31,230 research outputs found
Meromorphic continuation of Selberg zeta functions with twists having non-expanding cusp monodromy
We initiate the study of Selberg zeta functions for
geometrically finite Fuchsian groups and finite-dimensional
representations with non-expanding cusp monodromy. We show that for all
choices of , the Selberg zeta function
converges on some half-plane in . In addition, under the assumption
that admits a strict transfer operator approach, we show that
extends meromorphically to all of .Comment: 46 pages, v4: added results on nonconvergence beyond NECM; added
proofs for meromorphic continuation of derivatives of the Lerch transcendent;
final version accepted for publicatio
Parabolic Flows Renormalized by Partially Hyperbolic Maps
We consider parabolic flows on 3-dimensional manifolds which are renormalized
by circle extensions of Anosov diffeormorphisms. This class of flows includes
nilflows on the Heisenberg nilmanifold which are renormalized by partially
hyperbolic automorphisms. The transfer operators associated to the
renormalization maps, acting on anisotropic Sobolev spaces, are known to have
good spectral properties (this relies on ideas which have some resemblance to
representation theory but also apply to non-algebraic systems). The spectral
information is used to describe the deviation of ergodic averages and solutions
of the cohomological equation for the parabolic flow.Comment: Comments welcom
Integrable Floquet dynamics
We discuss several classes of integrable Floquet systems, i.e. systems which
do not exhibit chaotic behavior even under a time dependent perturbation. The
first class is associated with finite-dimensional Lie groups and
infinite-dimensional generalization thereof. The second class is related to the
row transfer matrices of the 2D statistical mechanics models. The third class
of models, called here "boost models", is constructed as a periodic interchange
of two Hamiltonians - one is the integrable lattice model Hamiltonian, while
the second is the boost operator. The latter for known cases coincides with the
entanglement Hamiltonian and is closely related to the corner transfer matrix
of the corresponding 2D statistical models. We present several explicit
examples. As an interesting application of the boost models we discuss a
possibility of generating periodically oscillating states with the period
different from that of the driving field. In particular, one can realize an
oscillating state by performing a static quench to a boost operator. We term
this state a "Quantum Boost Clock". All analyzed setups can be readily realized
experimentally, for example in cod atoms.Comment: 18 pages, 2 figures; revised version. Submission to SciPos
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