297 research outputs found
Langevin equations with multiplicative noise: resolution of time discretization ambiguities for equilibrium systems
A Langevin equation with multiplicative noise is an equation schematically of
the form dq/dt = -F(q) + e(q) xi, where e(q) xi is Gaussian white noise whose
amplitude e(q) depends on q itself. Such equations are ambiguous, and depend on
the details of one's convention for discretizing time when solving them. I show
that these ambiguities are uniquely resolved if the system has a known
equilibrium distribution exp[-V(q)/T] and if, at some more fundamental level,
the physics of the system is reversible. I also discuss a simple example where
this happens, which is the small frequency limit of Newton's equation d^2q/dt^2
+ e^2(q) dq/dt = - grad V(q) + e^{-1}(q) xi with noise and a q-dependent
damping term. The resolution does not correspond to simply interpreting naive
continuum equations in a standard convention, such as Stratanovich or Ito. [One
application of Langevin equations with multiplicative noise is to certain
effective theories for hot, non-Abelian plasmas.]Comment: 15 pages, 2 figures [further corrections to Appendix A
Remarks on NonHamiltonian Statistical Mechanics: Lyapunov Exponents and Phase-Space Dimensionality Loss
The dissipation associated with nonequilibrium flow processes is reflected by
the formation of strange attractor distributions in phase space. The
information dimension of these attractors is less than that of the equilibrium
phase space, corresponding to the extreme rarity of nonequilibrium states. Here
we take advantage of a simple model for heat conduction to demonstrate that the
nonequilibrium dimensionality loss can definitely exceed the number of
phase-space dimensions required to thermostat an otherwise Hamiltonian system.Comment: 5 pages, 2 figures, minor typos correcte
The role of soil water monitoring tools and agricultural innovation platforms in improving food security and income of farmers in smallholder irrigation schemes in Tanzania
Smallholder irrigation is an important pathway towards better livelihoods and food security in sub-Saharan Africa. This article assesses the contribution of farmer-friendly soil and water monitoring tools, and agricultural innovation platforms, towards household income
and food security in two small-scale irrigation schemes in Tanzania. Quantitative and qualitative data from farmer’s field books, household surveys and focus groups were used to assess the impacts of the two interventions. The two interventions together contributed to enhancing smallholders’ food security and household income in the
two schemes, as did the agricultural innovation platform on its own
Path Integral for Quantum Operations
In this paper we consider a phase space path integral for general
time-dependent quantum operations, not necessarily unitary. We obtain the path
integral for a completely positive quantum operation satisfied Lindblad
equation (quantum Markovian master equation). We consider the path integral for
quantum operation with a simple infinitesimal generator.Comment: 24 pages, LaTe
On the Geometry and Entropy of Non-Hamiltonian Phase Space
We analyze the equilibrium statistical mechanics of canonical, non-canonical
and non-Hamiltonian equations of motion by throwing light into the peculiar
geometric structure of phase space. Some fundamental issues regarding time
translation and phase space measure are clarified. In particular, we emphasize
that a phase space measure should be defined by means of the Jacobian of the
transformation between different types of coordinates since such a determinant
is different from zero in the non-canonical case even if the phase space
compressibility is null. Instead, the Jacobian determinant associated with
phase space flows is unity whenever non-canonical coordinates lead to a
vanishing compressibility, so that its use in order to define a measure may not
be always correct. To better illustrate this point, we derive a mathematical
condition for defining non-Hamiltonian phase space flows with zero
compressibility. The Jacobian determinant associated with time evolution in
phase space is altogether useful for analyzing time translation invariance. The
proper definition of a phase space measure is particularly important when
defining the entropy functional in the canonical, non-canonical, and
non-Hamiltonian cases. We show how the use of relative entropies can circumvent
some subtle problems that are encountered when dealing with continuous
probability distributions and phase space measures. Finally, a maximum
(relative) entropy principle is formulated for non-canonical and
non-Hamiltonian phase space flows.Comment: revised introductio
Evidence for a small hole pocket in the Fermi surface of underdoped YBa2Cu3Oy
The Fermi surface of a metal is the fundamental basis from which its
properties can be understood. In underdoped cuprate superconductors, the Fermi
surface undergoes a reconstruction that produces a small electron pocket, but
whether there is another, as yet undetected portion to the Fermi surface is
unknown. Establishing the complete topology of the Fermi surface is key to
identifying the mechanism responsible for its reconstruction. Here we report
the discovery of a second Fermi pocket in underdoped YBa2Cu3Oy, detected as a
small quantum oscillation frequency in the thermoelectric response and in the
c-axis resistance. The field-angle dependence of the frequency demonstrates
that it is a distinct Fermi surface and the normal-state thermopower requires
it to be a hole pocket. A Fermi surface consisting of one electron pocket and
two hole pockets with the measured areas and masses is consistent with a
Fermi-surface reconstruction caused by the charge-density-wave order observed
in YBa2Cu3Oy, provided other parts of the reconstructed Fermi surface are
removed by a separate mechanism, possibly the pseudogap.Comment: 23 pages, 5 figure
Stripe order and quasiparticle Nernst effect in cuprate superconductors
After a brief review of current ideas on stripe order in cuprate
high-temperature superconductors, we discuss the quasiparticle Nernst effect in
the cuprates, with focus on its evolution in non-superconducting stripe and
related nematic states. In general, we find the Nernst signal to be strongly
enhanced by nearby van-Hove singularities and Lifshitz transitions in the band
structure, implying that phases with translation symmetry breaking often lead
to a large quasiparticle Nernst effect due to the presence of multiple small
Fermi pockets. Open orbits may contribute to the Nernst signal as well, but do
so in a strongly anisotropic fashion. We discuss our results in the light of
recent proposals for a specific Lifshitz transition in underdoped YBCO and make
predictions for the doping dependence of the Nernst signal.Comment: 10 pages, 4 figs, article prepared for a special issue of New J Phy
Density functional formalism in the canonical ensemble
Density functional theory, when applied to systems with , is based
on the grand canonical extension of the Hohenberg-Kohn-Sham theorem due to
Mermin (HKSM theorem). While a straightforward canonical ensemble
generalization fails, work in nanopore systems could certainly benefit from
such extension. We show that, if the asymptotic behaviour of the canonical
distribution functions is taken into account, the HKSM theorem can be extended
to the canonical ensemble. We generate -modified correlation and
distribution functions hierarchies and prove that, if they are employed, either
a modified external field or the density profiles can be indistinctly used as
independent variables. We also write down the % -modified free energy
functional and prove that its minimum is reached when the equilibrium values of
the new hierarchy are used. This completes the extension of the HKSM theorem.Comment: revtex, to be submitted to Phys. Rev. Let
Quantum state-dependent diffusion and multiplicative noise: a microscopic approach
The state-dependent diffusion, which concerns the Brownian motion of a
particle in inhomogeneous media has been described phenomenologically in a
number of ways. Based on a system-reservoir nonlinear coupling model we present
a microscopic approach to quantum state-dependent diffusion and multiplicative
noise in terms of a quantum Markovian Langevin description and an associated
Fokker-Planck equation in position space in the overdamped limit. We examine
the thermodynamic consistency and explore the possibility of observing a
quantum current, a generic quantum effect, as a consequence of this
state-dependent diffusion similar to one proposed by B\"{u}ttiker [Z. Phys. B
{\bf 68}, 161 (1987)] in a classical context several years ago.Comment: To be published in Journal of Statistical Physics 28 pages, 3 figure
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