1,918 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
q-Legendre Transformation: Partition Functions and Quantization of the Boltzmann Constant
In this paper we construct a q-analogue of the Legendre transformation, where
q is a matrix of formal variables defining the phase space braidings between
the coordinates and momenta (the extensive and intensive thermodynamic
observables). Our approach is based on an analogy between the semiclassical
wave functions in quantum mechanics and the quasithermodynamic partition
functions in statistical physics. The basic idea is to go from the
q-Hamilton-Jacobi equation in mechanics to the q-Legendre transformation in
thermodynamics. It is shown, that this requires a non-commutative analogue of
the Planck-Boltzmann constants (hbar and k_B) to be introduced back into the
classical formulae. Being applied to statistical physics, this naturally leads
to an idea to go further and to replace the Boltzmann constant with an infinite
collection of generators of the so-called epoch\'e (bracketing) algebra. The
latter is an infinite dimensional noncommutative algebra recently introduced in
our previous work, which can be perceived as an infinite sequence of
"deformations of deformations" of the Weyl algebra. The generators mentioned
are naturally indexed by planar binary leaf-labelled trees in such a way, that
the trees with a single leaf correspond to the observables of the limiting
thermodynamic system
Semiclassical Estimates of Electromagnetic Casimir Self-Energies of Spherical and Cylindrical Metallic Shells
The leading semiclassical estimates of the electromagnetic Casimir stresses
on a spherical and a cylindrical metallic shell are within 1% of the field
theoretical values. The electromagnetic Casimir energy for both geometries is
given by two decoupled massless scalars that satisfy conformally covariant
boundary conditions. Surface contributions vanish for smooth metallic
boundaries and the finite electromagnetic Casimir energy in leading
semiclassical approximation is due to quadratic fluctuations about periodic
rays in the interior of the cavity only. Semiclassically the non-vanishing
Casimir energy of a metallic cylindrical shell is almost entirely due to
Fresnel diffraction.Comment: 12 pages, 2 figure
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
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
On the Thermal Stability of Graphone
Molecular dynamics simulation is used to study thermally activated migration
of hydrogen atoms in graphone, a magnetic semiconductor formed of a graphene
monolayer with one side covered with hydrogen so that hydrogen atoms are
adsorbed on each other carbon atom only. The temperature dependence of the
characteristic time of disordering of graphone via hopping of hydrogen atoms to
neighboring carbon atoms is established directly. The activation energy of this
process is found to be Ea=(0.05+-0.01) eV. The small value of Ea points to
extremely low thermal stability of graphone, this being a serious handicap for
practical use of the material in nanoelectronics.Comment: 3 figure
Semiclassical Description of Wavepacket Revival
We test the ability of semiclassical theory to describe quantitatively the
revival of quantum wavepackets --a long time phenomena-- in the one dimensional
quartic oscillator (a Kerr type Hamiltonian). Two semiclassical theories are
considered: time-dependent WKB and Van Vleck propagation. We show that both
approaches describe with impressive accuracy the autocorrelation function and
wavefunction up to times longer than the revival time. Moreover, in the Van
Vleck approach, we can show analytically that the range of agreement extends to
arbitrary long times.Comment: 10 pages, 6 figure
Thermodynamics of a Fermi liquid beyond the low-energy limit
We consider the non-analytic temperature dependences of the specific heat
coefficient, C(T)/T, and spin susceptibility, \chi_{s} (T), of 2D interacting
fermions beyond the weak-coupling limit. We demonstrate within the
Luttinger-Ward formalism that the leading temperature dependences of C(T)/T and
\chi_s (T) are linear in T, and are described by the Fermi liquid theory. We
show that these temperature dependences are universally determined by the
states near the Fermi level and, for a generic interaction, are expressed via
the spin and charge components of the exact backscattering amplitude of
quasi-particles. We compare our theory to recent experiments on monolayers of
3He.Comment: 5 pages, 1 eps figure, submitted to PR
On the Temperature Dependence of the Lifetime of Thermally Isolated Metastable Clusters
The temperature dependence of the lifetime of the thermally isolated
metastable N8 cubane up to its decay into N2 molecules has been calculated by
the molecular dynamics method. It has been demonstrated that this dependence
significantly deviates from the Arrhenius law. The applicability of the finite
heat bath theory to the description of thermally isolated atomic clusters has
been proved using statistical analysis of the results obtained.Comment: 14 pages, 4 figure
A conjugate for the Bargmann representation
In the Bargmann representation of quantum mechanics, physical states are
mapped into entire functions of a complex variable z*, whereas the creation and
annihilation operators and play the role of
multiplication and differentiation with respect to z*, respectively. In this
paper we propose an alternative representation of quantum states, conjugate to
the Bargmann representation, where the roles of and
are reversed, much like the roles of the position and momentum operators in
their respective representations. We derive expressions for the inner product
that maintain the usual notion of distance between states in the Hilbert space.
Applications to simple systems and to the calculation of semiclassical
propagators are presented.Comment: 15 page
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