428,447 research outputs found
Integral TQFT for a one-holed torus
We give new explicit formulas for the representations of the mapping class
group of a genus one surface with one boundary component which arise from
Integral TQFT. Our formulas allow one to compute the h-adic expansion of the
TQFT-matrix associated to a mapping class in a straightforward way. Truncating
the h-adic expansion gives an approximation of the representation by
representations into finite groups. As a special case, we study the induced
representations over finite fields and identify them up to isomorphism. The key
technical ingredient of the paper are new bases of the Integral TQFT modules
which are orthogonal with respect to the Hopf pairing. We construct these
orthogonal bases in arbitrary genus, and briefly describe some other
applications of them.Comment: 18 pages, 8 figures. version 3: Minor expository changes.
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Analytical expression for a post-quench time evolution of the one-body density matrix of one-dimensional hard-core bosons
We apply the logic of the quench action to give an exact analytical
expression for the time evolution of the one-body density matrix after an
interaction quench in the Lieb-Liniger model from the ground state of the free
theory (BEC state) to the infinitely repulsive regime. In this limit there
exists a mapping between the bosonic wavefuntions and the free fermionic ones
but this does not help the computation of the one-body density matrix which is
sensitive to particle statistics. The final expression, given in terms of the
difference of the square root of two Fredholm determinants, can be numerically
evaluated and is valid in the thermodynamic limit and for all times after the
quench.Comment: 24 pages, 2 figur
High-momentum tail in the Tonks gas under harmonic confinement
We use boson-fermion mapping to show that the single-particle momentum
distribution in a one-dimensional gas of hard point-like bosons (Tonks gas)
inside a harmonic trap decays as at large momentum . The relevant
integrals expressing the one-body density matrix are evaluated for small
numbers of particles in a simple Monte Carlo approach to test the extent of the
asymptotic law and to illustrate the slow decay of correlations between the
matter-wave field at different points.Comment: 8 pages, 3 figures, accepted for publication in Phys. Lett.
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