6,628 research outputs found
Factorization of quantum charge transport for non-interacting fermions
We show that the statistics of the charge transfer of non-interacting
fermions through a two-lead contact is generalized binomial, at any temperature
and for any form of the scattering matrix: an arbitrary charge-transfer process
can be decomposed into independent single-particle events. This result
generalizes previous studies of adiabatic pumping at zero temperature and of
transport induced by bias voltage.Comment: 13 pages, 3 figures, typos corrected, references adde
Counting free fermions on a line: a Fisher-Hartwig asymptotic expansion for the Toeplitz determinant in the double-scaling limit
We derive an asymptotic expansion for a Wiener-Hopf determinant arising in
the problem of counting one-dimensional free fermions on a line segment at zero
temperature. This expansion is an extension of the result in the theory of
Toeplitz and Wiener-Hopf determinants known as the generalized Fisher-Hartwig
conjecture. The coefficients of this expansion are conjectured to obey certain
periodicity relations, which renders the expansion explicitly periodic in the
"counting parameter". We present two methods to calculate these coefficients
and verify the periodicity relations order by order: the matrix Riemann-Hilbert
problem and the Painleve V equation. We show that the expansion coefficients
are polynomials in the counting parameter and list explicitly first several
coefficients.Comment: 11 pages, minor corrections, published versio
Characterizing correlations with full counting statistics: classical Ising and quantum XY spin chains
We propose to describe correlations in classical and quantum systems in terms
of full counting statistics of a suitably chosen discrete observable. The
method is illustrated with two exactly solvable examples: the classical
one-dimensional Ising model and the quantum spin-1/2 XY chain. For the
one-dimensional Ising model, our method results in a phase diagram with two
phases distinguishable by the long-distance behavior of the Jordan-Wigner
strings. For the quantum XY chain, the method reproduces the previously known
phase diagram.Comment: 6 pages, section on Lee-Yang zeros added, published versio
Analytic approximations to the phase diagram of the Jaynes-Cummings-Hubbard model with application to ion chains
We discuss analytic approximations to the ground state phase diagram of the
homogeneous Jaynes-Cummings-Hubbard (JCH) Hamiltonian with general short-range
hopping. The JCH model describes e.g. radial phonon excitations of a linear
chain of ions coupled to an external laser field tuned to the red motional
sideband with Coulomb mediated hopping or an array of high- coupled cavities
containing a two-level atom and photons. Specifically we consider the cases of
a linear array of coupled cavities and a linear ion chain. We derive
approximate analytic expressions for the boundaries between Mott-insulating and
superfluid phases and give explicit expressions for the critical value of the
hopping amplitude within the different approximation schemes. In the case of an
array of cavities, which is represented by the standard JCH model we compare
both approximations to numerical data from density-matrix renormalization group
(DMRG) calculations.Comment: 9 pages, 5 figures, extended and corrected second versio
On the number of types in sparse graphs
We prove that for every class of graphs which is nowhere dense,
as defined by Nesetril and Ossona de Mendez, and for every first order formula
, whenever one draws a graph and a
subset of its nodes , the number of subsets of which are of
the form
for some valuation of in is bounded by
, for every . This provides
optimal bounds on the VC-density of first-order definable set systems in
nowhere dense graph classes.
We also give two new proofs of upper bounds on quantities in nowhere dense
classes which are relevant for their logical treatment. Firstly, we provide a
new proof of the fact that nowhere dense classes are uniformly quasi-wide,
implying explicit, polynomial upper bounds on the functions relating the two
notions. Secondly, we give a new combinatorial proof of the result of Adler and
Adler stating that every nowhere dense class of graphs is stable. In contrast
to the previous proofs of the above results, our proofs are completely
finitistic and constructive, and yield explicit and computable upper bounds on
quantities related to uniform quasi-wideness (margins) and stability (ladder
indices)
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