6,605 research outputs found
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
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
Frozen Rotor Approximation in the Mixed Quantum/Classical Theory for Collisional Energy Transfer: Application to Ozone Stabilization
A frozen-rotor approximation is formulated for the mixed quantum/classical theory of collisional energy transfer and ro-vibrational energy flow [M. Ivanov and D. Babikov, J. Chem. Phys.134, 144107 (Year: 2011)]. Numerical tests are conducted to assess its efficiency and accuracy, compared to the original version of the method, where rotation of the molecule in space is treated explicitly and adiabatically. New approach is considerably faster and helps blocking the artificial ro-vibrational transitions at the pre- and post-collisional stages of the process. Although molecular orientation in space is fixed, the energy exchange between rotational, vibrational, and translational digresses of freedom still occurs, allowing to compute ro-vibrational excitation and quenching. Behavior of the energy transfer function through eight orders of magnitude range of values and in a broad range of ΔE is reproduced well. In the range of moderate −500 ⩽ ΔE ⩽ +500 cm−1 the approximate method is rather accurate. The absolute values of stabilization cross sections for scattering resonances trapped behind the centrifugal threshold are a factor 2-to-3 smaller (compared to the explicit-rotation approach). This performance is acceptable and similar to the well-known sudden-rotation approximation in the time-independent inelastic scattering methods
Primary Sequences of Protein-Like Copolymers: Levy Flight Type Long Range Correlations
We consider the statistical properties of primary sequences of two-letter HP
copolymers (H for hydrophobic and P for polar) designed to have water soluble
globular conformations with H monomers shielded from water inside the shell of
P monomers. We show, both by computer simulations and by exact analytical
calculation, that for large globules and flexible polymers such sequences
exhibit long-range correlations which can be described by Levy-flight
statistics.Comment: 4 pages, including 2 figures; several references added, some
formulations improve
Rare decay pi0 -> e+e-: theory confronts KTeV data
Within the dispersive approach to the amplitude of the rare decay pi0 -> e+e-
the nontrivial dynamics is contained only in the subtraction constant. We
express this constant, in the leading order in (m_e/\Lambda)^2 perturbative
series, in terms of the inverse moment of the pion transition form factor given
in symmetric kinematics. By using the CELLO and CLEO data on the pion
transition form factor given in asymmetric kinematics the lower bound on the
decay branching ratio is found. The restrictions following from QCD allow us to
make a quantitative prediction for the branching B(pi0 -> e+e-) =(6.2\pm
0.1)*10^{-8} which is 3\sigma below the recent KTeV measurement. We confirm our
prediction by using the quark models and phenomenological approaches based on
the vector meson dominance. The decays \eta -> l^+l^- are also discussed.Comment: 7 pages, 1 figur
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