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

Effective coupling between two Brownian particles

We use the system-plus-reservoir approach to study the dynamics of a system composed of two independent Brownian particles. We present an extension of the well-known model of a bath of oscillators which is capable of inducing an effective coupling between the two particles depending on the choice made for the spectral function of the bath oscillators. The coupling is non-linear in the variables of interest and an exponential dependence on these variables is imposed in order to guarantee the translational invariance of the model if the two particles are not subject to any external potential. The effective equations of motion for the particles are obtained by the Laplace transform method and besides recovering all the local dynamical properties for each particle we end up with an effective interaction potential between them. We explicitly analyze one of its possible forms.Comment: 4 pages, 1 figur

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

Flow equation approach to diagonal representation of an unbounded Hamiltonian with complex eigenvalues

The flow equation approach investigated by Wegner et al. is applied to an unbounded Hamiltonian system with a generalization. We show that a well-known quantized complex energy eigenvalues which is related to decay widths can be given with this approach.Comment: Revtex, 4 pages, 2 figures. To appear in Physics Letters

Does the system of allocation of intergovernmental transfers in Senegal eliminate politically motivated targeting?

While there is a large body of literature on the determinants of allocation of intergovernmental …fiscal transfers in developed countries, this kind of study is still very limited for developing countries, especially Subsaharan countries. Using an original micro-level public fi…nance panel data from Senegal, we address three issues: (1) Does the Senegalese allocation system of …fiscal transfers conform to the guidance of the normative theory, in particular, to the equity principle? (2) Does this allocation system eliminate the politically motivated targeting of transfers? (3) If not, what kind of political factors explain the horizontal allocation of resources? By estimating a panel data for 67 local gov- ernments ("communes"), from 1997 to 2009, we fi…nd that equity concerns do not affect the allocation of intergovernmental transfers in Senegal, leading to the conclusion that the resources distribution system does not comply with the dictates of normative theory. Moreover, we …find evidence that political considerations influence the horizontal allocation of …fiscal transfers. In particular, our analysis suggests that transfers allocation follows a pattern of tactical redistribution more than patronage, swing communes being targeted while partisan communes are not.decentralization;political economy;Intergovernmental transfers;senegal

Yardstick competition in a Federation: Theory and Evidence from China

While some scholars argue that fiscal decentralization gave Chinese local officials strong incentives to promote local economic growth, traditional fiscal federalism theories are not directly relevant to explain such an effect in the particular context of China. In this paper, we explain the existence of interjurisdictional competition among Chinese local officials using a model of yardstick competition "from the top", in which the central government (and not local voters) creates a competition among local officials by rewarding or punishing them on the basis of relative economic performance. Our model predicts that, in this context, local governments are forced to care about what other incumbents are doing and that public spending settings are strategic complements. Then, by estimating a spatial lag dynamic model for a panel data of 29 Chinese provinces from 1980 to 2004, we provide empirical evidence of the existence of such public spending interactions. We propose a rigorous empirical framework which takes into account heterogeneity, simultaneity and endogeneity problems and spatial error dependence. The results are encouraging to the view that there are some strategic interactions among Chinese provinces, resulting from a yardstick competition created by the central government.decentralization;China;public spending interactions;yardstick competition;spatial panel data

Does the system of allocation of intergovernmental transfers in Senegal eliminate politically motivated targeting?

While there is a large body of literature on the determinants of allocation of intergovernmental …fiscal transfers in developed countries, this kind of study is still very limited for developing countries, especially Subsaharan countries. Using an original micro-level public fi…nance panel data from Senegal, we address three issues: (1) Does the Senegalese allocation system of …fiscal transfers conform to the guidance of the normative theory, in particular, to the equity principle? (2) Does this allocation system eliminate the politically motivated targeting of transfers? (3) If not, what kind of political factors explain the horizontal allocation of resources? By estimating a panel data for 67 local gov- ernments ("communes"), from 1997 to 2009, we fi…nd that equity concerns do not affect the allocation of intergovernmental transfers in Senegal, leading to the conclusion that the resources distribution system does not comply with the dictates of normative theory. Moreover, we …find evidence that political considerations influence the horizontal allocation of …fiscal transfers. In particular, our analysis suggests that transfers allocation follows a pattern of tactical redistribution more than patronage, swing communes being targeted while partisan communes are not.decentralization, political economy, Intergovernmental transfers, senegal