The Experts below are selected from a list of 10887 Experts worldwide ranked by ideXlab platform
Martin Holthaus - One of the best experts on this subject based on the ideXlab platform.
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the Saddle Point Method for condensed bose gases
1999Co-Authors: Martin Holthaus, Eva KalinowskiAbstract:The application of the conventional Saddle-Point approximation to condensed Bose gases is thwarted by the approach of the Saddle-Point to the ground-state singularity of the grand canonical partition function. We develop and test a variant of the Saddle-Point Method which takes proper care of this complication, and provides accurate, flexible, and computationally efficient access to both canonical and microcanonical statistics. Remarkably, the error committed when naively employing the conventional approximation in the condensate regime turns out to be universal, that is, independent of the system's single-particle spectrum. The new scheme is able to cover all temperatures, including the critical temperature interval that marks the onset of Bose--Einstein condensation, and reveals in analytical detail how this onset leads to sharp features in gases with a fixed number of particles. In particular, within the canonical ensemble the crossover from the high-temperature asymptotics to the condensate regime occurs in an error-function-like manner; this error function reduces to a step function when the particle number becomes large. Our Saddle-Point formulas for occupation numbers and their fluctuations, verified by numerical calculations, clearly bring out the special role played by the ground state.
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condensate fluctuations in trapped bose gases canonical vs microcanonical ensemble
1998Co-Authors: Martin Holthaus, Eva Kalinowski, Klaus KirstenAbstract:We study the fluctuation of the number of particles in ideal Bose–Einstein condensates, both within the canonical and the microcanonical ensemble. Employing the Mellin–Barnes transformation, we derive simple expressions that link the canonical number of condensate particles, its fluctuation, and the difference between canonical and microcanonical fluctuations to the poles of a Zeta function that is determined by the excited single-particle levels of the trapping potential. For the particular examples of one- and three-dimensional harmonic traps we explore the microcanonical statistics in detail, with the help of the Saddle-Point Method. Emphasizing the close connection between the partition theory of integer numbers and the statistical mechanics of ideal Bosons in one-dimensional harmonic traps, and utilizing thermodynamical arguments, we also derive an accurate formula for the fluctuation of the number of summands that occur when a large integer is partitioned.
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fluctuations of the particle number in a trapped bose einstein condensate
1997Co-Authors: Siegfried Grossmann, Martin HolthausAbstract:We develop a reliable procedure for calculating the microcanonical fluctuations of the ground state occupation number for harmonically trapped ideal Bose gases, and show that these fluctuations vanish uniformly when the temperature approaches zero. The key Point is the precise determination of the number of microstates from the {ital canonical} partition sum, thus avoiding a failure of the usual Saddle Point Method. We also demonstrate why the magnitude of the condensate fluctuations does not depend on the total particle number. {copyright} {ital 1997} {ital The American Physical Society}
Nicola Pavoni - One of the best experts on this subject based on the ideXlab platform.
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on the recursive Saddle Point Method
2004Co-Authors: Matthias Messner, Nicola PavoniAbstract:In this paper a simple dynamic optimization problem is solved with the help of the recursive Saddle Point Method developed by Marcet and Marimon (1999). According to Marcet and Marimon, their technique should yield a full characterization of the set of solutions for this problem. We show though, that while their Method allows us to calculate the true value of the optimization program, not all solutions with it admits are correct. Indeed, some of the policies which it generates as solutions to our problem, are either suboptimal or do not even satisfy feasibility. We identify the reasons underlying this failure and discuss its implications for the numerous existing applications.
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on the recursive Saddle Point Method
2004Co-Authors: Nicola Pavoni, Ramon Marimon, Matthias MessnerAbstract:In this paper a simple dynamic optimization problem is solved with the help of the recursive Saddle Point Method developed by Marcet and Marimon (1999). According to Marcet and Marimon, their technique should yield a full characterization of the set of solutions for this problem. We show though, that while their Method allows us to calculate the true value of the optimization program, not all solutions which it admits are correct. Indeed, some of the policies which it generates as solutions to our problem, are either suboptimal or do not even satisfy feasibility. We identify the reasons underlying this failure and discuss its implications for the numerous existing applications.(This abstract was borrowed from another version of this item.)
Eva Kalinowski - One of the best experts on this subject based on the ideXlab platform.
