1,103 research outputs found
Gell-Mann - Low Function in QED for the arbitrary coupling constant
The Gell-Mann -- Low function \beta(g) in QED (g is the fine structure
constant) is reconstructed. At large g, it behaves as \beta_\infty g^\alpha
with \alpha\approx 1, \beta_\infty\approx 1.Comment: 5 pages, PD
Analytical realization of finite-size scaling for Anderson localization. Does the band of critical states exist for d>2?
An analytical realization is suggested for the finite-size scaling algorithm
based on the consideration of auxiliary quasi-1D systems. Comparison of the
obtained analytical results with the results of numerical calculations
indicates that the Anderson transition point is splitted into the band of
critical states. This conclusion is supported by direct numerical evidence
(Edwards and Thouless, 1972; Last and Thouless, 1974; Schreiber, 1985; 1990).
The possibility of restoring the conventional picture still exists but requires
a radical reinterpretetion of the raw numerical data.Comment: PDF, 11 page
H-theorem in quantum physics
Remarkable progress of quantum information theory (QIT) allowed to formulate
mathematical theorems for conditions that data-transmitting or data-processing
occurs with a non-negative entropy gain. However, relation of these results
formulated in terms of entropy gain in quantum channels to temporal evolution
of real physical systems is not thoroughly understood. Here we build on the
mathematical formalism provided by QIT to formulate the quantum H-theorem in
terms of physical observables. We discuss the manifestation of the second law
of thermodynamics in quantum physics and uncover special situations where the
second law can be violated. We further demonstrate that the typical evolution
of energy-isolated quantum systems occurs with non-diminishing entropy.Comment: 8 pages, 4 figure
Scaling near the upper critical dimensionality in the localization theory
The phenomenon of upper critical dimensionality d_c2 has been studied from
the viewpoint of the scaling concepts. The Thouless number g(L) is not the only
essential variable in scale transformations, because there is the second
parameter connected with the off-diagonal disorder. The investigation of the
resulting two-parameter scaling has revealed two scenarios, and the switching
from one to another scenario determines the upper critical dimensionality. The
first scenario corresponds to the conventional one-parameter scaling and is
characterized by the parameter g(L) invariant under scale transformations when
the system is at the critical point. In the second scenario, the Thouless
number g(L) grows at the critical point as L^{d-d_c2}. This leads to violation
of the Wegner relation s=\nu(d-2) between the critical exponents for
conductivity (s) and for localization radius (\nu), which takes the form
s=\nu(d_c2-2). The resulting formulas for g(L) are in agreement with the
symmetry theory suggested previously [JETP 81, 925 (1995)]. A more rigorous
version of Mott's argument concerning localization due topological disorder has
been proposed.Comment: PDF, 7 pages, 6 figure
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