Search results for "Expression"
showing 10 items of 5168 documents
Frenkel-Kontorova model with anharmonic interactions
1986
It is shown that consideration of more realistic interatomic potentials (with limited tensile strength) within the framework of the Frenkel-Kontorova model may lead to a breakdown of the soliton picture in systems with competing periodicities. Closed analytical expressions for the form of a single soliton in an anharmonic chain reveal discontinuities which indicate a disintegration of the entire system beyond some critical values of the misfit, and/or of the height of the periodic substrate potential. The length of anharmonic solitons depends essentially on both the sign and the magnitude of the misfit. The influence of misfit on the pinning-unpinning transition is also investigated.
Approximate triangle amplitude for three-body charge exchange processes.
1996
The single-rescattering contribution to the amplitude pertaining to three-body charge exchange reactions (triangle amplitude) contains the off-shell Coulomb {ital T}-matrix {ital T}{sup {ital C}} describing the intermediate-state Coulomb scattering of charged subsystems. For ease of computation, the latter is usually replaced by the potential {ital V}{sup {ital C}} which, however, is unsatisfactory in many cases. An alternative approximation, obtained by {open_quote}{open_quote}renormalizing{close_quote}{close_quote} the {open_quote}{open_quote}triangle{close_quote}{close_quote} contribution with {ital V}{sup {ital C}} instead of {ital T}{sup {ital C}} by a simple analytic expression, is sh…
Estimation of the Repeatedly-Projected Reduced Density Matrix under Decoherence
2007
Decoherence is believed to deteriorate the ability of a purification scheme that is based on the idea of driving a system to a pure state by repeatedly measuring another system in interaction with the former and hinder for a pure state to be extracted asymptotically. Nevertheless, we find a way out of this difficulty by deriving an analytic expression of the reduced density matrix for a two-qubit system immersed in a bath. It is shown that we can still extract a pure state if the environment brings about only dephasing effects. In addition, for a dissipative environment, there is a possibility of obtaining a dominant pure state when we perform a finite number of measurements.
Incompatibility in Multi-Parameter Quantum Metrology with Fermionic Gaussian States
2019
In this article we derive a closed form expression for the incompatibility condition in multi-parameter quantum metrology when the reference states are Fermionic Gaussian states. Together with the quantum Fisher information, the knowledge of the compatibility condition provides a way of designing optimal measurement strategies for multi-parameter quantum estimation. Applications range from quantum metrology with thermal states to non-equilibrium steady states with Fermionic and spin systems.
Risken–Nummedal–Graham–Haken instability in class-B lasers
1999
We determine analytical expressions for the Risken-Nummedal-Graham-Haken multimode laser instability outside the uniform field limit in the case of very fast polarization decay (class-B laser). A new condition for the observability of that instability, concerning the value of the cavity mirrors reflectivity, is predicted.
Point field models for the galaxy point pattern modelling the singularity of the two-point correlation function
2002
There is empirical evidence that the two-point correlation function of the galaxy distribution follows, for small scales, reasonably well a power-law expression $\xi(r)\propto r^{-\gamma}$ with $\gamma$ between 1.5 and 1.9. Nevertheless, most of the point field models suggested in the literature do not have this property. This paper presents a new class of models, which is produced by modifying point fields commonly used in cosmology to mimic the galaxy distribution, but where $\gamma=2$ is too large. The points are independently and randomly shifted, leading to the desired reduction of the value of $\gamma$.
Generalized curvature and the equations of D=11 supergravity
2005
It is known that, for zero fermionic sector, the bosonic equations of Cremmer-Julia-Scherk eleven-dimensional supergravity can be collected in a compact expression which is a condition on the curvature of the generalized connection. Here we peresent the equation which collects all the bosonic equations of D=11 supergravity when the gravitino is nonvanishing.
On the general structure of gauged Wess-Zumino-Witten terms
1998
The problem of gauging a closed form is considered. When the target manifold is a simple Lie group G, it is seen that there is no obstruction to the gauging of a subgroup H\subset G if we may construct from the form a cocycle for the relative Lie algebra cohomology (or for the equivariant cohomology), and an explicit general expression for these cocycles is given. The common geometrical structure of the gauged closed forms and the D'Hoker and Weinberg effective actions of WZW type, as well as the obstructions for their existence, is also exhibited and explained.
Threshold expansion of Feynman diagrams within a configuration space technique
2000
The near threshold expansion of generalized sunset-type (water melon) diagrams with arbitrary masses is constructed by using a configuration space technique. We present analytical expressions for the expansion of the spectral density near threshold and compare it with the exact expression obtained earlier using the method of the Hankel transform. We formulate a generalized threshold expansion with partial resummation of the small mass corrections for the strongly asymmetric case where one particle in the intermediate state is much lighter than the others.
Virtual Compton Scattering off Spin-Zero Particles at Low Energies
1996
We discuss the low-energy behavior of the virtual Compton scattering amplitude off a spin-zero target. We first compare various methods of obtaining a low-energy expression based either on the soft-photon approximation or the use of Ward-Takahashi identities. We point out that structure-dependent terms are defined with respect to a low-energy approximation of the pole terms which commonly is separated from the full amplitude. We derive a general expression for the structure-dependent terms in an expansion in terms of the momenta $k_1$ and $k_2$ of the initial and final virtual photon, respectively, up to and including terms of order ${\cal O}(k^4)$. At order ${\cal O}(k^2)$ two terms appear…