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the Saddle Point Method for condensed bose gases
1999Co-Authors: Martin Holthaus, Eva KalinowskiAbstract:The application of the conventional Saddle-Point approximation to condensed Bose gases is thwarted by the approach of the Saddle-Point to the ground-state singularity of the grand canonical partition function. We develop and test a variant of the Saddle-Point Method which takes proper care of this complication, and provides accurate, flexible, and computationally efficient access to both canonical and microcanonical statistics. Remarkably, the error committed when naively employing the conventional approximation in the condensate regime turns out to be universal, that is, independent of the system's single-particle spectrum. The new scheme is able to cover all temperatures, including the critical temperature interval that marks the onset of Bose--Einstein condensation, and reveals in analytical detail how this onset leads to sharp features in gases with a fixed number of particles. In particular, within the canonical ensemble the crossover from the high-temperature asymptotics to the condensate regime occurs in an error-function-like manner; this error function reduces to a step function when the particle number becomes large. Our Saddle-Point formulas for occupation numbers and their fluctuations, verified by numerical calculations, clearly bring out the special role played by the ground state.
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condensate fluctuations in trapped bose gases canonical vs microcanonical ensemble
1998Co-Authors: Martin Holthaus, Eva Kalinowski, Klaus KirstenAbstract:We study the fluctuation of the number of particles in ideal Bose–Einstein condensates, both within the canonical and the microcanonical ensemble. Employing the Mellin–Barnes transformation, we derive simple expressions that link the canonical number of condensate particles, its fluctuation, and the difference between canonical and microcanonical fluctuations to the poles of a Zeta function that is determined by the excited single-particle levels of the trapping potential. For the particular examples of one- and three-dimensional harmonic traps we explore the microcanonical statistics in detail, with the help of the Saddle-Point Method. Emphasizing the close connection between the partition theory of integer numbers and the statistical mechanics of ideal Bosons in one-dimensional harmonic traps, and utilizing thermodynamical arguments, we also derive an accurate formula for the fluctuation of the number of summands that occur when a large integer is partitioned.
K.s. Kniazeva - One of the best experts on this subject based on the ideXlab platform.
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Saddle Point Method for transient processes in waveguides.
2021Co-Authors: A.v. Shanin, A. I. Korolkov, K.s. KniazevaAbstract:A modification of the Saddle Point Method is proposed for computation of non-stationary wave processes (pulses) in waveguides. The dispersion diagram of the waveguide is continued analytically. A set of possible Saddle Points on the dispersion diagram is introduced. A Method of checking whether the particular Saddle Points contribute terms to the field decomposition is proposed. A classification of the waveguides based on the topology of the set of possible Saddle Points is outlined.
Dejan B. Milošević - One of the best experts on this subject based on the ideXlab platform.
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High-order harmonic generation by aligned heteronuclear diatomic molecules in an orthogonally polarized two-color laser field
2021Co-Authors: Dino Habibović, Wilhelm Becker, Dejan B. MiloševićAbstract:Using the molecular strong-field approximation, we investigate high-order harmonic generation by heteronuclear diatomic molecules exposed to an orthogonally polarized two-color laser field, which consists of two mutually orthogonal linearly polarized fields with frequencies $$r\omega $$ and $$s\omega $$. Here, r and s are integers and $$\omega $$ is the fundamental frequency. The harmonic emission rate and the harmonic ellipticity can be controlled using the laser-field parameters, in particular the relative phase and the intensity ratio of the laser-field components. The value of the relative phase, for which the emission rate is optimal, and the position of the cutoff can be estimated using a classical model. Also, we analyze the harmonic emission rate and the harmonic ellipticity as functions of the molecular orientation, which can also be used as a control parameter. Two types of minima are present in the spectra, depending on r and s. For $$r+s$$ even, interference minima are present in the spectra of the T-matrix component either parallel or perpendicular to the internuclear axis. Using quantum-orbit theory and the Saddle-Point Method, we derive a condition for the interference minima, which relates the molecular orientation angle $$\theta _L$$ and the harmonic order n. The corresponding curves in the ($$\theta _L$$, n) plane well reproduce the minima of the numerically calculated spectra. For $$r+s$$ odd, minima are present in the spectra for a particular molecular orientation angle. These minima are explained using the explicit form of the T-matrix element. A heteronuclear as opposed to a homonuclear molecule affords a larger region in the parameter space where both the harmonic ellipticity and the harmonic intensity vary smoothly and both are large
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high order harmonic generation in the presence of a static electric field
2005Co-Authors: S Odžak, Dejan B. MiloševićAbstract:We consider high-order harmonic generation by a linearly polarized laser field and a parallel static electric field. We first develop a modified Saddle-Point Method which enables a quantitative analysis of the harmonic spectra even in the presence of Coulomb singularities. We introduce a classification of the Saddle-Point solutions and show that, in the presence of a static electric field which breaks the inversion symmetry, an additional classification number has to be introduced and that the usual Saddle-Point approximation and the uniform approximation in the case of the coalescing Saddle Points have to be modified. The theory developed offers a simple and accurate explanation of the static-field-induced multiplateau structure of the harmonic spectra. The longer quantum orbits are responsible for a long extension of the harmonic plateau, while the larger initial electron velocities are the reason of lower harmonic emission rates.
