2,160 research outputs found
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
Nonlinear dynamics of soft fermion excitations in hot QCD plasma III: Soft-quark bremsstrahlung and energy losses
In general line with our early works [Yu.A. Markov, M.A. Markova, Nucl. Phys.
A770 (2006) 162; 784 (2007) 443] within the framework of a semiclassical
approximation the general theory of calculation of effective currents and
sources generating bremsstrahlung of an arbitrary number of soft quarks and
soft gluons at collision of a high-energy color-charged particle with thermal
partons in a hot quark-gluon plasma, is developed. For the case of one- and
two-scattering thermal partons with radiation of one or two soft excitations,
the effective currents and sources are calculated in an explicit form. In the
model case of `frozen' medium, approximate expressions for energy losses
induced by the most simple processes of bremsstrahlung of soft quark and soft
gluon, are derived. On the basis of a conception of the mutual cancellation of
singularities in the sum of so-called `diagonal' and `off-diagonal'
contributions to the energy losses, an effective method of determining color
factors in scattering probabilities, containing the initial values of Grassmann
color charges, is suggested. The dynamical equations for Grassmann color
charges of hard particle used by us early are proved to be insufficient for
investigation of the higher radiative processes. It is shown that for correct
description of these processes the given equations should be supplemented
successively with the higher-order terms in powers of the soft fermionic field.Comment: 93 pages, 20 figure
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
Quasithermodynamics and a Correction to the Stefan--Boltzmann Law
We provide a correction to the Stefan--Boltzmann law and discuss the problem
of a phase transition from the superfluid state into the normal state.Comment: Latex, 9page
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
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
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