Fokker-Planck and Langevin Equations from Forward--Backward Path Integral

Starting from a forward--backward path integral of a point particle in a bath of harmonic oscillators, we derive the Fokker-Planck and Langevin equations with and without inertia. Special emphasis is placed upon the correct operator order in the time evolution operator. The crucial step is the evaluation of a Jacobian with a retarded time derivative by analytic regularization.Comment: Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of paper (including all PS fonts) at http://www.physik.fu-berlin.de/~kleinert/31

Study of the Dalitz plot of the η→π+π−π0\eta \rightarrow \pi^+ \pi^- \pi^0 decay with the KLOE detector

The decay $\eta \rightarrow \pi^+ \pi^- \pi^0$ is studied with the KLOE detector, at the DA$\phi$NE e$^+$e$^-$ collider. Using a data sample corresponding to an integrated luminosity of $1.6$ fb$^{-1}$ a new study of the Dalitz plot is presented.Comment: 7 pages, 3 figure

Exponential Decay of Wavelength in a Dissipative System

Applying a technique developed in a recent work[1] to calculate wavefunction evolution in a dissipative system with Ohmic friction, we show that the wavelength of the wavefunction decays exponentially, while the Brownian motion width gradually increases. In an interference experiment, when these two parameters become equal, the Brownian motion erases the fringes, the system thus approaches classical limit. We show that the wavelength decay is an observable phenomenon.Comment: 12 pages, 3 Postscript figures, uses standard late

Schrodinger Equation for Particle with Friction

A new quantum mechanical wave equation describing a particle with frictional forces is derived. It depends on a parameter $\alpha$ whose range is determined by the coefficient of friction $\gamma$, that is, $0 \leq \alpha \leq \gamma$. For one extreme value of this parameter, $\alpha = 0$, we recover Kostin's equation. For the other extreme value, $\alpha = \gamma$, we obtain an equation in which friction manifests in "magnetic" type terms. It further exhibits breakdown of translational invariance, manifesting through a symmetry breaking parameter $\beta$, as well as localized stationary states in the absence of external potentials. Other physical properties of this new class of equations are also discussed.Comment: 11 page

Contact Terms and Duality Symmetry in The Critical Dissipative Hofstadter Model

The dissipative Hofstadter model describes the quantum mechanics of a charged particle in two dimensions subject to a periodic potential, uniform magnetic field, and dissipative force. Its phase diagram exhibits an SL(2,Z) duality symmetry and has an infinite number of critical circles in the dissipation/magnetic field plane. In addition, multi-critical points on a particular critical circle correspond to non-trivial solutions of open string theory. The duality symmetry is expected to provide relations between correlation functions at different multi-critical points. Many of these correlators are contact terms. However we expect them to have physical significance because under duality they transform into functions that are non-zero for large separations of the operators. Motivated by the search for exact, regulator independent solutions for these contact terms, in this paper we derive many properties and symmetries of the coordinate correlation functions at the special multi-critical points. In particular, we prove that the correlation functions are homogeneous, piecewise-linear functions of the momenta, and we prove a weaker version of the anticipated duality transformation. Consequently, the possible forms of the correlation functions are limited to lie in a finite dimensional linear space. We treat the potential perturbatively and these results are valid to all orders in perturbation theory.Comment: 65 pages, six figures, CTP#217

Dynamical decoupling induced renormalization of the non-Markovian dynamics

In this work we develop a numerical framework to investigate the renormalization of the non-Markovian dynamics of an open quantum system to which dynamical decoupling is applied. We utilize a non-Markovian master equation which is derived from the non-Markovian quantum trajectories formalism. It contains incoherent Markovian dynamics and coherent Schr\"odinger dynamics as its limiting cases and is capable of capture the transition between them. We have performed comprehensive simulations for the cases in which the system is either driven by the Ornstein-Uhlenbeck noise or or is described by the spin-boson model. The renormalized dynamics under bang-bang control and continuous dynamical decoupling are simulated. Our results indicate that the renormalization of the non-Markovian dynamics depends crucially on the spectral density of the environment and the envelop of the decoupling pulses. The framework developed in this work hence provides an unified approach to investigate the efficiency of realistic decoupling pulses. This work also opens a way to further optimize the decoupling via pulse shaping

Soil Microbial Biomass And Activity In A Cork Oak Savanna

Cork oak savannas are composed by a sparse tree canopy (30-70 trees/ha) and a grassland understory predominantly composed of C3 annuals that survive the hot and dry Mediterranean summers as seeds in the soil. Microbial communities can be more or less efficient at converting organic substrates into microbial biomass carbon depending on the quantity and quality of organic matter inputs. The cork oak savannas have two distinct types of plant litter that can affect soil microbial biomass and activity differently: herbaceous litter and the more recalcitrant woody plant litter resulting from the trees. Spatial variability of soil microbial biomass and activity due to the tree-grassland component of cork oak savannas were evaluated in order to better understand the soil carbon dynamics of these systems.

To quantify changes in soil microbial biomass and activity, measurements were performed in a Cork oak savanna in Southern Portugal. At this site 8 plots were randomly established under mature cork oak trees and paired with 8 open grassland plots. During one year soil cores (0-10 cm) were monthly collected at each site for measuring soil microbial biomass C and other eco-physiology parameters.


