4,801 research outputs found
The Schr\"odinger formulation of the Feynman path centroid density
We present an analysis of the Feynman path centroid density that provides new
insight into the correspondence between the path integral and the Schr\"odinger
formulations of statistical mechanics. The path centroid density is a central
concept for several approximations (centroid molecular dynamics, quantum
transition state theory, and pure quantum self-consistent harmonic
approximation) that are used in path integral studies of thermodynamic and
dynamical properties of quantum particles. The centroid density is related to
the quasi-static response of the equilibrium system to an external force. The
path centroid dispersion is the canonical correlation of the position operator,
that measures the linear change in the mean position of a quantum particle upon
the application of a constant external force. At low temperatures, this
quantity provides an approximation to the excitation energy of the quantum
system. In the zero temperature limit, the particle's probability density
obtained by fixed centroid path integrals corresponds to the probability
density of minimum energy wave packets, whose average energy define the Feynman
effective classical potential.Comment: 29 pages, 2 figures, 1 Table, J. Chem. Phys. (in press
FRW in cosmological self-creation theory: Hamiltonian approach
We use the Brans-Dicke theory from the framework of General Relativity
(Einstein frame), but now the total energy momentum tensor fulfills the
following condition . We take as a first model the flat FRW metric in the
Hamilton-Jacobi scheme and we present the Lagrange-Charpit approach in order to
find classical solutions. In the quantum scheme, once we determine the
characteristic surfaces, the quantum solution is obtained. These two classes of
solutions are found for all values of the barotropic parameter .Comment: 9 pages, latex2e. arXiv admin note: substantial text overlap with
arXiv:1206.541
Willingness to Comply with Corporate Law: An Interdisciplinary Teaching Method in Higher Education
Using an innovation training project, an interdisciplinary cross-sectional teaching strategy
was developed to enhance studentsâ willingness to comply with the law. Thirty-five business, finance
and accounting teachers examined the effects of ethical education on 484 university studentsâ
willingness to comply with corporate law. Ethical education was based on building studentsâ
ethical decisions on three court judgments in the new Spanish Corporate Governance Code.
The ethical training was carried out by developing and applying social justice counter arguments.
This perspective allowed students to imagine what decisions other person could have taken if they
had managed the company ethically. The results suggest that ethics education in higher education
can improve the willingness to comply the law. This methodology can be applied to interdisciplinary
departments teaching ethics in business, finance and accounting
Exponentially small asymptotic formulas for the length spectrum in some billiard tables
Let be a period. There are at least two -periodic
trajectories inside any smooth strictly convex billiard table, and all of them
have the same length when the table is an ellipse or a circle. We quantify the
chaotic dynamics of axisymmetric billiard tables close to their borders by
studying the asymptotic behavior of the differences of the lengths of their
axisymmetric -periodic trajectories as . Based on
numerical experiments, we conjecture that, if the billiard table is a generic
axisymmetric analytic strictly convex curve, then these differences behave
asymptotically like an exponentially small factor times
either a constant or an oscillating function, and the exponent is half of
the radius of convergence of the Borel transform of the well-known asymptotic
series for the lengths of the -periodic trajectories. Our experiments
are restricted to some perturbed ellipses and circles, which allows us to
compare the numerical results with some analytical predictions obtained by
Melnikov methods and also to detect some non-generic behaviors due to the
presence of extra symmetries. Our computations require a multiple-precision
arithmetic and have been programmed in PARI/GP.Comment: 21 pages, 37 figure
Diffusion of muonium and hydrogen in diamond
Jump rates of muonium and hydrogen in diamond are calculated by quantum
transition-state theory, based on the path-integral centroid formalism. This
technique allows us to study the influence of vibrational mode quantization on
the effective free-energy barriers Delta F for impurity diffusion, which are
renormalized respect to the zero-temperature classical calculation. For the
transition from a tetrahedral (T) site to a bond-center (BC) position, Delta F
is larger for hydrogen than for muonium, and the opposite happens for the
transition from BC to T. The calculated effective barriers decrease for rising
temperature, except for the muonium transition from T to BC sites. Calculated
jump rates are in good agreement to available muon spin rotation data.Comment: 4 pages, 3 figure
On the length and area spectrum of analytic convex domains
Area-preserving twist maps have at least two different -periodic
orbits and every -periodic orbit has its -periodic action for
suitable couples . We establish an exponentially small upper bound for
the differences of -periodic actions when the map is analytic on a
-resonant rotational invariant curve (resonant RIC) and is
"sufficiently close" to . The exponent in this upper bound is closely
related to the analyticity strip width of a suitable angular variable. The
result is obtained in two steps. First, we prove a Neishtadt-like theorem, in
which the -th power of the twist map is written as an integrable twist map
plus an exponentially small remainder on the distance to the RIC. Second, we
apply the MacKay-Meiss-Percival action principle.
