115 research outputs found
New Algebraic Quantum Many-body Problems
We develop a systematic procedure for constructing quantum many-body problems
whose spectrum can be partially or totally computed by purely algebraic means.
The exactly-solvable models include rational and hyperbolic potentials related
to root systems, in some cases with an additional external field. The
quasi-exactly solvable models can be considered as deformations of the previous
ones which share their algebraic character.Comment: LaTeX 2e with amstex package, 36 page
Explicit solution of the (quantum) elliptic Calogero-Sutherland model
We derive explicit formulas for the eigenfunctions and eigenvalues of the
elliptic Calogero-Sutherland model as infinite series, to all orders and for
arbitrary particle numbers and coupling parameters. The eigenfunctions obtained
provide an elliptic deformation of the Jack polynomials. We prove in certain
special cases that these series have a finite radius of convergence in the nome
of the elliptic functions, including the two particle (= Lam\'e) case for
non-integer coupling parameters.Comment: v1: 17 pages. The solution is given as series in q but only to low
order. v2: 30 pages. Results significantly extended. v3: 35 pages. Paper
completely revised: the results of v1 and v2 are extended to all order
Integrals of motion of the Haldane Shastry Model
In this letter we develop a method to construct all the integrals of motion
of the Haldane-Shastry model of spins, equally spaced around a circle,
interacting through a exchange interaction. These integrals of motion
respect the Yangian symmetry algebra of the Hamiltonian.Comment: 13 pages, REVTEX v3.
A Novel Long Range Spin Chain and Planar N=4 Super Yang-Mills
We probe the long-range spin chain approach to planar N=4 gauge theory at
high loop order. A recently employed hyperbolic spin chain invented by
Inozemtsev is suitable for the SU(2) subsector of the state space up to three
loops, but ceases to exhibit the conjectured thermodynamic scaling properties
at higher orders. We indicate how this may be bypassed while nevertheless
preserving integrability, and suggest the corresponding all-loop asymptotic
Bethe ansatz. We also propose the local part of the all-loop gauge transfer
matrix, leading to conjectures for the asymptotically exact formulae for all
local commuting charges. The ansatz is finally shown to be related to a
standard inhomogeneous spin chain. A comparison of our ansatz to semi-classical
string theory uncovers a detailed, non-perturbative agreement between the
corresponding expressions for the infinite tower of local charge densities.
However, the respective Bethe equations differ slightly, and we end by refining
and elaborating a previously proposed possible explanation for this
disagreement.Comment: 48 pages, 1 figure. v2, further results added: discussion of the
relationship to an inhomogeneous spin chain, normalization in sec 3 unified,
v3: minor mistakes corrected, published versio
Quantum Inozemtsev model, quasi-exact solvability and N-fold supersymmetry
Inozemtsev models are classically integrable multi-particle dynamical systems
related to Calogero-Moser models. Because of the additional q^6 (rational
models) or sin^2(2q) (trigonometric models) potentials, their quantum versions
are not exactly solvable in contrast with Calogero-Moser models. We show that
quantum Inozemtsev models can be deformed to be a widest class of partly
solvable (or quasi-exactly solvable) multi-particle dynamical systems. They
posses N-fold supersymmetry which is equivalent to quasi-exact solvability. A
new method for identifying and solving quasi-exactly solvable systems, the
method of pre-superpotential, is presented.Comment: LaTeX2e 28 pages, no figure
Phenomenology of a light scalar: the dilaton
We make use of the language of non-linear realizations to analyze
electro-weak symmetry breaking scenarios in which a light dilaton emerges from
the breaking of a nearly conformal strong dynamics, and compare the
phenomenology of the dilaton to that of the well motivated light composite
Higgs scenario. We argue that -- in addition to departures in the
decay/production rates into massless gauge bosons mediated by the conformal
anomaly -- characterizing features of the light dilaton scenario (as well as
other scenarios admitting a light CP-even scalar not directly related to the
breaking of the electro-weak symmetry) are off-shell events at high invariant
mass involving two longitudinally polarized vector bosons and a dilaton, and
tree-level flavor violating processes. Accommodating both electro-weak
precision measurements and flavor constraints appears especially challenging in
the ambiguous scenario in which the Higgs and the dilaton fields strongly mix.
We show that warped higgsless models of electro-weak symmetry breaking are
explicit and tractable realizations of this limiting case.
The relation between the naive radion profile often adopted in the study of
holographic realizations of the light dilaton scenario and the actual dynamical
dilaton field is clarified in the Appendix.Comment: 21 page
Elite opinion and foreign policy in post-communist Russia
Russian elite opinion on matters of foreign policy may be classified as ‘Liberal Westerniser’, ‘Pragmatic Nationalist’ and ‘Fundamentalist Nationalist’, terms that reflect longstanding debates about the country’s relationship with the outside world. An analysis of press
statements and election manifestoes together with a programme of elite interviews between 2004 and 2006 suggests a clustering of opinion on a series of strategic issues. Liberal Westernisers seek the closest possible relationship with Europe, and favour eventual membership of the EU and NATO. Pragmatic Nationalists are more inclined to favour practical co-operation, and do not assume an identity of values or interests with the Western countries. Fundamentalist Nationalists place more emphasis on the other former Soviet republics, and on Asia as much as Europe, and see the West as a threat to Russian values as well as to its state interests. Each of these positions,
in turn, draws on an identifiable set of domestic constituencies: Liberal Westernisers on the promarket political parties, Pragmatic Nationalists on the presidential administration and defence and security ministries, and Fundamentalist Nationalists on the Orthodox Church and Communists
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
The Poisson bracket compatible with the classical reflection equation algebra
We introduce a family of compatible Poisson brackets on the space of polynomial matrices, which contains the reflection equation algebra bracket.
Then we use it to derive a multi-Hamiltonian structure for a set of integrable
systems that includes the Heisenberg magnet with boundary conditions, the
generalized Toda lattices and the Kowalevski top.Comment: 13 pages, LaTeX with AmsFont
Exactly solvable potentials of Calogero type for q-deformed Coxeter groups
We establish that by parameterizing the configuration space of a
one-dimensional quantum system by polynomial invariants of q-deformed Coxeter
groups it is possible to construct exactly solvable models of Calogero type. We
adopt the previously introduced notion of solvability which consists of
relating the Hamiltonian to finite dimensional representation spaces of a Lie
algebra. We present explicitly the -case for which we construct the
potentials by means of suitable gauge transformations.Comment: 22 pages Late
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