1,578 research outputs found
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
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
Mathematical Conception of "Phenomenological" Equilibrium Thermodynamics
In the paper, the principal aspects of the mathematical theory of equilibrium
thermodynamics are distinguished. It is proved that the points of degeneration
of a Bose gas of fractal dimension in the momentum space coincide with critical
points or real gases, whereas the jumps of critical indices and the Maxwell
rule are related to the tunnel generalization of thermodynamics. Semiclassical
methods are considered for the tunnel generalization of thermodynamics and also
for the second and ultrasecond quantization (operators of creation and
annihilation of pairs). To every pure gas there corresponds a new critical
point of the limit negative pressure below which the liquid passes to a
dispersed state (a foam). Relations for critical points of a homogeneous
mixture of pure gases are given in dependence on the concentration of gases.Comment: 37 pages, 9 figure, more precise explanations, more references. arXiv
admin note: substantial text overlap with arXiv:1202.525
Initial Conditions for Semiclassical Field Theory
Semiclassical approximation based on extracting a c-number classical
component from quantum field is widely used in the quantum field theory.
Semiclassical states are considered then as Gaussian wave packets in the
functional Schrodinger representation and as Gaussian vectors in the Fock
representation. We consider the problem of divergences and renormalization in
the semiclassical field theory in the Hamiltonian formulation. Although
divergences in quantum field theory are usually associated with loop Feynman
graphs, divergences in the Hamiltonian approach may arise even at the tree
level. For example, formally calculated probability of pair creation in the
leading order of the semiclassical expansion may be divergent. This observation
was interpretted as an argumentation for considering non-unitary evolution
transformations, as well as non-equivalent representations of canonical
commutation relations at different time moments. However, we show that this
difficulty can be overcomed without the assumption about non-unitary evolution.
We consider first the Schrodinger equation for the regularized field theory
with ultraviolet and infrared cutoffs. We study the problem of making a limit
to the local theory. To consider such a limit, one should impose not only the
requirement on the counterterms entering to the quantum Hamiltonian but also
the requirement on the initial state in the theory with cutoffs. We find such a
requirement in the leading order of the semiclassical expansion and show that
it is invariant under time evolution. This requirement is also presented as a
condition on the quadratic form entering to the Gaussian state.Comment: 20 pages, Plain TeX, one postscript figur
Universal Behavior of One-Dimensional Gapped Antiferromagnets in Staggered Magnetic Field
We study the properties of one-dimensional gapped Heisenberg antiferromagnets
in the presence of an arbitrary strong staggered magnetic field. For these
systems we predict a universal form for the staggered magnetization curve. This
function, as well as the effect the staggered field has on the energy gaps in
longitudinal and transversal excitation spectra, are determined from the
universal form of the effective potential in O(3)-symmetric 1+1--dimensional
field theory. Our theoretical findings are in excellent agreement with recent
neutron scattering data on R_2 Ba Ni O_5 (R = magnetic rare earth) linear-chain
mixed spin antiferromagnets.Comment: 4 pages, 2 figure
Conductance of a Mott Quantum Wire
We consider transport through a one-dimensional conductor subject to an
external periodic potential and connected to non-interacting leads (a "Mott
quantum wire"). For the case of a strong periodic potential, the conductance is
shown to jump from zero, for the chemical potential lying within the
Mott-Hubbard gap, to the non-interacting value of 2e^2/h, as soon as the
chemical potential crosses the gap edge. This behavior is strikingly different
from that of an optical conductivity, which varies continuously with the
carrier concentration. For the case of a weak potential, the perturbative
correction to the conductance due to Umklapp scattering is absent away from
half-filling.Comment: 4 pages, RevTex, 1 ps figure included; published versio
Homogeneous Focusing Field for Short Relativistic Electron Bunches in Plasma
Plasma wake lens in which all short relativistic electron bunches of sequence
are focused identically and uniformly is studied analytically and by numerical
simulation. For two types of lenses necessary parameters of focused sequence of
relativistic electron bunches are formulated. Verification of these parameters
is performed by numerical simulation
Universality in scattering by large-scale potential fluctuations in two-dimensional conductors
We study electron propagation through a random array of rare, opaque and
large (compared the de Broglie wavelength of electrons) scatterers. It is shown
that for any convex scatterer the ratio of the transport to quantum lifetimes
\eta=\tau_{tr}/\tau_{tot}$ does not depend on the shape of the scatterer but
only on whether scattering is specular or diffuse and on the spatial
dimensionality (D). In particular, for specular scattering, \eta is a universal
constant determined only by the dimensionality of the system: \eta = 2 for D =
3 and \eta = 3/2 for D = 2. The crossover between classical and quantum regimes
of scattering is discussed.Comment: 4 pages, 3 figures, submitted to PR
Fission barriers in covariant density functional theory: extrapolation to superheavy nuclei
Systematic calculations of fission barriers allowing for triaxial deformation
are performed for even-even superheavy nuclei with charge number
using three classes of covariant density functional models. The softness of
nuclei in the triaxial plane leads to an emergence of several competing fission
pathes in the region of the inner fission barrier in some of these nuclei. The
outer fission barriers are considerably affected by triaxiality and octupole
deformation. General trends of the evolution of the inner and the outer fission
barrier heights are discussed as a function of the particle numbers.Comment: 24 pages, 8 tables, 12 figure
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