We apply our exponentially small upper bound to several billiard problems.
The resonant RIC is a boundary of the phase space in almost all of them. For
instance, we show that the lengths (respectively, areas) of all the
-periodic billiard (respectively, dual billiard) trajectories inside
(respectively, outside) analytic strictly convex domains are exponentially
close in the period . This improves some classical results of Marvizi,
Melrose, Colin de Verdi\`ere, Tabachnikov, and others about the smooth case
Simulation of quantum zero-point effects in water using a frequency-dependent thermostat
Molecules like water have vibrational modes with a zero-point energy well
above room temperature. As a consequence, classical molecular dynamics
simulations of their liquids largely underestimate the energy of modes with a
higher zero-point temperature, which translates into an underestimation of
covalent interatomic distances due to anharmonic effects. Zero-point effects
can be recovered using path integral molecular dynamics simulations, but these
are computationally expensive, making their combination with ab initio
molecular dynamics simulations a challenge. As an alternative to path integral
methods, from a computationally simple perspective, one would envision the
design of a thermostat capable of equilibrating and maintaining the different
vibrational modes at their corresponding zero-point temperatures. Recently,
Ceriotti et al. (Phys. Rev. Lett. 102 020601 (2009)) introduced a framework to
use a custom-tailored Langevin equation with correlated noise that can be used
to include quantum fluctuations in classical molecular dynamics simulations.
Here we show that it is possible to use the generalized Langevin equation with
suppressed noise in combination with Nose-Hoover thermostats to efficiently
impose a zero-point temperature on independent modes in liquid water. Using our
simple and inexpensive method, we achieve excellent agreement for all atomic
pair correlation functions compared to the path integral molecular dynamics
simulation.Comment: 27 pages, 12 figs, Published versio
On the length and area spectrum of analytic convex domains
Area-preserving twist maps have at least two different (p, q)-periodic orbits and every (p, q)-periodic orbit has its (p, q)-periodic action for suitable couples (p, q). We establish an exponentially small upper bound for the differences of (p, q)-periodic actions when the map is analytic on a (m, n)-resonant rotational invariant curve (resonant RIC) and p/q is 'sufficiently close' to m/n. The exponent in this upper bound is closely related to the analyticity strip width of a suitable angular variable. The result is obtained in two steps. First, we prove a Neishtadt-like theorem, in which the n-th power of the twist map is written as an integrable twist map plus an exponentially small remainder on the distance to the RIC. Second,
we apply the MacKay-Meiss-Percival action principle. We apply our exponentially small upper bound to several billiard problems. The resonant RIC is a boundary of the phase space in almost all of them. For instance, we show that the lengths (respectively, areas) of all the (1, q)-periodic billiard (respectively, dual billiard) trajectories inside (respectively, outside) analytic strictly convex domains are exponentially close in the period q. This improves some classical results of Marvizi, Melrose, Colin de Verdiere, Tabachnikov, and others about the smooth case.Peer ReviewedPostprint (author's final draft
Environmental Policies and Mergersâ Externalities
A Cournot oligopolistic setting model of trade is characterized by local and foreign firms competing in the presence of pollution quota and tax. Local firms are foreign-owned (FDI) and repatriate their profits. First, we analyze the impact on welfare given by the merger of the local firms, as a response to external firmsâ competition and pollution abatement costs. Second, when merger is welfare decreasing, we study the best response of the government in order to compensate this negative externality. Finally, we compare the pollution quota and tax in order to determine their efficiency as a policy instrument.environmental policies, mergers, emission permits
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