558 research outputs found
Twisted mass chiral perturbation theory for 2+1+1 quark flavours
We present results for the masses of pseudoscalar mesons in twisted mass
lattice QCD with a degenerate doublet of u and d quarks and a non-degenerate
doublet of s and c quarks in the framework of next-to-leading order chiral
perturbation theory, including lattice effects up to O(a^2). The masses depend
on the two twist angles for the light and heavy sectors. For maximal twist in
both sectors, O(a)-improvement is explicitly exhibited. The mixing of
flavour-neutral mesons is also discussed, and results in the literature for the
case of degenerate s and c quarks are corrected.Comment: LaTeX2e, 12 pages, corrected typo
The microcanonical thermodynamics of finite systems: The microscopic origin of condensation and phase separations; and the conditions for heat flow from lower to higher temperatures
Microcanonical thermodynamics allows the application of statistical mechanics
both to finite and even small systems and also to the largest, self-gravitating
ones. However, one must reconsider the fundamental principles of statistical
mechanics especially its key quantity, entropy. Whereas in conventional
thermostatistics, the homogeneity and extensivity of the system and the
concavity of its entropy are central conditions, these fail for the systems
considered here. For example, at phase separation, the entropy, S(E), is
necessarily convex to make exp[S(E)-E/T] bimodal in E. Particularly, as
inhomogeneities and surface effects cannot be scaled away, one must be careful
with the standard arguments of splitting a system into two subsystems, or
bringing two systems into thermal contact with energy or particle exchange. Not
only the volume part of the entropy must be considered. As will be shown here,
when removing constraints in regions of a negative heat capacity, the system
may even relax under a flow of heat (energy) against a temperature slope. Thus
the Clausius formulation of the second law: ``Heat always flows from hot to
cold'', can be violated. Temperature is not a necessary or fundamental control
parameter of thermostatistics. However, the second law is still satisfied and
the total Boltzmann entropy increases. In the final sections of this paper, the
general microscopic mechanism leading to condensation and to the convexity of
the microcanonical entropy at phase separation is sketched. Also the
microscopic conditions for the existence (or non-existence) of a critical
end-point of the phase-separation are discussed. This is explained for the
liquid-gas and the solid-liquid transition.Comment: 23 pages, 2 figures, Accepted for publication in the Journal of
Chemical Physic
Gribov no-pole condition, Zwanziger horizon function, Kugo-Ojima confinement criterion, boundary conditions, BRST breaking and all that
We aim to offer a kind of unifying view on two popular topics in the studies
of nonperturbative aspects of Yang-Mills theories in the Landau gauge: the
so-called Gribov-Zwanziger approach and the Kugo-Ojima confinement criterion.
Borrowing results from statistical thermodynamics, we show that imposing the
Kugo-Ojima confinement criterion as a boundary condition leads to a modified
yet renormalizable partition function. We verify that the resulting partition
function is equivalent with the one obtained by Gribov and Zwanziger, which
restricts the domain of integration in the path integral within the first
Gribov horizon. The construction of an action implementing a boundary condition
allows one to discuss the symmetries of the system in the presence of the
boundary. In particular, the conventional BRST symmetry is softly broken.Comment: 5 pages. v2 matches version to appear in PhysRevD (RC
On a new definition of quantum entropy
It is proved here that, as a consequence of the unitary quantum evolution,
the expectation value of a properly defined quantum entropy operator (as
opposed to the non-evolving von Neumann entropy) can only increase during non
adiabatic transformations and remains constant during adiabatic ones. Thus
Clausius formulation of the second law is established as a theorem in quantum
mechanics, in a way that is equivalent to the previously established
formulation in terms of minimal work principle [A. E. Allahverdyan and T. M.
Nieuwenhuizen, Phys. Rev. E 71, 046107 (2005)]. The corresponding Quantum
Mechanical Principle of Entropy Increase is then illustrated with an exactly
solvable example, namely the driven harmonic oscillator. Attention is paid to
both microcanonical and canonical initial condition. The results are compared
to their classical counterparts.Comment: 4 pages, 3 figure
Fluctuations in the presence of fields -Phenomenological Gaussian approximation and a new class of thermodynamic inequalities-
The work approaches the study of the fluctuations for the thermodynamic
systems in the presence of the fields. The approach is of phenomenological
nature and developed in a Gaussian approximation. The study is exemplified on
the cases of a magnetizable continuum in a magnetoquasistatic field, as well as
for the so called discrete systems. In the last case one finds that the
fluctuations estimators depends both on the intrinsic properties of the system
and on the characteristics of the environment. Following some earlier ideas of
one of the authors we present a new class of thermodynamic inequalities for the
systems investigated in this paper. In the case of two variables the mentioned
inequalities are nothing but non-quantum analogues of the well known quantum
Heisenberg (''uncertainty'') relations. Also the obtained fluctuations
estimators support the idea that the Boltzmann's constant k has the
signification of a generic indicator of stochasticity for thermodynamic
systems.
Pacs number(s): 05.20.-y, 05.40.-a, 05.70.-a, 41.20.GzComment: preprint, 24 page
Derivation of Boltzmann Principle
We present a derivation of Boltzmann principle
based on classical mechanical models of thermodynamics. The argument is based
on the heat theorem and can be traced back to the second half of the nineteenth
century with the works of Helmholtz and Boltzmann. Despite its simplicity, this
argument has remained almost unknown. We present it in a modern, self-contained
and accessible form. The approach constitutes an important link between
classical mechanics and statistical mechanics
Mass Spectrum and Bounds on the Couplings in Yukawa Models With Mirror-Fermions
The symmetric Yukawa model with mirror-fermions
in the limit where the mirror-fermion is decoupled is studied both analytically
and numerically. The bare scalar self-coupling is fixed at zero and
infinity. The phase structure is explored and the relevant phase transition is
found to be consistent with a second order one. The fermionic mass spectrum
close to that transition is discussed and a first non-perturbative estimate of
the influence of fermions on the upper and lower bounds on the renormalized
scalar self-coupling is given. Numerical results are confronted with
perturbative predictions.Comment: 7 (Latex) page
Interaction effects in the spectrum of the three-dimensional Ising model
The two-point correlation functions of statistical models show in general
both poles and cuts in momentum space. The former correspond to the spectrum of
massive excitations of the model, while the latter originate from interaction
effects, namely creation and annihilation of virtual pairs of excitations. We
discuss the effect of such interactions on the long distance behavior of
correlation functions in configuration space, focusing on certain time-slice
operators which are commonly used to extract the spectrum. For the 3D Ising
model in the scaling region of the broken-symmetry phase, a one-loop
calculation shows that the interaction effects on time-slice correlations is
non negligible for distances up to a few times the correlation length, and
should therefore be taken into account when analysing Monte Carlo data.Comment: 10 pages, LaTeX file + 1 ps figure, uses axodraw.st
Bubble formation in potential
Scalar field theory with an asymmetric potential is studied at zero
temperature and high-temperature for potential. The equations of
motion are solved numerically to obtain O(4) spherical symmetric and O(3)
cylindrical symmetric bounce solutions. These solutions control the rates for
tunneling from the false vacuum to the true vacuum by bubble formation. The
range of validity of the thin-wall approximation (TWA) is investigated. An
analytical solution for the bounce is presented, which reproduces the action in
the thin-wall as well as the thick-wall limits.Comment: 22 pag
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