8,466 research outputs found
Hydrodynamic fluctuations in relativistic superfluids
The Hamiltonian formulation of superfluids based on noncanonical Poisson
brackets is studied in detail. The assumption that the momentum density is
proportional to the flow of the conserved energy is shown to lead to the
covariant relativistic theory previously suggested by Khalatnikov, Lebedev and
Carter, and some potentials in this theory are given explicitly. We discuss
hydrodynamic fluctuations in the presence of dissipative effects and we derive
the corresponding set of hydrodynamic correlation functions. Kubo relations for
the transport coefficients are obtained.Comment: 13 pages, no figures, two references adde
Self-assembled Zeeman slower based on spherical permanent magnets
We present a novel type of longitudinal Zeeman slower. The magnetic field
profile is generated by a 3D array of permanent spherical magnets, which are
self-assembled into a stable structure. The simplicity and stability of the
design make it quick to assemble and inexpensive. In addition, as with other
permanent magnet slowers, no electrical current or water cooling is required.
We describe the theory, assembly, and testing of this new design
Baxter operator and Archimedean Hecke algebra
In this paper we introduce Baxter integral Q-operators for finite-dimensional
Lie algebras gl(n+1) and so(2n+1). Whittaker functions corresponding to these
algebras are eigenfunctions of the Q-operators with the eigenvalues expressed
in terms of Gamma-functions. The appearance of the Gamma-functions is one of
the manifestations of an interesting connection between Mellin-Barnes and
Givental integral representations of Whittaker functions, which are in a sense
dual to each other. We define a dual Baxter operator and derive a family of
mixed Mellin-Barnes-Givental integral representations. Givental and
Mellin-Barnes integral representations are used to provide a short proof of the
Friedberg-Bump and Bump conjectures for G=GL(n+1) proved earlier by Stade. We
also identify eigenvalues of the Baxter Q-operator acting on Whittaker
functions with local Archimedean L-factors. The Baxter Q-operator introduced in
this paper is then described as a particular realization of the explicitly
defined universal Baxter operator in the spherical Hecke algebra H(G(R),K), K
being a maximal compact subgroup of G. Finally we stress an analogy between
Q-operators and certain elements of the non-Archimedean Hecke algebra
H(G(Q_p),G(Z_p)).Comment: 32 pages, typos corrected
Yangian Algebras and Classical Riemann Problems
We investigate different Hopf algebras associated to Yang's solution of
quantum Yang-Baxter equation. It is shown that for the precise definition of
the algebra one needs the commutation relations for the deformed algebra of
formal currents and the specialization of the Riemann problem for the currents.
Two different Riemann problems are considered. They lead to the central
extended Yangian double associated with and to the degeneration of
scaling limit of elliptic affine algebra. Unless the defining relations for the
generating functions of the both algebras coincide their properties and the
theory of infinite-dimensional representations are quite different. We discuss
also the Riemann problem for twisted algebras and for scaled elliptic algebra.Comment: 36 pages, 3 figures under bezier.sty, corrected some typo
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