2,272 research outputs found
Propagation of fluctuations in interaction networks governed by the law of mass action
Using an example of physical interactions between proteins, we study how
perturbations propagate in interconnected networks whose equilibrium state is
governed by the law of mass action. We introduce a comprehensive matrix
formalism which predicts the response of this equilibrium to small changes in
total concentrations of individual molecules, and explain it using a heuristic
analogy to a current flow in a network of resistors. Our main conclusion is
that on average changes in free concentrations exponentially decay with the
distance from the source of perturbation. We then study how this decay is
influenced by such factors as the topology of a network, binding strength, and
correlations between concentrations of neighboring nodes. An exact analytic
expression for the decay constant is obtained for the case of uniform
interactions on the Bethe lattice. Our general findings are illustrated using a
real biological network of protein-protein interactions in baker's yeast with
experimentally determined protein concentrations.Comment: 4 pages; 2 figure
Probability Theory Compatible with the New Conception of Modern Thermodynamics. Economics and Crisis of Debts
We show that G\"odel's negative results concerning arithmetic, which date
back to the 1930s, and the ancient "sand pile" paradox (known also as "sorites
paradox") pose the questions of the use of fuzzy sets and of the effect of a
measuring device on the experiment. The consideration of these facts led, in
thermodynamics, to a new one-parameter family of ideal gases. In turn, this
leads to a new approach to probability theory (including the new notion of
independent events). As applied to economics, this gives the correction, based
on Friedman's rule, to Irving Fisher's "Main Law of Economics" and enables us
to consider the theory of debt crisis.Comment: 48p., 14 figs., 82 refs.; more precise mathematical explanations are
added. arXiv admin note: significant text overlap with arXiv:1111.610
Resistivity of non-Galilean-invariant Fermi- and non-Fermi liquids
While it is well-known that the electron-electron (\emph{ee}) interaction
cannot affect the resistivity of a Galilean-invariant Fermi liquid (FL), the
reverse statement is not necessarily true: the resistivity of a
non-Galilean-invariant FL does not necessarily follow a T^2 behavior. The T^2
behavior is guaranteed only if Umklapp processes are allowed; however, if the
Fermi surface (FS) is small or the electron-electron interaction is of a very
long range, Umklapps are suppressed. In this case, a T^2 term can result only
from a combined--but distinct from quantum-interference corrections-- effect of
the electron-impurity and \emph{ee} interactions. Whether the T^2 term is
present depends on 1) dimensionality (two dimensions (2D) vs three dimensions
(3D)), 2) topology (simply- vs multiply-connected), and 3) shape (convex vs
concave) of the FS. In particular, the T^2 term is absent for any quadratic
(but not necessarily isotropic) spectrum both in 2D and 3D. The T^2 term is
also absent for a convex and simply-connected but otherwise arbitrarily
anisotropic FS in 2D. The origin of this nullification is approximate
integrability of the electron motion on a 2D FS, where the energy and momentum
conservation laws do not allow for current relaxation to leading
--second--order in T/E_F (E_F is the Fermi energy). If the T^2 term is
nullified by the conservation law, the first non-zero term behaves as T^4. The
same applies to a quantum-critical metal in the vicinity of a Pomeranchuk
instability, with a proviso that the leading (first non-zero) term in the
resistivity scales as T^{\frac{D+2}{3}} (T^{\frac{D+8}{3}}). We discuss a
number of situations when integrability is weakly broken, e.g., by inter-plane
hopping in a quasi-2D metal or by warping of the FS as in the surface states of
Bi_2Te_3 family of topological insulators.Comment: Submitted to a special issue of the Lithuanian Journal of Physics
dedicated to the memory of Y. B. Levinso
Peculiarities of dynamics of Dirac fermions associated with zero-mass lines
Zero-mass lines result in appearance of linear dispersion modes for Dirac
fermions. These modes play an important role in various physical systems.
However, a Dirac fermion may not precisely follow a single zero-mass line, due
to either tunneling between different lines or centrifugal forces. Being
shifted from a zero-mass line the Dirac fermion acquires mass which can
substantially influence its expected "massless" behavior. In the paper we
calculate the energy gap caused by the tunneling between two zero-mass lines
and show that its opening leads to the delocalization of linear dispersion
modes. The adiabatic bending of a zero-mass line gives rise to geometric
phases. These are the Berry phase, locally associated with a curvature, and a
new phase resulting from the mass square asymmetry in the vicinity of a
zero-mass line.Comment: 6 pages, 4 figures. In the second version some references were added
and minor changes were made in the introductio
Quantum Correction to Conductivity Close to Ferromagnetic Quantum Critical Point in Two Dimensions
We study the temperature dependence of the conductivity due to quantum
interference processes for a two-dimensional disordered itinerant electron
system close to a ferromagnetic quantum critical point. Near the quantum
critical point, the cross-over between diffusive and ballistic regimes of
quantum interference effects occurs at a temperature , where is the parameter associated with the Landau
damping of the spin fluctuations, is the impurity scattering time, and
is the Fermi energy. For a generic choice of parameters, is
smaller than the nominal crossover scale . In the ballistic quantum
critical regime, the conductivity behaves as .Comment: 5 pages, 1 figur
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