105 research outputs found
The critical compressibility factor of fluids from the Global Isomorphism approach
The relation between the critical compressibility factors of the
Lennard-Jones fluid and the Lattice Gas (Ising model) is derived within the
global isomorphism approach. On this basis we obtain the alternative form for
the value of the critical compressibility factor which is different from widely
used phenomenological Timmermans relation. The estimates for the critical
pressure and of the Lennard-Jones fluid are obtained in case of two
and three dimensions. The extension of the formalism is proposed to include the
Pitzer's acentric factor into consideration.Comment: 10 pages, 1 table, 1 Figur
The Vliegenthart-Lekkerkerker relation. The case of the -fluids
The Vliegenthart-Lekkerkerker relation for the second virial coefficient
value at the critical temperature found in [G. A. Vliegenthart and H. N. W.
Lekkerkerker, J. Chem. Phys. \textbf{112} 5364 (2000)] is discussed in
connection with the scale invariant mean-field approach proposed in [V. L.
Kulinskii and L. A. Bulavin, J. Chem. Phys. \textbf{133} 134101 (2010)]. We
study the case of the Mie-class potentials which is widely used in simulations
of the phase equilibrium of the fluids. It is shown that due to the homogeneity
property of the -class potentials it is possible to connect the loci of
the fluids with these model potentials in different dimensions
Asymmetry of the Hamiltonian and the Tolman's length
Using the canonical transformation of the order parameter which restores the
Ising symmetry of the Hamiltonian we derive the expression for the Tolman
length as a sum of two terms. One of them is the term generated by the
fluctuations of the order parameter the other one is due to the entropy. The
leading singular behavior of the Tolman length near the critical point is
analyzed. The obtained results are in correspondence with that of M.A.
Anisimov, Phys. Rev. Lett., \textbf{98} 035702 (2007).Comment: 7 pages
Global isomorphism between the Lenard-Jones fluids and the Ising model
The interpretation of the linear character of the observable classic
rectilinear diameter law and the linear character of the Zeno-line (unit
compressibility line Z=1) on the basis of global isomorphism between Ising
model (Lattice Gas) and simple fluid is proposed. The correct definition of the
limiting nontrivial Zeno state is given and its relation with the locus of the
critical point is derived within this approach. We show that the liquid-vapor
part of the phase diagram of the molecular fluids can be described as the
isomorphic image of the phase diagram of the Lattice Gas. It is shown how the
the position of the critical points of the fluids of the Lenard-Jones type can
be determined basing on the scaling symmetry. As a sequence the explanation of
the well known fact about "global" cubic character of the coexistence curve of
the molecular fluids is proposed.Comment: 15 pages, 3 figures (2 figures added and the references
Mass-jump and mass-bump boundary conditions for singular self-adjoint extensions of the Schr\"odinger operator in one dimension
Physical realizations of non-standard singular self-adjoint extensions for
one-dimensional Schr\"odinger operator in terms of the mass-jump are
considered. It is shown that corresponding boundary conditions can be realized
for the Hamiltonian with the position-dependent effective mass in two
qualitatively different profiles of the effective mass inhomogeneity: the
mass-jump and the mass-bump. The existence of quantized magnetic flux in a case
of the mass-jump is proven by explicit demonstration of the Zeeman-like
splitting for states with the opposite projections of angular momentum.Comment: 11 pages, 7 figure
Thermodynamics without ergodicity
We show that fundamental thermodynamic relations can be derived from
deterministic mechanics for a non-ergodic system. This extend a similar
derivation for ergodic systems and suggests that ergodicity should not be
considered as a requirement for a system to exhibit a thermodynamic behavior.
Our analysis emphasizes the role of adiabatic invariants in deterministic
description and strengthens the link between mechanics and thermodynamics. In
particular, we argue that macroscopic thermodynamic behavior of a system is
caused by the existence of different time scales in its deterministic
microscopic evolution
Zero-range potential model for the study of the ground states near the vortex core in the quantum limit
We propose the treatment of the lowest bound states near the vortex core on
the basis of the self-adjoint extension of the Hamiltonian with the localized
magnetic flux of Aaronov-Bohm type. It is shown that in the limit {\varkappa}
>> 1 the potential for the vortex core excitations can be treated in terms of
the generalized zero-range potential method. The spectrum of the Caroli-de
Gennes-Matricon states is obtained and the comparison with the numerical
calculations of Hayashi, N. et al. [Phys. Rev. Lett. 80, p. 2921 (1998)] is
performed. The analytical expression for the ground state energy depending on
the boundary condition parameter b was obtained by us.Comment: 10 pages, 2 figure
The vortex pinning on the cylindrical defects and the electronic structure of the vortex core
The model of the Abrikosov vortex pinning on a cylindrical defect is
proposed. It is shown that in the limit the potential for the
vortex core excitations can be treated in terms of the zero-range potentials
method. Using the variational method the estimates for the energy of pinning,
the pinning force and the density of critical current defect are obtained.Comment: 12 pages, 4 figure
Stable sound wave generation in weakly ionized air medium
We consider the generation of sound waves in the air medium between
electrodes at the voltages near electrical breakdown in the presence of the
time dependent constituent of the electric field. Within the standard
multicomponent hydrodynamic model of the weakly ionized gas it is shown that
the generation of sound is possible due to instantaneous character of the
ionization equilibrium. The influence of the electronegative ions on the sound
intensity is also discussed.Comment: 15 pages, 10 figure
Physical interpretation of point-like interactions of one-dimensional Schr\"odinger operator
We consider physical interpretations of non-trivial boundary conditions of
self-adjoint extensions for one-dimensional Schr\"odinger operator of free
spinless particle. Despite its model and rather abstract character this
question is worth of investigation due to application for one-dimensional
nanostructures. The main result is the physical interpretation of peculiar
self-adjoint extension with discontinuity of both the probability density and
the derivative of the wave function. We show that this case differs very much
from other three which were considered before and corresponds to the presence
of mass-jump in a sense of works of Ganella et. al., (Journal of Physics A:
Mathematical and Theoretical 42, 465207 (2009)) along with the quantized
magnetic flux. Real physical system which can be modeled by such boundary
conditions is the localized quantazied flux in the Josephson junction of two
superconductors with different effective masses of the elementary excitations.Comment: 14 page
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