1,756 research outputs found
On the superfluidity of classical liquid in nanotubes
In 2001, the author proposed the ultra second quantization method. The ultra
second quantization of the Schr\"odinger equation, as well as its ordinary
second quantization, is a representation of the N-particle Schr\"odinger
equation, and this means that basically the ultra second quantization of the
equation is the same as the original N-particle equation: they coincide in
3N-dimensional space.
We consider a short action pairwise potential V(x_i -x_j). This means that as
the number of particles tends to infinity, , interaction is
possible for only a finite number of particles. Therefore, the potential
depends on N in the following way: . If V(y) is finite
with support , then as the support engulfs a finite
number of particles, and this number does not depend on N.
As a result, it turns out that the superfluidity occurs for velocities less
than , where
is the critical Landau velocity and R is the radius of
the nanotube.Comment: Latex, 20p. The text is presented for the International Workshop
"Idempotent and tropical mathematics and problems of mathematical physics",
Independent University of Moscow, Moscow, August 25--30, 2007 and to be
published in the Russian Journal of Mathematical Physics, 2007, vol. 15, #
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
Towards optimization of quantum circuits
Any unitary operation in quantum information processing can be implemented
via a sequence of simpler steps - quantum gates. However, actual implementation
of a quantum gate is always imperfect and takes a finite time. Therefore,
seeking for a short sequence of gates - efficient quantum circuit for a given
operation, is an important task. We contribute to this issue by proposing
optimization of the well-known universal procedure proposed by Barenco et.al
[1]. We also created a computer program which realizes both Barenco's
decomposition and the proposed optimization. Furthermore, our optimization can
be applied to any quantum circuit containing generalized Toffoli gates,
including basic quantum gate circuits.Comment: 10 pages, 11 figures, minor changes+typo
Application of the informational reference system OZhUR to the automated processing of data from satellites of the Kosmos series
The structure and potential of the information reference system OZhUR designed for the automated data processing systems of scientific space vehicles (SV) is considered. The system OZhUR ensures control of the extraction phase of processing with respect to a concrete SV and the exchange of data between phases.The practical application of the system OZhUR is exemplified in the construction of a data processing system for satellites of the Cosmos series. As a result of automating the operations of exchange and control, the volume of manual preparation of data is significantly reduced, and there is no longer any need for individual logs which fix the status of data processing. The system Ozhur is included in the automated data processing system Nauka which is realized in language PL-1 in a binary one-address system one-state (BOS OS) electronic computer
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
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
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
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
Spontaneous Magnetisation in a Quantum Wire
An existence of predominant symmetrical spin configuration (spin polarised
phase) and "diluted" density of states (pseudo-gap) in a layer under the Fermi
level in a quantum wire is predicted. The condition of cross-over from
non-polarised phase to polarised one was derived. The transition occurs for
sufficiently low electron density in a wire and is accompanied by an acute
decrease of electron density of states near the Fermi level.It may result in a
corresponding decrease of conductance. A similar effect may exist in a
two-dimensional electron gas.Comment: 8 pages, 1 figur
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