1,866 research outputs found
Geometric variational problems of statistical mechanics and of combinatorics
We present the geometric solutions of the various extremal problems of
statistical mechanics and combinatorics. Together with the Wulff construction,
which predicts the shape of the crystals, we discuss the construction which
exhibits the shape of a typical Young diagram and of a typical skyscraper.Comment: 10 page
Non-ergodic phases in strongly disordered random regular graphs
We combine numerical diagonalization with a semi-analytical calculations to
prove the existence of the intermediate non-ergodic but delocalized phase in
the Anderson model on disordered hierarchical lattices. We suggest a new
generalized population dynamics that is able to detect the violation of
ergodicity of the delocalized states within the Abou-Chakra, Anderson and
Thouless recursive scheme. This result is supplemented by statistics of random
wave functions extracted from exact diagonalization of the Anderson model on
ensemble of disordered Random Regular Graphs (RRG) of N sites with the
connectivity K=2. By extrapolation of the results of both approaches to
N->infinity we obtain the fractal dimensions D_{1}(W) and D_{2}(W) as well as
the population dynamic exponent D(W) with the accuracy sufficient to claim that
they are non-trivial in the broad interval of disorder strength W_{E}<W<W_{c}.
The thorough analysis of the exact diagonalization results for RRG with
N>10^{5} reveals a singularity in D_{1,2}(W)-dependencies which provides a
clear evidence for the first order transition between the two delocalized
phases on RRG at W_{E}\approx 10.0. We discuss the implications of these
results for quantum and classical non-integrable and many-body systems.Comment: 4 pages paper with 5 figures + Supplementary Material with 5 figure
Supersymmetrical Separation of Variables for Scarf II Model: Partial Solvability
Recently, a new quantum model - two-dimensional generalization of the Scarf
II - was completely solved analytically by SUSY method for the integer values
of parameter. Now, the same integrable model, but with arbitrary values of
parameter, will be studied by means of supersymmetrical intertwining relations.
The Hamiltonian does not allow the conventional separation of variables, but
the supercharge operator does allow, leading to the partial solvability of the
model. This approach, which can be called as the first variant of
SUSY-separation, together with shape invariance of the model, provides
analytical calculation of the part of spectrum and corresponding wave functions
(quasi-exact-solvability). The model is shown to obey two different variants of
shape invariance which can be combined effectively in construction of energy
levels and wave functions.Comment: 6 p.p., accepted for publication in EP
Correlator of Topological Charge Densities in Instanton Model in QCD
The QCD sum rule for the correlator of topological charge densities and
related to it longitudinal part of the correlator of singlet axial currents is
considered in the framework of instanton model. The coupling constant of
eta'-meson with the singlet axial current is determined. Its value appears to
be in a good coincidence with the value determined recently from the connection
of the part of proton spin, carried by u,d,s quarks, with the derivative of QCD
topological susceptibility. From the same sum rule eta-eta' mixing angle is
found in the framework of two mixing angles model. Its value is close to that
found in the chiral effective theory. The correlator of topological charge
densities at large momenta is calculated.Comment: 14 pages, 2 figure
Multifractal metal in a disordered Josephson Junction Array
We report the results of the numerical study of the non-dissipative quantum
Josephson junction chain with the focus on the statistics of many-body wave
functions and local energy spectra. The disorder in this chain is due to the
random offset charges. This chain is one of the simplest physical systems to
study many-body localization. We show that the system may exhibit three
distinct regimes: insulating, characterized by the full localization of
many-body wavefunctions, fully delocalized (metallic) one characterized by the
wavefunctions that take all the available phase volume and the intermediate
regime in which the volume taken by the wavefunction scales as a non-trivial
power of the full Hilbert space volume. In the intermediate, non-ergodic regime
the Thouless conductance (generalized to many-body problem) does not change as
a function of the chain length indicating a failure of the conventional
single-parameter scaling theory of localization transition. The local spectra
in this regime display the fractal structure in the energy space which is
related with the fractal structure of wave functions in the Hilbert space. A
simple theory of fractality of local spectra is proposed and a new scaling
relationship between fractal dimensions in the Hilbert and energy space is
suggested and numerically tested.Comment: 11 page
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