not only
able to desire the personal ownership of goods, but is also able to desire that
a good be owned by another person. In golden histories, free will is bound by
the ethic of reciprocity, which states that "you should wish upon others as you
would like others to wish upon yourself". In golden societies, the ethic of
reciprocity becomes a law that partially binds free will, and that must be
abided at all times. In other words, the verb "should" becomes the verb "must"
Knizhnik-Zamolodchikov equations and the Calogero-Sutherland-Moser integrable models with exchange terms
It is shown that from some solutions of generalized Knizhnik-Zamolodchikov
equations one can construct eigenfunctions of the Calogero-Sutherland-Moser
Hamiltonians with exchange terms, which are characterized by any given
permutational symmetry under particle exchange. This generalizes some results
previously derived by Matsuo and Cherednik for the ordinary
Calogero-Sutherland-Moser Hamiltonians.Comment: 13 pages, LaTeX, no figures, to be published in J. Phys.
Multipole radiation in a collisonless gas coupled to electromagnetism or scalar gravitation
We consider the relativistic Vlasov-Maxwell and Vlasov-Nordstr\"om systems
which describe large particle ensembles interacting by either electromagnetic
fields or a relativistic scalar gravity model. For both systems we derive a
radiation formula analogous to the Einstein quadrupole formula in general
relativity.Comment: 21 page
Generalization of a result of Matsuo and Cherednik to the Calogero-Sutherland- Moser integrable models with exchange terms
A few years ago, Matsuo and Cherednik proved that from some solutions of the
Knizhnik-Zamolodchikov (KZ) equations, which first appeared in conformal field
theory, one can obtain wave functions for the Calogero integrable system. In
the present communication, it is shown that from some solutions of generalized
KZ equations, one can construct wave functions, characterized by any given
permutational symmetry, for some Calogero-Sutherland-Moser integrable models
with exchange terms. Such models include the spin generalizations of the
original Calogero and Sutherland ones, as well as that with -function
interaction.Comment: Latex, 7 pages, Communication at the 4th Colloquium "Quantum Groups
and Integrable Systems", Prague (June 1995
Lax pairs, Painlev\'e properties and exact solutions of the alogero Korteweg-de Vries equation and a new (2+1)-dimensional equation
We prove the existence of a Lax pair for the Calogero Korteweg-de Vries
(CKdV) equation. Moreover, we modify the T operator in the the Lax pair of the
CKdV equation, in the search of a (2+1)-dimensional case and thereby propose a
new equation in (2+1) dimensions. We named this the (2+1)-dimensional CKdV
equation. We show that the CKdV equation as well as the (2+1)-dimensional CKdV
equation are integrable in the sense that they possess the Painlev\'e property.
Some exact solutions are also constructed
Spectrum of a spin chain with inverse square exchange
The spectrum of a one-dimensional chain of spins positioned at the
static equilibrium positions of the particles in a corresponding classical
Calogero system with an exchange interaction inversely proportional to the
square of their distance is studied. As in the translationally invariant
Haldane--Shastry model the spectrum is found to exhibit a very simple structure
containing highly degenerate ``super-multiplets''. The algebra underlying this
structure is identified and several sets of raising and lowering operators are
given explicitely. On the basis of this algebra and numerical studies we give
the complete spectrum and thermodynamics of the system.Comment: 9 pages, late
Nonlinear Schroedinger Equations within the Nelson Quantization Picture
We present a class of nonlinear Schroedinger equations (NLSEs) describing, in
the mean field approximation, systems of interacting particles. This class of
NLSEs is obtained generalizing expediently the approach proposed in Ref. [G.K.
Phys. Rev. A 55, 941 (1997)], where a classical system obeying to an
exclusion-inclusion principle is quantized using the Nelson stochastic
quantization. The new class of NLSEs is obtained starting from the most general
nonlinear classical kinetics compatible with a constant diffusion coefficient
D=\hbar/2m. Finally, in the case of s-stationary states, we propose a
transformation which linearizes the NLSEs here proposed.Comment: 5 pages, (RevTeX4), to appear in Rep. Math. Phys. 51 (2003
Abelian Chern-Simons Vortices and Holomorphic Burgers' Hierarchy
The Abelian Chern-Simons Gauge Field Theory in 2+1 dimensions and its
relation with holomorphic Burgers' Hierarchy is considered. It is shown that
the relation between complex potential and the complex gauge field as in
incompressible and irrotational hydrodynamics, has meaning of the analytic
Cole-Hopf transformation, linearizing the Burgers Hierarchy in terms of the
holomorphic Schr\"odinger Hierarchy. Then the motion of planar vortices in
Chern-Simons theory, appearing as pole singularities of the gauge field,
corresponds to motion of zeroes of the hierarchy. Using boost transformations
of the complex Galilean group of the hierarchy, a rich set of exact solutions,
describing integrable dynamics of planar vortices and vortex lattices in terms
of the generalized Kampe de Feriet and Hermite polynomials is constructed. The
results are applied to the holomorphic reduction of the Ishimori model and the
corresponding hierarchy, describing dynamics of magnetic vortices and
corresponding lattices in terms of complexified Calogero-Moser models.
Corrections on two vortex dynamics from the Moyal space-time non-commutativity
in terms of Airy functions are found.Comment: 15 pages, talk presented in Workshop `Nonlinear Physics IV: Theory
and Experiment`, 22-30 June 2006, Gallipoli, Ital
Sufficient conditions for the existence of bound states in a central potential
We show how a large class of sufficient conditions for the existence of bound
states, in non-positive central potentials, can be constructed. These
sufficient conditions yield upper limits on the critical value,
, of the coupling constant (strength), , of the
potential, , for which a first -wave bound state appears.
These upper limits are significantly more stringent than hitherto known
results.Comment: 7 page
Testing Hall-Post Inequalities With Exactly Solvable N-Body Problems
The Hall--Post inequalities provide lower bounds on -body energies in
terms of -body energies with . They are rewritten and generalized to
be tested with exactly-solvable models of Calogero-Sutherland type in one and
higher dimensions. The bound for spinless fermions in one dimension is
better saturated at large coupling than for noninteracting fermions in an
oscillatorComment: 7 pages, Latex2e, 2 .eps figure
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