699 research outputs found
Invariants of the vacuum module associated with the Lie superalgebra gl(1|1)
We describe the algebra of invariants of the vacuum module associated with
the affinization of the Lie superalgebra . We give a
formula for its Hilbert--Poincar\'{e} series in a fermionic (cancellation-free)
form which turns out to coincide with the generating function of the plane
partitions over the -hook. Our arguments are based on a super version of
the Beilinson--Drinfeld--Ra\"{i}s--Tauvel theorem which we prove by producing
an explicit basis of invariants of the symmetric algebra of polynomial currents
associated with . We identify the invariants with affine
supersymmetric polynomials via a version of the Chevalley theorem.Comment: 24 pages, final version; contribution to Rodney Baxter volume,
J.Phys.
On the low-temperature anomalies in the thermal conductivity of plastically deformed crystals due to phonon-kink scattering
Previous experimental studies of the thermal conductivity of plastically
deformed lead crystals in the superconducting state have shown strong anomalies
in the thermal conductivity. Similar effects were also found for the thermal
conductivity of bent samples. Until now, a theoretical
explanation for these results was missing. In this paper we will introduce the
process of phonon-kink scattering and show that it qualitatively explains the
anomalies that experiments had found.Comment: 3 pages, follow-up paper to appear soo
Spaces of quasi-exponentials and representations of gl_N
We consider the action of the Bethe algebra B_K on (\otimes_{s=1}^k
L_{\lambda^{(s)}})_\lambda, the weight subspace of weight of the
tensor product of k polynomial irreducible gl_N-modules with highest weights
\lambda^{(1)},...,\lambda^{(k)}, respectively. The Bethe algebra depends on N
complex numbers K=(K_1,...,K_N). Under the assumption that K_1,...,K_N are
distinct, we prove that the image of B_K in the endomorphisms of
(\otimes_{s=1}^k L_{\lambda^{(s)}})_\lambda is isomorphic to the algebra of
functions on the intersection of k suitable Schubert cycles in the Grassmannian
of N-dimensional spaces of quasi-exponentials with exponents K. We also prove
that the B_K-module (\otimes_{s=1}^k L_{\lambda^{(s)}})_\lambda is isomorphic
to the coregular representation of that algebra of functions. We present a
Bethe ansatz construction identifying the eigenvectors of the Bethe algebra
with points of that intersection of Schubert cycles.Comment: Latex, 29 page
Gaudin models for gl(m|n)
Date of Acceptance: 16/04/2015We establish the basics of the Bethe ansatz for the Gaudin model associated to the Lie superalgebra gl(m|n). In particular, we prove the completeness of the Bethe ansatz in the case of tensor products of fundamental representations.Peer reviewedFinal Accepted Versio
Dicke model semiclassical dynamics in superradiant dipolar phase follows the Euler heavy top
Analytic solution is presented of the nonlinear semiclassical dynamics of
superradiant photonic condensate that arises in the Dicke model of two-level
atoms dipolar coupled to the electromagnetic field in the microwave cavity. In
adiabatic limit with respect to photon degree of freedom the system is
approximately integrable and its evolution is expressed via Jacobi elliptic
functions of real time. Periodic trajectories of the semiclassical coordinate
of photonic condensate either localise around two degenerate minima of the
condensate ground state energy or traverse between them over the saddle point.
An exact mapping of the semiclassical dynamics of photonic condensate on the
motion of unstable Lagrange 'sleeping top' is found. Analytic expression is
presented for the frequency dependence of transmission coefficient along a
transmission line inductively coupled to the resonant cavity with superradiant
condensate. Sharp transmission drops reflect Fourier spectrum of the
semiclassical motion of photonic condensate and of 'sleeping top' nodding.Comment: 13 pages, 3 figures, submitted to PR
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