Results/Conclusion

Soil microbial biomass carbon (Cmic) and nitrogen (Nmic) were always higher under the tree canopy than in the open grasslands. Organic carbon (Corg) was also higher under the tree canopies. The Cmic/Corg ratio relates to the microbial activity and its potential to mineralize organic substances. The Cmic/Corg ratio was lower under the tree canopies than in the open grasslands. Less microbial biomass was supported per unit of Corg. Basal activity was always higher under the canopy than in the open grassland.

Trees scattered in the savanna function as islands inducing larger soil microbial communities and higher basal activity under the canopies. Lower Cmic/Corg ratio under the tree canopies suggests a more recalcitrant nature of the litter and a decrease in relative availability of organic matter under the trees.
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New Boundary Conformal Field Theories Indexed by the Simply-Laced Lie Algebras

We consider the field theory of $N$ massless bosons which are free except for an interaction localized on the boundary of their 1+1 dimensional world. The boundary action is the sum of two pieces: a periodic potential and a coupling to a uniform abelian gauge field. Such models arise in open string theory and dissipative quantum mechanics, and possibly in edge state tunneling in the fractional quantized Hall effect. We explicitly show that conformal invariance is unbroken for certain special choices of the gauge field and the periodic potential. These special cases are naturally indexed by semi-simple, simply laced Lie algebras. For each such algebra, we have a discrete series of conformally invariant theories where the potential and gauge field are conveniently given in terms of the weight lattice of the algebra. We compute the exact boundary state for these theories, which explicitly shows the group structure. The partition function and correlation functions are easily computed using the boundary state result.Comment: 24 pages in plain tex, requires harvmac.te

On the determination of the earthquake slip distribution via linear programming techniques

The description that one can have of the seismic source is the mani- festation of an imagined model, obviously outlined from Physic Theories and supported by mathematical methods. In that context, the modelling of earthquake rupture consists in finding values of the parameters of the selected physics-mathematical model, through which it becomes possible to reproduce numerically the records of earthquake effects on the Earths surface. We present and test a Linear Programming (LP) inversion in dual form, for reconstructing the kinematics of the rupture of large earthquakes through space-time seismic slip distribution on finite faults planes

Source rupture process, directivity and and Coulomb stress change of the 12 January 2010 (Port-au-Prince Haiti, Mw7.0) earthquake

The Haiti earthquake occurred on Tuesday, January 12, 2010 at 21:53:10 UTC. Its epi- center was at 18.46 degrees North, 72.53 degrees West, about 25 km WSW of Haiti’s capital, Port-au-Prince, along the tectonic boundary between Caribbean and North America plate dominated by left-lateral stri- ke slip motion and compression with 2 cm/yr of slip velocity eastward with respect to the North America plate. The earthquake was relatively shallow (about 13 km depth) with Mw 7.0 and CMT mechanism solution indica- ting left-lateral strike slip movement with a fault plane oriented toward the WNW-ESE. More than 10 aftershocks ranging from 5.0 to 5.9 in magnitude struck the area in hours following the main shock. Most of these af- tershocks have occurred to the west of the mainshock in the Mirogoane Lakes region and its distribution suggests that the length of the rupture was around 70 km. Rupture velocity and direction was constrained by using the directivity effect determined from broad-band waveforms recorded at regio- nal and teleseismic distances using DIRDOP computational code (DIRectivity DOPpler effect) [1]. The Results show that the rup- ture spread mainly from WNW to ESE with a velocity of 2.5 km/s. In order to obtain the spatiotemporal slip distribution of a fi- nite rupture model we have used teleseismic body wave and the Kikuchi and Kanamori’s method [2]. The inversion show complex source time function with a total scalar seismic moment of 2.2 x 1019Nm (Mw=6.9) a source duration of about 18 sec with a main energy relesea in the first 13 sec. Finally, we compared a map of aftershocks with the Coulomb stress changes caused by the main shock in the region [3]. [1] Kikuchi, M., and Kanamori, H., 1982, Inversion of com- plex body waves: Bull. Seismol. Soc. Am., v. 72, p. 491-506. [2] Caldeira B., Bezzeghoud M, Borges JF, 2009; DIRDOP: a directivity ap- proach to determining the seismic rupture velocity vector. J Seismology, DOI 10.1007/ s10950-009-9183-x [3] King, G. C. P., Stein, R. S. y Lin, J, 1994, Static stress changes and the triggering of earthquakes. Bull. Seismol. Soc. Am. 84,935-953. More than 10 aftershocks ranging from 5.0 to 5.9 in magnitude struck the area in hours following the main shock. Most of these aftershocks have occurred to the west of the mainshock in the Mirogoane Lakes region and its distribution suggests that the length of the rupture was around 70 km. In order to obtain the spatiotemporal slip distribution of a finite rupture model we have used teleseismic body wave and the Kikuchi and Kanamori's method [1]. Rupture velocity was constrained by using the directivity effect determined from waveforms recorded at regional and teleseismic distances [2]. The spatiotemporal slip estimated points to a unilateral rupture that propagates from WNW to ESE with a rupture velocity of 2.5 km/s. Finally, we compared a map of aftershocks with the Coulomb stress changes caused by the event in the region [3]. [1]- Kikuchi, M., and Kanamori, H., 1982, Inversion of complex body waves: Bull. Seismol. Soc. Am., v. 72, p. 491-506. [2] Caldeira B., Bezzeghoud M, Borges JF, 2009; DIRDOP: a directivity approach to determining the seismic rupture velocity vector. J Seismology, DOI 10.1007/s10950-009-9183-x [3] -King, G. C. P., Stein, R. S. y Lin, J, 1994, Static stress changes and the triggering of earthquakes. Bull. Seismol. Soc. Am. 84,935-953